The r-Process: The Astrophysical Origin of the Heavy Elements and Related Rare Isotope Accelerator Physics (Proceedings from the Institute for Nuclear Theory 13)

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Hartree-Fock-Bogoliubov (HFB) approximation (in coordinate space because of the weak binding of neutron-rich nuclei) for even-even parents, then a continuum ("canonical-basis") QRPA treatment of states in the daughters, with the same Skyrme interaction as used in HFB. This self consistency makes the QRPA equivalent to the small-amplitude limit of time-dependent HFB, and allows systematic corrections (yet to be implemented).

57

The authors began by finding a Skyrme interaction 9 SKO' that reproduced the energies and strengths of Gamow-Teller resonances reasonably well. They then adjusted a single parameter, the strength of T = 0 neutronproton pairing, by fitting the half-lives of nuclei near those whose rates were being calculated. T = 0 pairing, neglected in the global calculations, played an important role in moving Gamow-Teller strength from the resonance down to low-lying excitations; without it the calculated half-lives would have been too long. The calculated transition rates for the r-process ladder nuclei — in the allowed approximation — were faster at N = 50 and 82 than those of the global approach, even when forbidden transitions were included in the latter. [At N=126 the rates were slower, but there were no measured nuclei to which to fit the T = 0 pairing strength there.] Though self consistency is an important step, the effective Skyrme interaction was not good enough to make for a decisive improvement. These results are probably better than the more schematic ones discussed above, but the reason is more likely the limited focus than self consistency. 2.3. Shell

Model

Shortly after the HFB calculations were published, a shell model calculation appeared for N = 82 r-process nuclei7, supplemented by a later calculation 8 for N = 126. [A more recent calculation for N = 82, with similar results, has recently been published 10 .] The shell model uses a smaller single-particle space than the QRPA, but includes many more correlations, some of which appear to be essential for an accurate description of low-lying strength. It is subject, however, to uncertainties in the effective interaction and operators, just like the other calculations. The shell-model rates turned out to be even faster than those in the self-consistent HFB+QRPA calculations. Figure 2 shows the results of all three calculations discussed so far (FRDM without forbidden strength, the shell model (SM) and the HFB) together with results from the ETFSI framework mentioned above. The shell model rates are the fastest. Forbidden transitions have yet to be included in this approach, but doing so should be possible. 2.4. Density-Functional

+ Finite-Fermi-Systems

Theory

Most recently, a density-functional/Greens-function-based version11 of selfconsistent HFB+QRPA (Density-Functional + Finite-Fermi-Systems Theory (FFS), and not quite self consistent but with a well-developed phenomenology) has been applied to spherical nuclei. The author was able

58

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44 46 Charge Number Z

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Figure 2. Shell-model (SM), H F B + Q R P A (HFB), FRDM, and ETFSI calculations of half-lives for neutron-rich N = 82 and 126 nuclides, with experimental data where available (taken from Ref. 8).

to include forbidden transitions microscopically, something that the other methods have yet to do. As the left panel of Fig. 3 shows, without forbidden transitions included the rates are close to those of the HFB+QRPA, at least near N = 82. In that region the forbidden operators speed the transitions moderately, but at N — 126 they increase the rates by factors of several, so that the they are even faster than the those of the shell model (which included only allowed strength). 1

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Figure 3. Density-functional + F F S calculations in the r-process region for N = 82 and 126 (compared with shell-model and HFB results), showing effects of forbidden decay. The subscript "a" in the legend stands for "allowed" and " a + l f stands for "allowed plus first-forbidden." Taken from Ref. 11.

59 3. Development and Future of Self-Consistent Approach The calculations described here are all better than those of the previous generation and all indicate that transitions far from stability are faster than previously believed, but don't fully agree with one another. Some calculations attempt to include forbidden transitions, others still do not. Only the FRDM + schematic QRPA can be applied in all nuclides. But the other methods can all be generalized and improved, and not just through obvious steps such as including forbidden decay. Here I discuss what has and will be done within the framework of self-consistent HFB+QRPA. As noted above, self consistency is a virtue only in conjunction with a good effective interaction or energy functional. A recent paper 12 has taken the first steps toward improving Skyrme functionals by examining the effects of various "time-odd" terms (corresponding roughly to spindependent interactions) on Gamow-Teller strength distributions. Though there were not enough data in spherical nuclei to determine all the timeodd parameters, by adjusting one (the Landau spin-isospin parameter g'0) the authors constructed an improved version of SkO' that reproduces the strengths and energies of the available experimental resonances (see Fig. 4 below). Once the HFB+QRPA scheme is generalized to deformed nuclei, more data can be examined. More work within this framework is in progress. The continuum QRPA has been formulated in several different ways; the most efficient will be identified and extended to work in deformed nuclei, a step that will allow global calculations. Angular-momentum and particle-number symmetries, violated by the HFB, can be restored. And attempts are underway to systematically improve the "time-even" parts of Skyrme functionals (the only parts that play a role in the ground states of even-even nuclei) by treating them as expansions in the Fermi momentum (or the density). There is some hope of deriving the functionals from the bare nucleon-nucleon interaction 13 , rather than relying entirely on phenomenology. Ultimately, we will have to go beyond QRPA in treating excitations. This does not necessarily mean abandoning linear response theory. By adding time dependence to the density functional it is possible to include excited-state correlations that are absent from our current framework; there is work in the condensed-matter world from which we can draw 14 .

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4. Effects on the R Process It's hard to say exactly what a new set of rates in a particular region means for nucleosynthesis because we don't yet understand the conditions under which the r process takes place. It is crucial to measure or calculate the rates, and given a particular set of astrophysical conditions they fix many features of the abundance curve. At this point, however, uncertainties about the r-process environment dwarf those in the nuclear physics of nuclides far from stability. Nevertheless, it is possible to use beta-decay

61 rates to address particular issues. In a recent paper 15 it is argued on the basis of a measurement of a strength distribution far from stability that the transitions at N = 82 calculated by the shell model, HFB+QRPA, and Density-functional+FFS are too fast. As part of their argument, the authors show that slower rates better reproduce the width of the observed abundance peak. Although this conclusion depends on assumptions about the r-process environment, it will force the other groups to go back and examine their calculated strength distributions (so far they have focused on total decay half-lives). That the new rates are faster than previously believed at closed neutron shells was one of the main points made in recent work. The current suggestion that they may not be so fast after all is part of the give-and-take between observations, nuclear-structure theory, simulations, and astrophysics that promises to reveal the site of the r process and the details of how it occurs.

Acknowledgments This work was supported in part by the U.S. Department of Energy under grant DE-FG02-97ER41019.

References 1. P. Ring, and R. Schuck The Nuclear Many-Body Problem (Springer-Verlag, Berlin, 1980). 2. P. Moller, J. R. Nix, W. D. Myers,and W. J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 3. P. Moller, B. Bfeiffer, and K. -L. Kratz, Phys. Rev. C67, 055802 (2003). 4. M. Homma et al., Phys. Rev. C54, 2972 (1999) and references therein. 5. I. N. Borzov and S. Goriely, Phys. Rev. C62, 035501 (2000) and references therein. 6. J. Engel, M. Bender, J. Dobaczewski, W. Nazarewicz, and R. Surman, Phys. Rev. C60, 014302 (1999). 7. G. Martinez-Pinedo and K. Langanke, Phys. Rev. Lett. 83, 4502 (1999). 8. G. Martinez-Pinedo, Nucl. Phys. A668, 357c (2000). 9. P. -G. Reinhard et al., Phys. Rev. C60, 014316 (1999). 10. B.A. Brown et al., Nucl. Phys. A719, 177c (2003). 11. I. N. Borzov, Phys. Rev. C67, 025802 (2003). 12. M. Bender, J. Dobaczewski, J. Engel, and W. Nazaewicz, Phys. Rev. C65, 054322 (2002). 13. S. J. Puglia, A. Bhattacharyya, and R. J. Purnstahl, Nucl. Phys. A723, 145 (2003); R. J. Furnstahl, Int. J. Mod. Phys. B17, 5111 (2003).

62 14. M. A. L. Marques and E. K. U. Gross, in A Primer in Density Theory (Springer-Verlag, Berlin Heidelberg, 2003). 15. I. Dillmann et al., Phys. Rev. Lett 9 1 , 162503 (2003).

Functional

N E U T R O N C A P T U R E S A N D T H E R-PROCESS

T. RAUSCHER Department of Physics Klingelbergstr. E-mail:

and Astronomy, University of Basel 82, 4056 Basel, Switzerland [email protected]

The r-process involves neutron-rich nuclei far off stability for which no experimental cross sections are known. Therefore, one has to rely on theory. The difficulties in the predictions are briefly addressed. To investigate the impact of altered rates, a comparison of r-process production in hot bubble models with largely varied rates is shown. Due to the (n,7)-(7,n) equilibrium established at the onset of the r-process, only late-time neutron captures are important which mainly modify the abundances around the third r-process peak.

1. Introduction Nucleosynthesis of elements beyond the iron peak requires reactions with neutrons due to the high Coulomb barriers which prevent charged particle reactions. Except for the relatively underabundant proton-rich p nuclei, two processes have been identified for the production of intermediate and heavy nuclei: the slow neutron-capture process (s-process) and the rapid neutron-capture process (r-process). With neutron number densities around 108 c m - 3 and low effective neutron energies of around 30 keV, the s-process synthesizes nuclei along the line of stability as the neutron captures are generally slower than all beta-decays encountered along its path (with the exception of several branching points where the two timescales become similar). Approximately half of the intermediate and heavy elements are created in the much faster r-process with neutron number densities exceeding 1022 c m - 3 , effective neutron energies around 100 keV, and much shorter process times of up to a few seconds. These conditions point to an explosive site but the actual site has yet to be identified. The long favored idea of a high-entropy bubble in the neutrino wind ejected from a type II supernova shows persistent problems in explaining production across the full mass range of r-nuclei. Furthermore, there are indications that there must be two distinct sites ejecting r-process material at different frequencies (see 63

64

other contributions in this volume). In consequence, most r-process investigations focus on simplified, parameterized models which allow to study the required conditions and their sensitivities to nuclear inputs. Due to the high neutron densities the r-process synthesizes very neutron-rich nuclei far off stability which subsequently decay to stability when the process ceases due to lack of neutrons or low temperatures. This raises the question whether we can predict reactions far off stability sufficiently well to make statements about r-process conditions. In the following two main topics are briefly addressed: The difficulties in predicting neutron captures far off stability, and the impact of neutron captures on the resulting r-process abundances.

2. Predicting Neutron Capture As the astrophysical reaction rate is obtained by folding the energydependent cross section with the Maxwell-Boltzmann velocity distribution of the projectiles, the relevant energy window for neutrons is given by the location E0 « 0.172T 9 (^+ 1/2) [MeV] and width A w 0.194T 9 (£+ 1/2) 1 / 2 [MeV] of the maximum of the Maxwell-Boltzmann distribution at the given stellar temperature. Since the cross section is integrated over this energy window, the available number of levels within determines the dominating reaction mechanisms. With a sufficient number of overlapping resonances (about 10) the statistical model (Hauser-Feshbach) can be used which employs averaged transmission coefficients and describes the reaction proceeding via a compound nucleus [1]. Single, strong resonances destroy the notion of the simple energy window as the integrand is split in several terms. Finally, in between resonances or without resonances, direct capture will become important. The temperatures above which the statistical model is applicable for the calculation of neutron- and charged-particle induced reaction rates have been estimated in [2]. Explicit limits are given in the global calculation of statistical model rates of [1]. These limits should be taken as a guideline when applying the rates given therein. Fig. 1 shows how direct capture becomes more and more important for nuclei with lower and lower neutron separation energy. Basically, there are three groups of problems connected to the prediction of rates far from stability. The first two (partially overlapping) groups concern the difficulty in predicting nuclear properties relevant for HauserFeshbach and direct capture. For more details on these, see, e.g., [3]. Here, only the most important topics are outlined.

65

"n

"n

"n

~n

Figure 1. Portion of direct capture in the (11,7) cross section for a series of Ti isotopes from a comparison of Hauser-Feshbach and DC calculations. Clearly, the DC contribution increases with decreasing neutron separation energy.

Direct capture calculations are extremely sensitive to the nuclear input, such as neutron separation energies, spins, parities and excitation energy of low-lying states, and the potential used in the neutron channel [4]. One of the largest problems is the determination of the spectroscopic factor which is difficult to calculate. At stability it is usually derived from (d,p) data. However, even there a considerable uncertainty is involved as it is taken from a comparison of prediction and data and thus is not independent of theory. Due to the nature of the statistical model and its use of average quantities its sensitivity to most nuclear inputs is not as extreme as in the direct capture case. Nevertheless, it is yet uncertain how well the relevant nuclear properties, such as the particle separation energies, neutron optical potential, level density, and the low-energy tail of the GDR, can be described far off stability. Global models, in which the properties are not optimized to a few nuclei or a single mass region but rather are attempted to be consistently predicted for all nuclei, fare very well along stability. However, since the used descriptions are derived from data at stability (by either adjusting phenomenological or microscopic parameters) it remains

66 an interesting question whether they are still valid far off stability. Nevertheless, as pointed out above, the statistical model is not applicable at low neutron separation energies and therefore the impact of the uncertainties far off stability are limited. The third problem is the identification of the dominant reaction mechanism and the interplay of different reaction mechanisms when their contributions are of similar size. Clearly, more work has to be done on this in the future. Lacking other data, basically all astrophysical investigations use Hauser-Feshbach rates even for isotopes where it is not applicable. With a low level density it is usually expected that the statistical model overestimates the actual cross section, unless strong, wide resonances are found in the relevant energy window.

3. Implementation of Neutron Capture in the r-Process 3.1.

General

Given the difficulties in predicting rates far off stability, one might wonder whether it is possible at all to study the r-process, even if one resorts to simply parameterized networks. However, the situation is not that bad since it is not necessary to know the rates directly in the r-process path. Contrary to a sometimes still persisting misconception, the formation of r-isotopes cannot be viewed as occurring by a sequence of neutron captures until reaching an isotope with a /J-lifetime shorter than the neutron-capture lifetime, somewhat like an s-process but moving further out from stability. As shown in Fig. 2, all neutron captures and photodisintegrations occur faster by several orders of magnitude than any /3-decay in a given isotopic chain. In fact, the reactions are so fast that almost instantaneously (< 10~ 8 s) an equilibrium state is reached in which the abundance Y for each isotope is determined by the balance of the reactions creating and destroying it: r(n^)YA = r( 7i „)iOi+i. Since the two rates are related by detailed balance, the cross sections cancel out and the ratio is mainly depending on 5 n , T, and p. Neutron captures will only start to matter during freeze-out when the lifetimes become longer due to lower temperatures and lower neutron number densities. It has been shown that the freeze-out proceeds very quickly for realistic conditions [5]. On one hand this limits the importance of neutron captures, on the other hand it validates the investigations which were performed using approximations such as instantaneous freeze-out [6].

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Figure 2. Lifetimes against (11,7) (full line), (7,11) (dashed), and /3-decay (dotted) of neutron-rich T m isotopes. Captures and photodisintegrations are much faster than j3decays and abundances are determined by an (n,7)-(7,n) equilibrium. (Lifetimes at the edges of the considered chain have been set to high values to prevent mass loss from the network.)

3.2.

Dynamic

r-process

simulations

In order to study neutron captures in the freeze-out it is necessary to perform dynamic r-process simulations. As an example, calculations in the model of an adiabatically expanding hot bubble were performed, similar to [5] but with updated, temperature-dependent rates, including the theoretical rates of [1]. In this model of a primary r-process, a blob of matter at high temperature (Tg m 9) expands and cools. For the calculations here the same expansion was chosen as used by [5] in their case of 50 ms expansion timescale. Due to the initial high temperature, all reactions, including charged-particle reactions, are in equilibrium and the resulting abundances can be calculated for each temperature from the equations describing a full NSE. The charged-particle reactions, in particular the a captures, cease at around TQ RJ 2.5. Below that temperature it is not necessary to use a full network but one can utilize a simpler network, only including (n,7), (7,n), and /3-decays. The seed abundances for this r-process network are given

68

S=150,t=1 S=150,f=100 S=150,f=0.01

-j 60

oi

i 80

Li_i—ii 100

i 120

L_^ 140

1 160

1 180

Hi 200

Mass Number A

Figure 3. Decayed final abundances of the S = 150 models. The neutron rates were multiplied by factors 1.0 (full line), 100. (dashed), and 0.01 (dotted), respectively.

by the freeze-out abundances of the charged particle network. More specifically, depending on the freeze-out conditions the slow triple-a rate will either be able to convert all a's to heavy mass nuclei or it will be too slow, leaving a certain a mass fraction. The latter is called o r i c h freeze-out. The process conditions are specified by the entropy S, the electron abundance Ye, and the expansion timescale. Depending on the conditions, more or less free neutrons per heavy seed nucleus are available after the charge-particle freeze-out. Due to the still high temperature an (n,7)-(7,n) equilibrium is established. The /?-halflife of the most abundant nuclei in each isotopic chain (these are only one or two due to the shape of the equilibrium equation) determine how fast material can be converted to the next element. Each chain remains in equilibrium until finally the r-process freezes out. For this comparative study, representative seed abundances were chosen without following the full charged particle network. The calculations always started by only populating the Fe chain but with realistic Yn/Yseed and Ya (depending on entropy and y e ) taken from parameterized results of full calculations. Since the uncertainties in the neutron capture rates might be large, for two entropies 3 exemplary cases are shown here: with standard

69 1e+28

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.

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1e+24

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0.01

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Figure 4. Time evolution of the neutron number density in the S = 150 models. The neutron rates were multiplied by factors 1.0 (full line), 100. (dashed), and 0.01 (dotted), respectively.

rates and with neutron captures multiplied by a factor of 100 and a factor of 0.01, respectively (this implies that the photodisintegrations are changed by the same factor). Figs. 3 and 5 show the final abundances, the neutron number densities as a function of time are shown in Figs. 4, 6. At low entropy there are not enough free neutrons to considerably change the seed abundance, the neutron freeze-out is also fast. It was already shown in [5] that the freeze-out at higher entropy is slower and that final neutron captures can alter the resulting abundances of heavy nuclei but not of light ones. The trough before the high-mass peak was filled by late neutron captures. The freeze-out behavior obtained here depends on the chosen neutron rates. The time at which the n n for the three cases diverge indicates the fallout from the rate equilibrium. After this point it depends on the entropy how far up in mass nuclei have been produced and on the neutron captures how their abundances are altered. As can be seen in Figs. 4 and 6, the final freeze-out phase is faster for larger rates. This reflects the increased capture when the forward and reverse rates fall out of equilibrium which uses up

70 0.001

S=250,f=1 S=250,f=100 S=250,f=0.01

0.0001 -

1e-05

1e-06

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120

140

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Figure 5. Decayed final abundances of the S = 250 models. The neutron rates were multiplied by factors 1.0 (full line), 100. (dashed), and 0.01 (dotted), respectively.

neutrons faster. The masses above about 140 are mainly produced in this late freeze-out phase and are therefore more sensitive to the value of the neutron captures. Especially in the high entropy case shown in Fig. 5 it is evident that faster neutron captures smooth the abundance distribution and fill the trough before the A as 200 peak. For both entropies, the artificially suppressed rates do not allow to build up considerable abundances beyond A w 140. 4. Conclusion The simple comparison shown above for the hot bubble model has to be interpreted cautiously. Despite the fact that there might be considerable uncertainties in the theoretical rates far off stability changing all rates in a range of 4 orders of magnitude seems unrealistic. Even if new effects (like pygmy resonances [7] or overestimated cross sections [3]) might change the rates by factors of 10 for extremely neutron-rich nuclei, late-time captures will not include such nuclei but will occur closer to stability. Moreover, for reproducing the solar r-process pattern it is necessary to superpose a number of components with different entropies. Thus, effects of rates

71 1e+28 S=250,f=1 S=250,f=100 S=250,f=0.01 1e+26

1e+24

1e+22

1e+18

1e+16

0.001

0.01

0.1 Time [s]

Figure 6. Time evolution of the neutron number density in the S = 250 models. The neutron rates were multiplied by factors 1.0 (full line), 100. (dashed), and 0.01 (dotted), respectively.

altered on a large scale, as shown above, can be compensated by a scaling in entropy and a different weight distribution. Thirdly, a more realistic seed abundance distribution might also decrease the difference in heavy element production between the different cases. Higher entropies realistically start with seed abundances in the A ss 110 region and require less neutrons to form more heavy elements. However, this was not taken into account here to purely show the influence of altered neutron captures. Despite the above caveats the main conclusions are consistent with other studies [5,8]. Components with high entropy freeze out slower and latetime neutron captures can modify the final abundance distribution mainly in the region A > 140. Therefore, emphasis has to be put on improving the prediction of nuclear cross sections and astrophysical reaction rates in that mass region. Acknowledgments This work was supported by the Swiss NSF, grant 2000-061031.02. T. R. acknowledges a PROFIL professorship of the Swiss NSF (grant 2024-

72 067428.01). References 1. T. Rauscher and F.-K. Thielemann, Atomic Data Nucl. Data Tables 75, 1 (2000). 2. T. Rauscher, F.-K. Thielemann andK.-L. Kratz, Phys. Rev. C56, 1613 (1997). 3. P. Descouvemont and T. Rauscher, Nucl. Phys., in press; astro-ph/0402668. 4. T. Rauscher, R. Bieber, H. Oberhummer, K.-L. Kratz, J. Dobaczewski, P. Moller and M. M. Sharma, Phys. Rev. C 5 7 , 2031 (1998). 5. C. Freiburghaus et al, Ap. J. 516, 381 (1999). 6. K.-L. Kratz, J.-P. Bitouzet, F.-K. Thielemann, P. Moller and B. Pfeiffer, Ap. J. 403, 216 (1993). 7. S. Goriely and E. Khan, Nucl. Phys. A706, 217 (2002). 8. R. Surman and J. Engel, Phys. Rev. C 64, 035801 (2001).

SUPERNOVA NEUTRINO-NUCLEUS PHYSICS A N D THE R-PROCESS

W. C. HAXTON Institute for Nuclear Theory and Department of Physics Box 351550, University of Washington Seattle, WA 98155 E-mail: [email protected] This talk reviews three inputs important to neutrino-induced nucleosynthesis in a supernova: 1) "standard" properties of the supernova neutrino flux, 2) effects of phenomena like neutrino oscillations on that flux, and 3) nuclear structure issues in estimating cross sections for neutrino-nucleus interactions. The resulting possibilities for neutrino-induced nucleosynthesis - or the i/-process - in massive stars are discussed. This includes two relatively recent extensions of v-process calculations to heavier nuclei, one focused on understanding the origin of 138 La and 180 Ta and the second on the effects following r-process freezeout. Prom calculations of the neutrino post-processing of the r-process distribution, limits can be placed on the neutrino fluence after freezeout and thus on the dynamic timescale for the expansion.

1. Basic Supernova Neutrino Characteristics A massive star, perhaps 15-25 solar masses, evolves through hydrostatic burning to an "onion-skin" structure, with a inert iron core produced from the explosive burning of Si. When that core reaches the Chandresekhar mass, the star begins to collapse. Gravitational work is done on the infalling matter, the temperature increases, and the increased density and elevated electron chemical potential begin to favor weak-interaction conversion of protons to neutrons, with the emission of i/es. Neutrino emission is the mechanism by which the star radiates energy and lepton number. Once the density exceeds ~ 10 12 g/cm 3 in the infall of a Type II supernova, however, neutrinos become trapped within the star by neutral-current scattering, —diffusion \ -.collapse

/-i \

That is, the time required for neutrinos to random walk out of the star exceeds T c o " o p s e . Thus neither the remaining lepton number nor the gravitational energy released by further collapse can escape. 73

74

After core bounce a hot, puffy protoneutron star remains. Over times on the order of a few seconds, much longer than the 100s of milliseconds required for collapse, the star gradually cools by emission of neutrinos of all flavors. As the neutrinos diffuse outward, they tend to remain in flavor equilibrium through reactions such as ve + ve 4+ i/M + i/M

(2)

producing a rough equipartition of energy/flavor. Near the trapping density of 10 12 g/cm 3 the neutrinos decouple, and this decoupling depends on flavor due to the different neutrino-matter cross sections, vx + e 44 vx + e : aVli /aVt ~ 1/6 ue + n +•> p + e+ De+p<+n + e+.

(3)

One concludes that heavy-flavor neutrinos, because of their weaker cross sections for scattering off electrons (and the absence of charged-current reactions off nucleons), will decouple at higher densities, deeper within the protoneutron star, where the temperature is higher. In the case of electron neutrinos, the i/es are more tightly coupled to the matter than the De$, as the matter is neutron rich. The result is the expectation of spectral differences among the flavors. If spectral peaks are used to define an effective FermiDirac temperature, then supernova models 1 typically yield values such as TVli ~ T„T ~ TP(/ ~ TPr ~ 8MeV TVe ~ Z.hMeV

T p . ~ 4.5MeV

(4)

Some of the issues relevant to subsequent neutrino-induced nucleosynthesis include: • The ue and Pe temperatures are important for the p / n chemistry of the "hot bubble" where the r-process is thought to occur. This is high-entropy material near the mass-cut that is blown off the protoneutron star by the neutrino wind. • Matter-enhanced neutrino oscillations, in principle, could generate temperature inversions affecting p +-• n charge-current balance, thus altering conditions in the "hot bubble" necessary for a successful r-process. • If the "hot bubble" is the r-process site, then synthesized nuclei are exposed to an intense neutrino fluence that could alter the r-process distribution. The relevant parameter is the neutrino fluence after r-process freezeout.

75

2. N e w Neutrino Physics Discoveries and Potential Supernova Implications Following the chlorine, GALLEX/SAGE, and Kamioka/Super-Kamiokande experiments, strong but circumstantial arguments led to the conclusion that the data indicated new physics. For example, it was observed that, even with arbitrary adjustments in the undistorted fluxes of pp, 7 Be, and 8 B fluxes, the experimental results were poorly reproduced 2 . When neutrino oscillations were included, however, several good fits to the data were found. These included the small-mixing-angle (SMA) and large-mixingangle (LMA) MSW solutions, the LOW solution, and even the possibility of "just-so" vacuum oscillations, where the oscillation length is comparable to the earth-sun separation. The ambiguities were convincingly removed by the charged- and neutral-current results of SNO, which demonstrated that about 2/3rds of the solar neutrino flux was carried by heavy-flavor neutrinos 3 . Similarly, anomalies in atmospheric neutrino measurements - a zenithangle dependence in the ratio of electron-like to muon-like events - indicated a distance-dependence in neutrino survival properties consistent with oscillations. The precise measurements of Super-Kamiokande provided convincing evidence for this conclusion, and thus for massive neutrinos 4 . A summary of recent discoveries in neutrino physics include: • Oscillations in matter can be strongly enhanced. • SNO identified a unique two-flavor solar neutrino solution corresponding to 0i2 ~ TT/6 and 5m\2 ~ 7 x K T 5 eV 2 . • The KamLAND reactor ue disappearance experiment has confirmed the SNO conclusions and narrowed the uncertainty on <Sm22 5• The Super-Kamiokande atmospheric neutrino results show that those data require a distinct 5m\3 ~ (2 — 3) x 10~ 3 eV2 and a mixing angle #23 ~ f / 4 that is maximal, to within errors. • The KEK-to-Kamioka oscillation experiment K2K is consistent with the Super-Kamiokande atmospheric results, finding Sm\3 ~ (1.5 — 3.9) x 1 0 - 3 eV2 under the assumption of maximal mixing 6 . • Chooz and Palo Verde searches for reactor ve disappearance over the <5m|3 distance scale have provided null results, limiting 6\z 7These results have determined two mass splittings, 8m\2 and the magnitude of |<Sm23|. But as only mass differences are known, the overall scale is undetermined. Likewise, because the sign of <Sm23 is so far unconstrained, two mass hierarchies are possible: the "ordinary" one where the nearly de-

76

generate 1,2 mass eigenstates are light while eigenstate 3 is heavy, and the inverted case where the 1,2 mass eigenstates are heavy while eigenstate 3 is light. The relationship between the mass eigenstates (1/1,1/2, "3) and the flavor eigenstates {ve,v,i,vT) is given by the mixing matrix, a product of the three rotations 1-2 (solar), 1-3, and 2-3 (atmospheric):

(

C12C13

S12C13

- S 1 2 C 2 3 - C12S233l3e'S S12S23 -

1

\

C12C23Sl3e

/

ci 3

C12C23 ,<5

-C12S23 -

Si3e~iS\

Si2S23Sl3e,(S Si2C23Si3etS

si3e_i,5\

S23C13 C23C13 /

/ v i \

I

"2 V ^ /

I C12 S12 \ / vi \ C23 s 23 1 -S12 c 12 ei^v2 (5) iS i0 -523 W \-s13e C13 / \ 1/ Ve ^3/ Here s\2 = sin #12, etc. We see, in addition to the unknown third mixing angle #13, this relationship depends on one Dirac CP-violating phase parameterized by S and two Majorana CP-violating phases parameterized by 0i and <j>2- The former could be measured in long-baseline neutrino oscillation experiments (with the ease of this depending on the size of 8\3), while the latter could influence rates for double beta decay. These new neutrino physics discoveries could have a number of implications for supernova physics: • Because of solar neutrinos, we have been able to probe matter effects up to densities p ~ 100 g/cm 3 characteristic of the solar core. As the density at the supernova neutrinosphere is p ~ 10 12 g/cm 3 , supernova neutrinos propagate in an MSW potential that can be 10 orders of magnitude greater than any we have tested experimentally. In addition, the neutrinos propagate in a dense neutrino background, generating new MSW potential contributions due to v — v scattering. Such effects, as well as the magnitude of the ordinary-matter MSW effects, may be unique to the supernova environment. • We do not know #13, which is the crucial mixing angle for supernovae. This angle governs the ve -heavy flavor level crossing encountered at depth in the star. This crossing occurs near the base of the carbon zone in the progenitor star, and remains adiabatic for sin2 2#i 3 > 10~ 4 . For the ordinary hierarchy, the resulting ve *rt fMir crossing would lead to a hotter ve spectrum. For an inverted hierarchy, the crossing would be ve ++ ^ , T • Presumably the position of this crossing will be influenced by the neutrino background contribution to the MSW potential. This nonlinear problem is rather complicated because the flavor content of the background evolves with time (being ve-dominated at early times).

77

V*

VT

V,

Vn

~10^g/cmJ

density

vacuum

Figure 1. A three-level MSW level-crossing diagram showing the second crossing that should occur at densities characteristic of the base of the carbon zone in a Type II supernova progenitor star.

3. Nuclear Structure Issues Inelastic neutrino-nucleus interactions are important to a range of supernova problems, including neutrino nucleosynthesis, the detection of supernova neutrinos in terrestrial detectors, and neutrino-matter heating that could boost the explosion. The heavy-flavor neutrinos have an average energy (E) ~ 3. I T ~ 25 MeV. However the most effective energy for generating nuclear transitions can be substantially higher because cross sections grow with energy and because nuclear thresholds are more easily overcome by neutrinos on the high-energy tail of the thermal distribution. For the neutrino energy range of interest the allowed approximation, which includes only the Gamow-Teller 5>icr(z)r±(f) and Fermi r±(i) operators, is often not adequate. (These are given for charge-current reactions; the allowed operator for inelastic neutral current reactions is gA
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for back-angle scattering. Consequently qR, where R is the nuclear size, may not be small. Such first-forbidden contributions may be as important as the allowed contribution for supernova fMs and uTs. For all but the lightest nuclei, cross sections must be estimated from nuclear models, such as the shell model. Shell model wave functions are generated by diagonalizing an effective interaction in some finite Hilbert space of Slater determinants formed from shells \n(ls)jmj). The space may be adequate for describing the low-momentum components of the true wave function, but not the high-momentum components induced by the rather singular short-range NN potential. The effective interaction, usually determined empirically, is a low-momentum interaction that corrects for the effects of the excluded, high-momentum excitations. Similarly, effective operators should be used in evaluating matrix elements, such as those of the weak interaction operators under discussion here, and the shell model wave function should have a nontrivial normalization. In effective interaction theory, that normalization is the overlap of the model-space wave function with the true wave function. Because effective interaction theory is difficult to execute properly in some sense it is as difficult as solving the original problem in the full, infinite Hilbert space - nuclear modelers take short cuts. Often all effective operator corrections are ignored: bare operators are used. In other cases, phenomenological operator corrections can been deduced from systematic comparisons of shell-model predictions and experimental data. The Gamow-Teller operator is an interesting case. Rather thorough comparisons of 2sld and 2 p l / shell-model predictions with measured allowed /3-decay rates have yielded a simple, phenomenological effective operator: the axial coupling ge/' ~ 1.0 should be used rather than the bare value 8 ' 9 . This observation is the basis for many shell-model estimates of the Gamow-Teller response that governs allowed neutrino cross sections. Many of the shell-model techniques are quite powerful. Moments techniques based on the Lanczos algorithm 9 have been used to treat spaces of dimension ~ 10 8 : important supernova neutrino cross sections for Fe and Ni isotopes have been derived in this way 1 0 . Another shell-model-based method uses Monte Carlo sampling n . There are reasons to have less confidence in corresponding estimates of first-forbidden effective operators. The first-forbidden operators include the vector operator qr(i) and the axial-vector operators [
79 Standard shell-model spaces satisfy the sum-rule contraints for the GamowTeller operator: the operator cannot generate transitions outside a full shell, for example. In contrast, for harmonic-oscillator Slater determinants, the first-forbidden operators generate transitions for which AJV = ± 1 , where N is the principal quantum number. Thus, underlying sum rules are violated as the operators always connect either initial or final configurations to states outside the shell-model space. When the full momentum dependence of the weak interaction operators is included, the resulting spin-spatial structure includes forms such as ji(qr(i))\Yi(n{i))®I.]jMj where ji is a spherical Bessel function, Yi a spherical harmonic, and Is is a single-particle spin function. (More complicated forms involve vector spherical harmonics combined with spatial operators such as V(i).) The fact that q cannot then be factored from the operator then makes Lanczos moments techniques less useful: at every desired q the Lanczos procedure has to be repeated. (There are techniques under development 12 which exploit special properties of the harmonic oscillator to circumvent this problem.) Thus most calculations that treat the full momentum-dependence of the weak operators have used simple spaces, ones for which state-by-state summations of the weak transition strengths are practical. The approaches include truncated shell-model spaces, models based on the Random Phase Approximation (RPA), and even the highly schematic Goldhaber-Teller model. Figure 2 compares continuum RPA results for charge-current reactions on 1 6 0 with shell-model results of the sort described above 13 . The quantities plotted are cross sections averaged over a thermal neutrino spectrum. This is an interesting test case because 1 6 0 , naively a closed-shell nucleus, has a smaller Gamow-Teller response than most mid-shell nuclei. Thus momentum-dependent contributions to the cross section should be more important than in many other cases. It is perhaps surprising, given the assumptions implicit in both the shell-model and CRPA calculations, that the results agree so well over the full range of interesting supernova neutrino temperatures. The only significant discrepancy, at very low temperatures, is due to the inclusion of contributions from 1 8 0 in the shell model calculation used in Fig. 2. (The calculations were done for a natural oxygen target.) Due to the very low threshold for 1 8 0 - • 1 8 F , this minor isotope (0.2% relative to 1 6 0 ) dominates the 0(ve,e) cross section at sufficiently low temperatures. The good agreement between the shell-model and CRPA calculations, of course, could mask problems associated with common as-

80

sumptions, such as the absence of a reliable procedure for assessing effective operators beyond the allowed approximation.

Temperature T(MeV) Figure 2. Comparison of CRPA (full lines) and shell-model (dash lines) cross section predictions, integrated over thermal neutrino spectra. The shell-model results include the contribution from l s O , important at low temperatures in natural water for the (i/e,e~) reaction. From Kolbe, Langanke, Martinez-Pinedo, and Vogel 13 .

4. The Neutrino Process Several rare isotopes are thought to be created during a core-collapse supernova by neutrino reactions in the mantle of the star 14 . The most common mechanism is inelastic neutral-current neutrino scattering off a target nucleus like 20 Ne or 1 2 C, with significant energy transfer, e.g., giant resonance excitation. The nucleus, excited above the continuum, then decays by nucleon or a emission, leading to new nuclei. A nuclear network calculation is required to assess the survival of the neutrino-process products, such as 19 F in the Ne shell and U B in the C shell. The co-produced nucleons can capture back on the daughter nucleus, destroying the product of interest. Similarly, passage of the shock wave leads to heating that can destroy the

81 product by (7, a) and similar reactions. Frequently the majority of the instantaneous production is lost due to such explosive processing. The enormous fluence of neutrinos can yield significant productions. Typically 1% of the nuclei in the deep mantle of the star - the C, Ne, and O shells - are transmuted by neutrinos. The most important products, like 10 F and 1 1 B, tend to be relatively rare odd-A isotopes neighboring very plentiful parent nuclei, such as 20 Ne and 1 2 C. (The parent isotopes are the hydrostatic burning products, typically.) The natural abundances of such odd-A isotopes could, in principle, be due to neutrino processing. Such nucleosynthesis calculations must be embedded in a model of the supernova event. Important factors include: • a neutrino flux that tends to diminish exponentially, with a typical time scale r„ ~ 3 sec; • a pre-processing phase where nuclei in the mantle are exposed to the neutrino flux at some fixed radius r, prior to shock arrival; • a post-processing phase after shock wave arrival, where the material exposed to the neutrino flux is heated by the shock wave (potentially destroying pre-processing productions), and then expands adiabatically off the star, with a temperature T that consequently declines exponentially; • integration of these neutrino contributions into an explosive nucleosynthesis network; and • integration over a galactic model, with some assumptions on the range of stellar masses that will undergo core collapse and mantle ejection. Calculations of this nature were done by Woosley et al. 14 . Potentially significant neutrino-process productions include the nuclei 1 9 F , 1 0 , 1 1 B, 7 Li, the gamma-ray sources 2 2 Na and 26 A1, 15 N, 3 1 P , 3 5 C1, 3 9 . 4 0 K, 5 1 V, and 45 Sc. Although the nuclear reaction network stopped at intermediate masses, the very rare isotopes 138 La and 180 Ta were also identified as likely i/-process candidates. Recent work by Heger et al. 15 extends these calculations in important ways. First, the evolution of the progenitor star includes the effects of mass loss. Second, a reaction network is employed that includes all of the heavy elements through Bi, using updated reaction rates. Third, the nuclear evaporation process - emission of a proton, neutron, or a by the excited nucleus - is treated in a more sophisticated statistical model that takes into account known nuclear levels and their spins and parities. While the calculations lack a full set of neutrino cross sections, those cross sections important to known (e.g., 1 9 F and n B ) and suspected (e.g., 1 3 8 La and 180 Ta) neutrino products were evaluated and incorporated into the network.

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The results are shown in Fig. 3, with production factors normalized to that of 1 6 0 . Thus a production factor of one would mean that the i/-process would fully account for the observed abundance of that isotope. While 11 B might be slightly overproduced and 1 8 F slightly underproduced, given nuclear and astrophysics uncertainties, the i/-process yields of these isotopes and 138 La are compatible with this being their primary origin. The case of 138 La is particularly interesting, as the primary channel for the production is charged-current reaction 138 Ba(i/,e) 138 La, where 138 Ba is enhanced in the progenitor star by the s-process. This production is the only known case where a charged-current channel dominates the production. Thus this yield is sensitive to the ve temperature - a potential indicator for oscillations if the transformation occurs deep within the star.

Figure 3. Neutrino-process production factors for U B , 1 9 F, 138 La, and 180 Ta, as calculated by Heger et al. 15 . The results are normalized to the production of l e O in 15 MQ (squares) and 25 M s (circles) progenitor stars. The open (filled) symbols represent stellar evolution studies in which neutrino reactions on nuclei were excluded (included).

While 180 Ta appears to be overproduced, the calculation does not distin-

83

guish production in the 9 _ isomeric state from production in the 1 + ground state. Only the isomeric fraction should be counted. An estimate of the v-process fraction that ends up in the isomeric state, following a 7 cascade, has not been made. However, initiating reactions such as 181 Hf(i/ e ,e~n) involve low-spin parent isotopes, and the neutrino reaction transfers little angular momentum. Thus one would anticipate that the majority of the yield would cascade to the ground state. The reduction factor of 3-4 required to bring the 180 Ta production in line with the others of Fig. 3 is compatible with this. There are other mechanisms for producing some of these f-process products. One interesting one, for example, is cosmic-ray spallation reactions on CNO nuclei in the interstellar medium, which can produce 1 0 ' 1 1 B and 6,7 Li. Some such process is required to explain the origin of 1 0 B, for example. Cosmic-ray production, a secondary process, and the i/-process, a primary mechanism, might be distinguished by measurements that would separately determine the evolution of 1 0 B and n B . If the i/-process fraction of n B could be convincingly determined, this production would then become a more quantitative test of explosive conditions within the supernova carbon shell. We note two recent observational results relevant to the v-process. Prochaska, Howk, and Wolfe 16 recently observed over 25 elements in a galaxy at redshift z — 2.626, whose young age and high metallicity implies a nucleosynthetic pattern dominated by short-lived, massive stars. Their finding of a solar B/O ratio in an approximately 1/3-solar-metallicity gas argues for a primary (metal-independent) production mechanism for B such as the v-process, rather than a secondary process. Similarly, new F abundance data of Cunha et ai. show a low F / O ratio in two u Centauri stars, which argues against AGB-star production of F (one competing suggestion), but would be consistent with the f-process production 17 .

5. Neutrino Process Effects in the r-process Other speakers have discussed the r-process and the likelihood that the "hot bubble" - the high-entropy nucleon gas that is blown off the protoneutron star surface by the neutrino wind - is the primary site for the r-process. The nuclear physics of the r-process tells us that the synthesis occurs when the neutron-rich nucleon soup is in the temperature range of (3 — 1) x 109K, which, in the hot bubble r-process, might correspond to a freeze-out radius of (600-1000) km and a time ~ 10 seconds after core

84

collapse. The neutrino fluence after freeze-out (when the temperature has dropped below 109K and the r-process stops) is then ~ (0.045-0.015) X1051 ergs/(100km) 2 . Thus, after completion of the r-process, the newly synthesized material experiences an intense flux of neutrinos. This suggests that v-process postprocessing could affect the r-process distribution. Comparing to our earlier discussion of carbon- and neon-zone synthesis by the i/-process, it is apparent that neutrino effects could be much larger in the hot bubble r-process: the synthesis occurs much closer to the star, at ~ 600-1000 km. (The Ne-shell radius is ~ 20,000 km.) For this radius and a freezeout time of 10s, the "post-processing" neutrino fluence - the fluence that can alter the nuclear distribution after the r-process is completed - is about 100 times larger than that responsible for fluorine production in the Ne zone. As approximately 1/300 of the nuclei in the Ne zone interact with neutrinos, and noting that the relevant neutrino-nucleus cross sections scale roughly as A (a consequence of the sum rules that govern first-forbidden responses), one quickly sees that the probability of a heavy r-process nucleus interacting with the neutrino flux is approximately unity. Because the hydrodynamic conditions of the r-process are highly uncertain, one way to attack this problem is to work backward 18 . We know the final r-process distribution (what nature gives us) and we can calculate neutrino-nucleus interactions relatively well. Thus by subtracting from the observed r-process distribution the neutrino post-processing effects, we can determine what the r-process distribution looked like at the point of freeze-out. In Fig. 4, the "real" r-process distribution - that produced at freeze-out - is given by the dashed lines, while the solid lines show the effects of the neutrino post-processing for a particular choice of fluence. The nuclear physics input into these calculations is precisely that previously described: GT and first-forbidden cross sections, with the responses centered at excitation energies consistent with those found in ordinary, stable nuclei, taking into account the observed dependence on \N — Z\. One important aspect of Fig. 4 is that the mass shift is significant. This has to do with the fact that a 20 MeV excitation of a neutron-rich nucleus allows multiple neutrons ( ~ 5) to be emitted. (The binding energy of the last neutron in an r-process neutron-rich nuclei is about 2-3 MeV under typical r-process conditions.) The second thing to notice is that the relative contribution of the neutrino process is particularly important in the "valleys" beneath the mass peaks: the reason is that the parents on the mass peak are abundant, and the valley daughters rare. In fact, it follows from this that the neutrino process effects can be dominant for precisely

85

X"

170

175

180

185

190

195

200

Figure 4. Comparison of the r-process distribution that would result from the freezeout abundances near the A ~ 195 mass peak (dashed line) to that where the effects of neutrino post-processing have been included (solid line). The fluence has been fixed by assuming that the A = 183-187 abundances are entirely due to the j/-process.

seven isotopes (Te, Re, etc.) lying in the valleys below the A=130 (not shown) and A=195 (Fig. 4) mass peaks. Furthermore if an appropriate neutrino fluence is picked, these isotope abundances are correctly produced (within abundance errors). The fluences are N = 82 peak

0.031 • 10 51 ergs/(100km) 2 /flavor

N = 126 peak

0.015 • 10 61 ergs/(100km) 2 /flavor,

values in fine agreement with those that would be found in a hot bubble reprocess. So this is circumstantial but significant evidence that the material near the mass cut of a Type II supernova is the site of the r-process: there is a neutrino fingerprint. A more conservative interpretation of these results, however, places a bound on the r-process post-processing neutrino fluence by insisting that these isotopes not be overproduced. This bound will hold even if there are

86

other mechanisms, such as neutron emission accompanying the /? decay of rprocess parent nuclei as they move to the valley of stability, that contribute to the abundances of these rare isotopes. This bound is then an interesting constraint on supernova dynamics: the neutrino fluence after freezeout depends on the flux at the time of freezeout and on the dynamic time scale (or the velocity of the material being expelled from the supernova). This constraint is plotted in Fig. 5 along with one imposed by the observed /S-flow equilibrium of nuclei near the mass peak. (The /?-flow equilibrium requires that the neutrino flux at freezeout not exceed the value where the neutrino reactions would compete with /? decay. This would destroy the observed correlation between abundance and 0 decay lifetime.) Together these two constraints place upper bounds on the luminosity at freezeout (equivalently, a lower bound on the freezeout radius) and on the dynamic timescale.

6. S u m m a r y This goal of this talk is to make some connections between supernova neutrino physics, the nuclear structure governing neutrino-nucleus interactions, and new neutrino properties. The main example used here, the neutrino process, connects observable abundances with supernova properties, such as the r-process freezeout radius and dynamic timescale. Thus by identifying i/-process products and by reducing the associated nuclear structure uncertainties that govern their abundances, one may be able to place significant constraints on the explosion mechanism. The conditions for the r-process itself and for various i/-process productions are set by neutrino physics. For example, the p / n chemistry of the "hot bubble" is largely governed by charged-current p +-> n reactions, while the productions of 138 La and 1 9 F depend primarily on charged-current interactions on 138 Ba and on neutral-current reactions on 20 Ne, respectively. Thus in principle such productions could be influenced by oscillations that invert ve and heavy-flavor neutrino spectra (or, in the case of an inverted hierarchy, De and heavy-flavor antineutrino spectra). This is another important reason for exploring the nucleosynthetic "fingerprints" of supernova neutrinos. The productions identified so far that would be influenced by neutrino oscillations, such as 138 La, are created at densities above those characterizing the naive 1-3 MSW matter crossing, at least in the preprocessing phase. However, we have noted that the location of MSW crossings could be perturbed by neutrino background effects. Furthermore, in

87 T

I

I

I

I

r

r

(b)

o,

.

0.1

— Allowed Conditions

e w

At The Freeze-Out 0.02 -

0.01 0.1

Of The A ~ 196 Peak

_1_

0.2

_i_

_L

_i_i_

0.5 T*.(S)

Figure 5. Constraints imposed on the neutrino flux parameter Lv/r2 at freezeout, where Lv is the luminosity and r the freezout radius, and on the dynamic timescale Tdyn governing the expansion. The horizontal solid line results from the condition of ,8-flow equilibrium for the A=195 peak. The diagonal solid line is the requirement that uprocess post-processing of the r-process peak not overproduce nuclei in the mass region A= 183-187. The calculation assumes a neutrino flux that evolves exponentially with T„ = 3s. Parameters lying on the dashed line corresponds to the fluence determined by attributing the full abundances of A=183-187 nuclei to the neutrino process.

the post-processing phase, crossings will arise in the rarified matter that expands off the star. This is a fascinating question for the r-process, and perhaps also for certain v-process productions. These observations should motivated further studies of the potential effects of new neutrino physics on supernova nucleosynthesis.

Acknowledgments This work was supported in part by the Office of Science, U.S. Department of Energy, under grants DE-FG02-00ER41132 and DE-FC02-01ER41187.

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References 1. M. Liebendoerfer, M. Rampp, H.-Th. Janka, and A. Mezzacappa, astroph/0310662/ and to be published in Ap. J.; A. Burrows, astro-ph/0405427/. 2. K. M. Heeger and R. G. H. Robertson, Phys. Rev. Lett. 77, 3720 (1996). 3. SNO Collaboration, Phys. Rev. Lett. 87, 071301 (2001); 89, 011301 (2002); 92, 181301 (2004). 4. Super-Kamiokande Collaboration, Phys. Rev. Lett. 81, 1562 (1998); 82, 2644 (1999); 85, 3999 (2000). 5. KamLAND Collaboration, Phys. Rev. Lett. 90, 021802 (2003); 92, 071301 (2004). 6. K2K Collaboration, Phys. Rev. Lett. 90, 041801 (2003). 7. M. Apollonio et al, Phys. Lett. B 420, 397 (1998); F. Boehm et al., Phys. Rev. D 64, 112001 (2001). 8. B. A. Brown and B. H. Wildenthal, At. Data Nucl. Data Tables 33, 347 (1985). 9. G. Martinez-Pinedo, A. Poves, E. Caurier, and A. P. Zucker, Phys. Rev. G 53, 2602 (1996). 10. E. Caurier, K. Langanke, G. Martinez-Pinedo, and F. Nowacki, Nucl. Phys. A 653, 439 (1999). 11. S. E. Koonin, D. J. Dean, and K. Langanke, Phys. Repts. 278, 1 (1997); T. Otsuka, M. Honma, and T. Mizusaki, Phys. Rev. Lett. 81, 1588 (1998). 12. W. C.Haxton, K. Nollett, and K. Zurek, in preparation. 13. E. Kolbe, K. Langanke, G. Martinez-Pinedo, and P. Vogel, J. Phys. G 29, 2569 (2003). 14. S. E. Woosley and W. C. Haxton, Nature 554, 45 (1988); S. E. Woosley, D. H. Hartmann, R. D. Hoffman, and W. C. Haxton, Astroph. J. 356, 272 (1990); G. V. Domogatskii and D. K. Nadyozhin, Sov. Astro. 22, 297 (1978). 15. A. Heger et al, astro-ph/0307546/. 16. J. X. Prochaska, J. C. Howk, and A.M. Wolfe, Nature 423, 57 (2003). 17. K. Cunha, V. V. Smith, D. L. Lambert, and K. H. Hinkle, Astron. J. 126, 1305 (2003). 18. Y.-Z. Qian, W. C. Haxton, K. Langanke, and P. Vogel, Phys. Rev. G 55, 1532 (1997); W. C. Haxton, K. Langanke, Y.-Z. Qian, and P. Vogel, Phys. Rev. Lett. 78, 2694 (1997).

EQUATION OF STATE A N D N E U T R I N O OPACITY OF D E N S E STELLAR MATTER *

SANJAY REDDY Theoretical Division Los Alamos National Laboratory, Los Alamos, NM 87545, USA E-mail: [email protected]

The properties of matter at densities similar to nuclear density plays an important role in core collapse supernova. In this talk I discuss aspects of the equation of state and weak interactions at high density. I highlight its relation to the temporal and spectral features of the neutrino emission from the newly born neutron star born in the aftermath of a core-collapse supernova. I will briefly comment on how this will impact r-process nucleosynthesis.

1. Introduction The hot and dense neutron star (proto-neutron star) born in the aftermath of a core collapse supernova provides a promising environment for r-process nucleosynthesis. The intense temperatures and neutrino fluxes in the vicinity of the proto-neutron star is expected to result in a high entropy neutron-rich wind necessary for successful r-process nucleosynthesis. Although theoretical efforts to simulate core collapse supernova have not been able to provide a mechanism for robust explosions, several key features of the supernova dynamics and early evolution of the proto-neutron star are well understood. Large scale numerical simulations of supernova and neutron star evolution are now being pursued by several groups *. Simulating core collapse supernova is challenging because it involves coupled multi-dimensional hydrodynamics and neutrino transport. The neutrinos play a key role since they are the dominant source of energy transport. It is expected that refinements in neutrino transport and better treatment of multi-dimensional effects are needed to understand the explosion mechanism 1 . The temporal and spectral features of the neutrino ""This work is supported by the department of energy under contract w-7405-eng-36

89

90 emission which is emitted from the proto-neutron star is an independent diagnostic of supernova explosion dynamics and early evolution of the protoneutron star. To accurately predict the ambient conditions just outside the newly born neutron star for the first 10 — 20 s, we will need to understand both the explosion mechanism and neutrino emission. In this talk I will discuss micro-physical issues that directly affect the latter. I begin by discussing the importance of the equation of state and neutrino transport in core collapse supernova in Sec. 2. Aspects of the equation of state and differences between predictions of mean field theories and variational calculations are discussed in Sec. 3. In Sec. 4, I discuss the micro-physics of neutrino opacity and its relation to linear response properties of dense matter. In Sec. 5, I conclude with a brief discussion of how neutrinos affect r-process nucleosynthesis. 2. Early Evolution of the Proto-Neutron Star

Supernova Neutrinos - a (proto) neutron star is born

J50q km i'.Jx/ \ I /~jvj

Core collapse tC0|,apse -100 ms

X .-'T"-\ L.. ' /'\ W * V

\*.

T\

10 km

Shock wave EShock~1051ergs

/ . • • - "••4 i< Meaning Mkin-' \ ,

Hot & dense Proto-neutron Star: t~l-2 S

Figure 1.

100 km

Schematic showing the various stages of a core-collapse supernova explosion.

The illustration in Fig.l, shows the important stages of core-collapse supernova and the birth of a proto-neutron stars. Successive nuclear burning from lighter to heavier elements, which fuels stellar evolution, inevitably results in the formation of a iron core in massive stars (M > 8MQ). Since iron

91

is the most stable nucleus, further energy release through nuclear burning is not possible. The Fe-core is supported against gravitational collapse by the electron degeneracy pressure. When the mass of the Fe-core exceeds the Chandrashekar mass (Mch ^ 1.4MQ), it becomes unstable to gravitational collapse. Detailed numerical simulations indicate that the core collapses, from its initial radius f?;n ~ 1500 km to a final radius R{n ~ 100 km, on a time-scale similar to the free-fall time-scale Tfree-faii — 100 ms. Soon after the onset of collapse, the core density exceeds 1012 g/cm 3 and the matter temperature T ~ 5 MeV. Under these conditions, thermal neutrinos become trapped on the dynamical time-scale of collapse. Consequently, collapse is nearly adiabatic. The enormous gravitational binding energy J3._E.Grav. — GM^ s /i?NS — 3 x 10 53 ergs, is stored inside the star as internal thermal energy of the matter components, and thermal and degeneracy energy of neutrinos. The newly born neutron star looses this energy on a time-scale determined by the rate of diffusion of neutrinos 2 ' 3 . Neutrino

Figure 2. Snap shots of the proto-neutron star during its early evolution. Profiles of density, temperature, entropy and neutrino chemical potential are shown.

emission from the proto-neutron star has been studied within the diffusion approximation in earlier work 3 . Fig. 2 shows several time slices of the temperature, entropy per baryon, neutrino chemical potential and neutrino fraction inside the star as neutrinos diffuse radially outward. Initially, the

92

driving term for neutrino fluxes is the large gradient in the electron neutrino chemical potential (see figure). This phase of the evolution is called the deleptonization epoch. This epoch is characterized by joule-heating of the inner regions by the neutrino current driven by the lepton number gradient 2 . Subsequently, the neutrino fluxes are driven by the temperature gradient and results in cooling of the core. For this reason, this epoch is called the cooling phase. Time scales for deleptonization and cooling can be identified by inspecting the diffusion equations and are given by d TD ~ lL Tc ~ v dYu c\e cXft respectively, where R is the radius of the proto-neutron star and c is the speed of neutrinos. In the above, Ae is the typical mean free path of electron neutrinos which transport lepton number and AM is the mean free path of /j, and r neutrinos which transport energy. | ^ is related to the isospin susceptibility of nuclear matter (the symmetry energy) and Cv is the specific heat.

:£.

c £-

(1)

3. Nuclear Equation of State The nuclear equation of state affects several aspects of the dynamics of core-collapse supernova. It directly affects the density and temperature profile to proto-neutron star and the location and energy of the shock wave. Here I will highlight some recent findings regarding the equation of state of neutron matter at sub nuclear density and identify generic differences between mean-field theoretic models for the EoS and the more microscopic variational calculations. Although there are several models of the nuclear EoS, for the purpose of this discussion I shall broadly classify them into two categories: 1) mean field models (MFT) and 2) microscopic variational models. In the former, the starting point is an effective Lagrangian with a simplified form for the nucleon-nucleon interaction. The properties of nuclei or nuclear matter are calculated in the mean field approximation (typically only Hartree terms are retained) and are then used to fit the strength of the effective interactions. Fig. 3 shows a comparison between the EoS calculated in MFT and the microscopic model due to Akmal, Pandharipande and Ravenhall 4 . The mean field results are based on the Walecka model, but the trends seen are generic to large class of nuclear mean field predictions. We see that compared to microscopic calculations, the mean field EoS is stiff (higher pressure at the same energy density) at low density and soft (lower pressure

93

at the same energy density) at high density. While the high density behavior

Figure 3. Comparison between mean field and microscopic equations of state. The resulting differences in the corresponding structure of a 1.4 M Q neutron star is shown in the right panel.

is fairly uncertain in both approaches, we should expect the non-relativistic microscopic theories to provide a better description at low density. This is because they are derived from two-nucleon potentials that are obtained from nucleon-nucleon scattering data and the variational methods provide very detailed description of light nuclei. Further, at low density the large swave nucleon-nucleon scattering length (as) must dominate the interaction contribution to the equation of state. On general grounds, a, -» oo, we can expect the energy per particle to scale as E-mt = a EFG where EFQ is the energy per particle of a Fermi gas- there are no dimension full parameters in the low density limit and a must be a number. Microscopic calculations of neutron matter show similar behavior and predict that a ~ 0.5 while the low density of the mean field models with s-wave interactions predict a different behavior. Intriguingly, microscopic calculations seem to indicate that this behavior persists even when the inter-particle distance become comparable to the range of nuclear interaction 5 .

4. Neutrino Interactions in Nucleonic Matter It was realized over a decade ago that the effects due to degeneracy and strong interactions significantly alter the neutrino mean free paths and neutrino emissivities in dense matter 6 ' 7 , it is only recently that detailed calculations have become available 8 ' 9 ' 1 0 ' u . The scattering and absorption

94

reactions that contribute to the neutrino opacity are ue+p^*e++n,

i/e+n—>e~+p, vx +A^> vx +A,

vx + n[p) -> vx + n(p),

vx + e~ -» vx + e~ ,

where n,p, e^,A represent neutrons, protons, positrons, electrons and heavy Fe-like nuclei, respectively. At low temperature (T ^ 3 — 5 MeV) and relatively low density (p ~ 1012 — 1013 g/cm 3 , heavy nuclei are present and dominate the neutrino opacity due to coherent scattering. When the density is higher, p ^ 10 13 —1014 g/cm 3 , novel heterogeneous phases of matter, called the "pasta" phases have been predicted to occur, where nuclei become extended and deformed progressively from spherical to rod-like and slab-like configurations12. For densities greater than 10 14 g/cm 3 , matter is expected to be a homogenous nuclear liquid. In what follows, we discuss the neutrino opacity in these different physical settings. p ~ 10 12 g/cm 3 : At low temperature (T < 5 MeV), matter at these densities comprises of heavy nuclei (fully ionized), nucleons and degenerate electrons. The typical inter-particle distance, d ^ 20 — 40fm. At these large distances, the nuclear force is small and the correlations between particles is dominated by the coulomb interaction. Since nuclei carry a large charge (Z ~ 25) , the coulomb force between nuclei .Fcouiomb — Z2e2/d dominates the non-ideal behavior of the plasma. Further, for low energy neutrinos which couple coherently to the total weak charge Qw 25 — 40 of the nucleus, neutrino scattering off nuclei is far more important than processes involving free nucleons and electrons 13 . The elastic cross-section for low energy coherent scattering off a nucleus (A,Z) with weak charge Qw = A — Z + Zsin 2 6\v, where 9w is the weak mixing angle, is given by 13

^

= ^01

gng(i + =os*>

(2)

When neutrinos scattering off nuclei in a plasma we must properly account for the presence of other nuclei since scattering from these different sources can interfere. In the language of many-body theory, this screening is encoded in the density-density correlation function 6 ' 7 . The cross'section for scattering of a neutrino with energy transfer w and momentum transfer q is given by dff

V du dcosO where

-

G F

* Q2W(1+ 167T

S(\q\,w) = ^—^

0030)8(1$^)

(3)

I dt exp(iut){p(q,t)p(-q,0)).

(4)

95 The function 5(|<^,u>) is called the dynamic structure function and embodies all spatial and temporal correlations between target particles arising from strong or electromagnetic interactions. For a classical system of point

Figure 4. Dynamic structure function of a plasma of ions interacting as a function of energy transfer w (measured in units of the plasma frequency up = 0.2 MeV) and fixed momentum transfer \q\ = 6TT/L — 18.6 MeV.

particles interacting via a 2-body potential it is possible to simulate the real system using the methods of molecular dynamics (MD). Such numerical simulations confine N particles to a box with periodic boundary conditions and calculate the force on each particle at any time and evolve the particles by using their equations of motion. For T > 1 MeV, the De-Broglie wavelength AD < d s o the ionic gas is classical and we can use MD to calculate S(\q\,uj). Fig.4 , shows the results of such a calculation. We chose to simulate 54 ions (A=50,Z=25) in a box of length L = 200 fm. For the classical simulations, a single, dimensionless, quantity T = Z2e2/(47r
96

RPA and the free gas response do poorly compared to MD. MD is exact in the classical limit and corrections to the classical evolution are small and expected to scale as \o/d. These results clearly illustrate that correlations can greatly affect the shape of the response and that approximate manybody methods such as RPA can fail when the coupling is strong, even at long-wavelengths. p ~ 10 13 g/cm 3 : With increasing density, the nuclei get bigger and the inter-nuclear distance become smaller. Under these conditions, the nuclear surface and coulomb contributions to the Free energy of the system become important. It becomes energetically favorable for nuclei to become very deformed and assume novel, non-spherical, shapes such as rods and slabs 12 . Further, the energy differences between these various shapes are small AE ~ 10 —100 keV. The dynamics of such an exotic heterogeneous phase is a complex problem involving several scales and forces. For temperatures of interest, T < 5 MeV, the De-Broglie wavelength and the inter-particle distance are comparable and quantum effects cannot be neglected. Recently, there have been attempts to model the behavior of these pasta phases using quantum molecular dynamics 15 and also find rod and slab like configurations. How does the heterogeneity and existence of several low energy excitations involving shape fluctuations influence the response of this phase to neutrinos ? In the simplest description, the structure size (r) and the inter-structure (R) distance characterize the system. We can expect that neutrinos with wavelength large compared to the structure size but small compared to the inter-structure distance can couple coherently to the total weak charge (excess) of the structure, much like the coherence we discussed in the previous section. The effects of this coherent enhancement in the neutrino cross-sections has recently been investigated 16 . In agreement with our naive expectation, this study finds that the neutrino cross sections are enhanced by as much as an order of magnitude for neutrinos with energy

1/r > Ev > 1/R. p ~ 10 14 g/cm 3 : With increasing density, the novel structures discussed previously merge to form a homogeneous liquid of neutrons, protons and electrons. The response of such a Fermi-liquid has been investigated by several authors 8,10,11 . The general expression for the differential cross section

97 for the reaction v\ + 2 —+v3 + 4 is 1 d3a V d?n3dE3

_ ~

Gj, 128TT2

E3 EY

x (1 - f3(E3))

1 — exp Im ( L ^ I I * , ) ,

(5)

where the incoming neutrino energy is Ei and the outgoing electron energy is E3, 2 is the initial state of the target particle and 4 is its final state 8 , 1 0 . The factor [1 — exp((—qo — M2 + M4)/^)] - 1 maintains detailed balance, for particles labeled '2' and '4' which are in thermal equilibrium at temperature T and in chemical equilibrium with chemical potentials /i2 and /i4, respectively. The final state blocking of the outgoing lepton is accounted for by the Pauli blocking factor (1 — f3(E3)). The lepton tensor La0and the target particle retarded polarization tensor YlQp may be found in Ref. 10 . To account for the effects of strong and electromagnetic correlations between target neutrons, protons and electrons we must find ways to improve n Qj/ g. This involves improving the Greens functions for the particles and the associated vertex corrections that modify the current operators. In strongly coupled systems, these improvements are notoriously difficult and no exact analytic methods exist. One usually resorts to using mean-field theory to improve the Greens functions. Dressing the single particle Greens functions must be accompanied by corresponding corrections to the neutrino - dressed-particle vertex function. The random-phase approximation (RPA) can be thought of as such a vertex correction. Model calculations indicate that neutrino mean free paths computed in RPA tend to be a factor 2-3 times larger than in the uncorrelated system 10 . This is primarily because of repulsive forces in the spin-isospin channel, that suppress the axial response at low energies. 5. Discussion Despite decades of work on supernova, the immediate vicinity of the protoneutron star and the neutrino fluxes at early times are not well understood theoretically. In addition to macroscopic issues, the role of microphysics in the hydro and neutrino transport is only now being explored systematically. The physics issues discussed in this article, I hope have provided an overview of the current status. Both the EoS and neutrino opacities are sensitive to strong and electromagnetic corrections. Mean field theories and approximate many body methods such as RPA for response functions my provide qualitative guidance but more microscopic efforts are need for

98 quantitative predictions. These quantitative predictions for t h e neutrino luminosity and energy spectrum is important for the r-process since it affects b o t h the entropy and the neutron-proton ratio of the neutron star wind 1 7 . Acknowledgments I would like to t h a n k Joe Carlson, Chuck Horowitz, Jim Lattimer, Jose Pons, M a d a p p a Prakash for enjoyable collaborations a n d / o r useful discussions. This work is supported in part by funds provided by the U.S. Dep a r t m e n t of Energy (D.O.E.) under the D.O.E. contract W-7405-ENG-36.

References 1. R. Buras, et al., Phys. Rev, Lett. 90, 241101 (2003); A. Mezzacappa et al., Phys. Rev. Lett. 86, 1935 (2001); Burrows, et al., Astrophys. J. 539, 865 (2000) 2. A. Burrows, J.M. Lattimer: Astrophys. J. 307, 178 (1986) 3. J. A. Pons, S. Reddy, M. Prakash, J. M. Lattimer and J. A. Miralles, Astrophys. J. 513, 780 (1999). 4. A. Akmal, V. R. Pandharipande and D. G. Ravenhall, Phys. Rev. C 58, 1804 (1998). 5. J. Carlson, J. . J. Morales, V. R. Pandharipande and D. G. Ravenhall, Phys. Rev. C 68, 025802 (2003). 6. R. F. Sawyer, Phys. Rev. D 11, 2740 (1975). 7. N. Iwamoto and C. J. Pethick, Phys. Rev. D 25, 313 (1982). 8. C.J. Horowitz, K. Wehrberger: Nucl. Phys. A 531, (1991) 665 ; Phys. Rev. Lett. 66, 272 (1991); Phys. Lett. B 226, 236 (1992) 9. G. Raffelt, D. Seckel: Phys. Rev. D 52, 1780 (1995) 10. S. Reddy, M. Prakash, J.M. Lattimer: Phys. Rev. D 58, 013009 (1998); S. Reddy, M. Prakash, J.M. Lattimer, J.A. Pons: Phys. Rev. C 59, 2888 (1999) 11. A. Burrows, R.F. Sawyer: Phys. Rev. C 58, 554 (1998); A. Burrows, R.F. Sawyer: Phys. Rev. C 59, 510 (1999) 12. D. G. Ravenhall, C. J. Pethick and J. R. Wilson, Phys. Rev. Lett. 50, 2066 (1983). 13. D. Z. Freedman, Phys. Rev. D 9, 1389 (1974). 14. J.-P. Hansen, I. R. McDonald and E. L. Pollock, Phys. Rev. D 11, 1025 (1975) 15. G. Watanabe, K. Sato, K. Yasuoka and T. Ebisuzaki, Phys. Rev. C 68, 035806 (2003) 16. C. J. Horowitz, M. A. Perez-Garcia and J. Piekarewicz, arXiv:astroph/0401079. 17. Y. Z. Qian, Prog. Part. Nucl. Phys. 50, 153 (2003).

A N OVERVIEW OF OBSERVATIONS OF NEUTRON-CAPTURE ELEMENTS IN METAL-POOR STARS

JENNIFER A. JOHNSON DAO/HIA/NRC 5071 West Saanich Road Victoria, BC V9E 2E7, Canada Email: [email protected]. ca

Observations of the abundance of neutron-capture elements in metal-poor stars provide a detailed look at the output of individual r-process events. Data currently show that the abundance ratios are similar between Ba and Yb in metal-poor stars and in the solar system r-process contributions. There is some variation in the E u / T h ratio, but the current small samples need to be expanded before we understand the true scatter in the production of the heaviest nuclei. There is also a spread in the [Y/Ba] and a disagreement with the solar system r-process pattern in the Nb-Ag region, which argue of the presence of at least two r-process type of events, or perhaps a continuum of conditions in r-process sites. Intriguing information can be also be gleaned from the abundance ratios in stars that do not have detectable r-process elements in their atmospheres. Few stars have been found without heavy elements, but some of those have unusual abundance ratios in the lighter elements. We are beginning to go beyond the solar neighborhood to study the production of the r-process elements in regions with a very different history, such as the Bulge and globular clusters.

1. Introduction Over 50 elements are produced entirely or in part in the rapid neutroncapture process, also known as the r-process. While many astrophysical sites have been suggested, we still do not know the site of the r-process. Observations of the abundances of neutron-capture elements in the oldest stars in our Galaxy give important constraints. Stars are generally identified as old because their atmospheres contain little besides hydrogen and helium, indicating they were born out of gas that had been polluted by very few stars. Elements heavier than He are termed metals, and their amount is usually noted by comparing the ratio of iron to hydrogen to that in the 99

100 sun, denoted [Fe/H] a . Some of these stars show large overenhancements in the neutron-capture elements (Figure 1). Since few stars have exploded

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[Eu/Fe] vs. [Fe/H] for Galactic stars. Data is from Refs [1-6].

and polluted the interstellar gas and the Galaxy is not yet well-mixed, the heavy elements in these stars probably come from one nucleosynthesis event, rather than the average of many that we see in the solar system. This early in the history of the Galaxy, the r-process is the only source of heavy elements, since the s-process has not yet begun to operate in lowmass stars [7]. Therefore, observations of metal-poor stars can provide a pure view of single r-process events. In this proceeding, I will review some of the recent observations of the r-process elements in metal-poor stars that any successful model of the r-process will need to reproduce. 2. Observations Abundances are measured through absorption lines in the spectra of the star (Figure 2). The old stars that we are principally interested in are cool in a

We

adopt

log10(NA/NB)sun

the

usual

spectroscopic

notation.

[A/B]s

log 1 0 (Af A /Ar B ) s t a r

-

101

general. As a result, we are limited to elements that have strong lines in the

Observations of Neutron—Capture E l e m e n t s I

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Figure 2. Examples of stellar spectra and absorption features of r-process elements such as Dy, Er, and Yb. We are limited in our ability to measure heavy elements by the weakness of the lines in some stars.

visible or near UV from neutral or singly ionized species. The best lines are sometimes blended with strong lines of other elements, in particular Fe and molecular species. We would like to obtain isotopic information, but the isotope shifts are generally not large enough to affect the profiles of the absorption features enough to reliably measure isotopic fractions. With very high-resolution and signal-to-noise, progress is being made on measuring the isotope ratios for Ba and Eu in a small sample of metal-poor stars [8-11]. Eu is a favorite element to observe, since it has fairly strong lines and is mostly produced in the r-process throughout the history of the Galaxy (94% of the solar system Eu comes from the r-process [12].) In Figure 1, we plot the [Eu/Fe] ratio in stars to trace the yields of the r-process compared to Fe production. Clearly, Eu and Fe are produced at least somewhat separately [13], with Eu being produced more efficiently earlier in the Galaxy, and Fe production catching up later. Second, there is large scatter in [Eu/Fe] at low metallicities. This spread lessens at higher metallicities as the Galaxy

102 becomes well-mixed. For stars with [Eu/Fe] >0.5 dex, we can measure the abundances of many heavy elements from Z=38 to Z=92. 3. r-pro cess-rich stars

_o X) I—I

Th

o GO

x

Ta r „ Arlandini et al. r „ Kaeppeler et al.

40

60

80

Figure 3. Abundances of the heavy elements in five r-process-rich stars plotted with two predictions for the r-process contributions to the solar system [12,14]). The abundances have been scaled to match the solar system data in the Ba-Gd region. The stars are (circles) HD 186478, (stars) HD 115444 (triangles) BD + 8 2548 [15], (squares) CS 22892052 [16] and (crosses) CS 31082-001 [17].

One reason why we think the r-process is responsible for the presence of heavy elements in metal-poor stars is the good match between the abundance ratios we observe and the predictions for the r-process contribution to the solar system. Figure 3 shows this comparison for five r-process-rich stars. For elements from Ba to Yb, the match is particularly good (e.g.

103 [3,18,19]). The metal-poor stars show a larger odd-even effect in the Pd-Ag region [20], and large spread in Y to Ba. The data for the heaviest elements are scarce but show that while the majority of stars agree with the solar system r-process, clear deviations are possible. We can elaborate on that point by plotting the initial T h / E u ratios in the eleven stars with measured Th in Figure 4. When the typical observational errors are taken into account, only one point, CS 31082-001 has a value different from the other ten. This sample should be expanded in the coming years to determine the true distribution of T h / E u ratios produced in the r-process.

0.2 |— • « • |

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Figure 4. Initial ( T h / E u ) ratios in metal-poor stars. The Th abundances have been corrected for 14 Gyr of decay. One star, CS 31082-001, has a different T h / E u than the other stars. Data from Refs [3,16,17,21,22]

The disconnect between Y and Ba is evident when we plot [Y/Ba] as a function of [Fe/H] (Figure 5). Either there is one source for elements such as Sr, Y, and Zr, and another for Ba through Yb, or physical conditions vary enough at the r-process site to produce the variation in [Y/Ba] that we see here.

104 -i

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1 1 1 1 r This study McWilliam et al 95,98 Fulbright 00 Sneden el al 00b Hill et al 01 Sneden et al 00a

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Figure 5. [Y/Ba] vs. [Fe/H]. The production of Y (Z=39) is clearly not completely correlated with Ba (Z=56). There appears to be a floor at [Y/Ba] ~ —0.4, indicated by the extremely r-process-rich stars CS 22892-052 and CS 31082-001. This may be the minimum [Y/Ba] produced by the r-process.

4. "s+r" stars Eu is much easier to manufacture in the r-process than in the s-process. However, there is a class of stars that have a large amount of Eu, but otherwise look like they were polluted by an asymptotic giant branch star rich in C, N, and s-processed material. Refs [23,24] suggested that the Eu was actually contributed by the r-process, and Ref. [25] proposed a model where a site for the r-process required binary star system. Refs [26,27] disagreed the diagnosis of an r-process contribution, based in particular on detailed abundance ratios for other elements produced mostly or entirely in the r-process such as Tb and Th. Resolution of the source of Eu in C-rich stars will reveal either a site of the r-process or new physics regarding the s-process.

5. r-process-poor stars One question we would like to answer is whether the r-process has to be made in the first stars in the Galaxy, or whether there are old stars without

105 any heavy elements in their atmospheres. Eu is the usual tracer of the r-

1

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[Ba/Fe] vs. [Fe/H]. Data from Refs [2,3,4,7]

process, but Figure 1 shows that at the metal-poor end, Eu often cannot be measured, and the limits are not illuminating. Ref [5] has improved the situation for three stars with a heroic effort. However, we have noted that Ba at these metallicities is due to the r-process, and because its lines are stronger than those of Eu, more interesting lower limits can be obtained. In Figure 6, we plot [Ba/Fe] ratios and limits for metal-poor stars and see that most stars either have detectable Ba, or limits that put them close to where the other stars are. One dramatic exception is the star Draco 119, a red giant star in the nearby dwarf spheroidal galaxy Draco [28]. Not only is Ba not seen, but neither is Sr, though the upper limit on Sr is weaker than on Ba. This star has a high Mg/Ca ratio, which could indicate that it was polluted by a high mass SN, although examination of a larger sample does not reveal an correlation between Mg/Ca ratio and Ba abundance. A second exception is the star at [Fe/H]~ —2.0. This is BD +80 245, one of three stars identified by [29] that, when compared with the majority of stars at that metallicity, have low Ba, high Cr, Mn, and Zn, and low Mg and Ca.

106

6. The Bulge and the Globular Clusters We have focused in the previous sections on what can be learned from detailed abundance studies of stars that are relatively nearby. However, if we extend our analysis to stars in different environments, we can use the fact that these regions have different star formation histories to our advantage. If a particular mass of star, for example, is responsible for the r-process, then by comparing different chemical evolution histories, we can start to identify the site of the r-process. The nucleosynthesis in the Bulge was dominated by massive stars, but ones that seemed to produce more Ca and Ti than O [30]. The r-process seems to track the production of Ca more than O, remaining higher than the Galactic Disk at similar [Fe/H]. Another unique environment can be found in the Galactic globular clusters. All the stars in a particular globular cluster were formed at the same time, and they are remarkably homogeneous in their [Fe/H], [Ca/H] and [Si/H]. Recent investigations of multiple stars in each cluster shows that there is a spread larger in observational error in M 15 and that this spread decreases as metallicity increases, though it is not clear if the spread is still larger than the observational errors. Therefore any site of the r-process must explain why it is so inhomogeneous mixed while the iron-peak elements are so constant. 7. Conclusion Several observational facts have become well-established over the last several years. These include the uniformity in the r-process pattern between Ba and Yb, and the disconnect between the production of Ba and the lightest (Y) and heaviest (Th) elements. There have been exciting new observations from r-process-poor stars and Bulge and globular clusters stars that also need to be explained by any model for the r-process site. These include the class of Ba-poor stars noted by Ref [28], and Ref[29], the scatter in [Eu/Fe] in globular clusters as a function of metallicity and finally the high Eu in very metal-poor C-rich stars. References 1. 2. 3. 4. 5.

A. McWilliam, G. W. Preston, C. Sneden, & L. Searle, A J, 109, 2757 (1995) S. G. Ryan, J. E. Norris, & T. C. Beers, ApJ, 471, 254 (1996) J. A. Johnson & M. Bolte, ApJ, 554, 888 (2001) J. P. Fulbright, AJ, 120, 184 (2000) Y. Ishimaru, S. Wanajo, W. Aoki, & S. G. Ryan, ApJ, 600, 471 (2004)

107 -i—i—i—r

n—i—i—r

n—i—i—r

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-0.5

Figure 7. The [Eu/Fe] ratios in individual stars for five clusters [31-35]. The scatter in M15 is too large to be explained by observational error. The scatter decreases as metallicity increases, but whether there is real scatter in the four other clusters is not yet clear. 6. B. E. Reddy, J. Tomkin, D. L. Lambert, k. C. Allende Prieto, MNRAS, 340, 304 (2003) 7. A. McWilliam, AJ, 115, 1640 (1998) 8. P. Magain & G. Zhao, A&A, 268 ,27 (1993) 9. C. Sneden, J. J. Cowan, J. E. Lawler, S. Buries, T. C. Beers G. M. Fuller, ApJ, 566, 25 (2002) 10. D. L. Lambert & C. Allende Prieto, MNRAS, 335, 325 (2002) 11. W. Aoki, S. Honda, T. C. Beers, & C. Sneden, ApJ, 586, 506 (2003) 12. C. Arlandini, F. Kappeler, K. Wisshak, R. Gallino, M. Lugaro, M. Busso, & O. Straniero, ApJ, 525, 886 (1999) 13. K. K. Gilroy, C. Sneden, C. A. Pilachowski, & J. J. Cowan, ApJ, 327, 298 (1988) bibitemkap F. Kappeler, H. Beer, k. K. Wisshak, Rep. Prog. Phys., 52, 945 (1989)

108 14. J. A. Johnson k M. Bolte, ApJ, 579, 616 (2002) 15. C. Sneden, et al., ApJ, 591, 936 (2003) 16. V. Hill, et al., A&A, 387, 560 (2002) bibitemsp C. Sneden k M. Parthasarathy, ApJ, 267, 757 (1983) 17. C. Sneden, A. McWilliam, G. W. Preston, J. J. Cowan, D. L. Burris, k B. J. Armosky, ApJ, 819, 819 (1996) 18. C. Sneden, J. J. Cowan, I. I. Ivans, G. M. Puller, S. Buries, T. C. Beers, k J. E. Lawler, ApJ, 533, L139 (2000) 19. C. Sneden, J. Johnson, R. P. Kraft, G. H. Smith, J. J. Cowan, k M. S. Bolte, ApJ, 536, 85 (2002) 20. J. J. Cowan et al., ApJ, 572, 861 (2002) 21. V. Hill, B. Barbuy, M. Spite, F. Spite, R. Cayrel, B. Plez, T. C. Beers, B. Nordstrom, &: P. E. Nissen, A&A, 353, 557 (2000) 22. J. G. Cohen, N. Christlieb, Y.-Z. Qian, k G. J. Wasserburg, ApJ, 588, 1082 (2003) 23. Y.-Z. Qian k G. J. Wasserburg, ApJ, 588, 1099 (2003) 24. W. Aoki, S. G. Ryan, J. E. Norris, T. C. Beers, H. Ando, k S. Tsangarides, ApJ, 580, 1149 (2002) 25. J. A. Johnson &: M. Bolte, ApJ, in press (2004) 26. J. P. Fulbright, R. M. Rich, k S. Castro, ApJ, submitted (2004) 27. I. I. Ivans, C. Sneden, C. R. James, G. W. Preston, J. P. Fulbright, P. A. Hoflich, B. W. Carney, k J. C. Wheeler, ApJ, 592, 906, (2003) 28. A. McWilliam k R. M. Rich in Carnegie Astrophysics Series Vol. 4: Origin and Evolution of the Elements ed. A. McWilliam and M. Rauch (Pasadena: Carnegie Observatories, http://www.ociw.edu/ociw/ symposia/series/symposium4/proceedings.html) (2003) 29. C. Sneden, R. P. Kraft, M. D. Shetrone, G. H. Smith, G. E. Langer, k C. F. Prosser, AJ, 114, 1964 (1997) 30. 1.1. Ivans, C. Sneden, R. P. Kraft, N. B. Suntzeff, V. V. Smith, G. E. Langer, J. P. Fulbright, AJ, 118, 1273 (1999) 31. I. I. Ivans, R. P. Kraft, C. Sneden, G. H. Smith, R. M. Rich, k M. Shetrone, AJ, 122, 1438 (2001) 32. S. V. Ramirez k J. G. Cohen, AJ, 125, 224 (2003) 33. G. James, et al., A&A, 414, 1071 (2004)

EFFICIENT SEARCHES FOR R-PROCESS-ENHANCED METAL-POOR STARS

T. C. BEERS Dept.

of Physics and Astronomy and JIN A: Joint Institute for Nuclear Astrophysics Michigan State University E. Lansing, MI 48824 USA email: [email protected] N. C H R I S T L I E B Hamburger Sternwarte Universitdt Hamburg Gojenbergsveg 112, 21029 Hamburg, GERMANY email: [email protected] P. S. B A R K L E M Dept.

of Astronomy and Space Physics Uppsala University, Box 515, S 751-20 Upsalla SWEDEN email: [email protected]

We describe the motivation and execution plan for HERES: The Hamburg/ESO R-process-Enhanced Star survey, an onging effort t o significantly increase t h e numbers of known metal-poor stars with highly elevated ratios of their r-process elements, similar to the first few stars of this class, CS 22892-052 and CS 31082-001. Such stars provide the best available probes of the operation of the astrophysical r-process, the opportunity to constrain the site(s) in which it occurs, and for exploration of the applicability of cosmo-chronometers, such as obtained from E u / T h and U / T h . We outline a number of the important questions t h a t need to be considered in order for progress to be made. First results from HERES should be available by the time this contribution appears in print.

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110

1. Motivation Understanding the origin of the elements is one of the great unsolved problems of modern physics, as noted in the popular press (Discover magazine, Feb. 2002 issue) and in recent decadal reports from the physics, nuclear physics, and astronomy communities. Although researchers from a wide range of academic specialties are actively pursuing this goal, it rests on the astronomy community to quantitatively explore the most powerful laboratory that nature has provided to answer this question — still-living stars, born in the early history of the Galaxy, that retain abundance information tied directly to the events responsible for the formation of the first elements. Over the past half century, astronomers have methodically proceeded from the initial recognition of stars with metallicities significantly lower than the Sun 1 , to the assembly of samples of thousands of stars with metallicities less than 1% of the solar abundance. The HK survey of Beers and colleagues2,3, for instance, has identified ~ 1000 stars with [Fe/H] < —2.0, ~ 100 with [Fe/H] < —3.0, and a handful of objects with abundances once thought to establish the limit of metal-deficiency in the Milky Way, at [Fe/H] = —4.0. The success of the HK survey inspired an expanded search for additional stars of extremely low metallicity, the Hamburg/ESO Survey (HES) 4,5 , which will soon eclipse the numbers of stars with [Fe/H] < — 2.0 identified in the HK survey, and which has already found the most iron-deficient star presently known, HE 0107-5240, with [Fe/H] = - 5 . 3 6 ' 7 . Over the past decade, the identification and analysis of MP stars that exhibit large over-abundances of elements beyond the iron peak, species that are almost exclusively formed as the result of neutron captures, have taken a leading role in many investigations. The first such star recognized, CS 22892-052, a giant with [Fe/H] = - 3 . 1 , exhibits a ratio of its rapid neutron-capture process (r-process) elements relative to iron [r/Fe] « +1.7, a factor of 50 times the ratio of these elements seen in the Sun 8,9 . This star has been studied intensively with essentially all 4m and 8m-class telescopes (equipped with high-resolution spectrographs) in the world, as well as over the course of 60 orbits with the Hubble Space Telescope10. A score of papers have been written over the past ten years assessing the impact of CS 22892-052 on our understanding of the nature of the r-process; this object is presently the best-studied star other than the Sun. Shortly after the discovery of CS 22892-052, another HK survey star was found that has had equally profound impact, CS 31082-001. This star, a giant with [Fe/H] = —2.9, exhibits a similar excess of r-process

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elements as CS 22892-052, [r/Fe] « +1.6. Because this star exhibits a much lower abundance of carbon (which can mask important neutron-capture species) than CS 22892-052, this was the first MP star with a measurable abundance of the radioactive element uranium 11 . Not only did CS 31082001 establish the class of highly r-process-enhanced MP stars (which we refer to collectively as r-II stars, having [r/Fe] > +1.0), it also enabled the first application of a valuable new cosmo-chronometer, U / T h 12>13. However, the "uranium star" CS 31082-001 also raised a number of unresolved questions concerning the operation of the r-process in the early Galaxy. Of greatest significance, the enhancement of the actinides Th and U is on the order of +0.4 dex higher, compared to the level of enhancement of other stable r-process elements (such as Eu), than observed in CS 22892052. Although application of the U/Th chronometer yields age estimates of this star that are consistent with expectation, « 15.5 ± 3.2 Gyrs 13 , application of the Th/Eu chronometer for CS 31082-001 yields ages that beg credulity (a few Gyrs, even including a negative age 12 ). Recently, additional stars have been noted that display the "actinide boost" problem 14 . The interest in the nature of the astrophysical r-process has also led to the discovery and analysis of a larger number of MP stars with moderately enhanced r-process elements (which we refer to collectively as r-I stars, having +0.3 < [r/Fe] < +1.0). A few particularly important examples include HD 11544415 and BD+17:3248 16 , the first MP star in which gold was detected. There are presently on the order of ten suspected r-I stars discussed in the literature. Many of these r-I stars have measurable abundances of Th, and estimates of ages based on the Th/Eu chronometer have been made that fall in the range 9-18 Gyrs 17 . Cowan et al. (2002) claimed the detection of uranium in BD+17:3248, at the ragged edge of believability, from which an lower limit on the age of 13.4 Gyr (with a large error bar) was derived from the U/Th chronometer 16 . The small number of r-II and r-I stars studied to date all exhibit a pattern of "heavy" r-process elements that closely follow the scaled solar pattern of r-process elements in the range 56 < Z < 76 18 . This immediately suggests that, at least for these elements, the astrophysical conditions leading to the r-process operated in a consistent manner throughout the history of the Galaxy. This may indicate that the so-called "strong" r-process is associated with a unique site (e.g., SN-II explosions of similar-mass progenitors). This apparent regularity does not apply to the observed patterns of the lighter r-process elements, in the range 40 < Z < 50 (e.g., Zr, Mo, Pd, Ag). These elements tend to fall below the scaled solar pattern, and proba-

112

bly (although the sample is still too small to be certain) exhibit star-to-star scatter even for objects of identical overall metallicity. These observations support the notion (also indicated from meteoritic isotopic analyses 19 ) that one may have to invoke the additional operation of a "weak" r-process. Finally, a handful of r-process-rich MP stars have been identified that exhibit elemental abundance patterns with apparent contributions from the slow neutron-capture process (s-process) as well as the r-process, the most recent example being HE 2148-124720. Full understanding of the nucleosynthetic events that led to these stars (which we refer to collectively as r-s stars) is still lacking, but interesting possibilities have been discussed in the recent literature. There is no shortage of suggestions to account for the astrophysical origin of the small number of r-process-rich MP stars identified to date. What is clearly lacking is a sufficiently large sample of these stars to explore the critical questions that will constrain current ideas. In order to address this need, we have undertaken an observing campaign that will dramatically increase the numbers of known r-II stars in the Galaxy, to on the order of 7-10 (and identify a similar number of r-I and r-s stars).

2. T h e H E R E S A p p r o a c h The central difficulty in obtaining large samples of r-process-enhanced MP stars is their extreme rarity. Based on high-resolution spectroscopy that has been performed on the most metal-deficient giants, it appears that r-II stars occur no more frequently than about 1 in 30 for giants with [Fe/H] < —2.5, i.e., roughly 3-4%. Due to the steep decrease of the metallicity distribution function of the Galactic halo at low metallicities, the candidates to be examined are rare themselves, although modern spectroscopic wideangle efforts, such as the HK and HES surveys, have succeeded in identifying such stars with success rates as high as 10-20% ? ' 5 . So, we are faced with the daunting prospect of searching for a rare phenomenon amongst rare objects. The r-I stars appear to be found with a frequency that is at least a factor of two greater than this, and fortunately extend into the higher metallicity stars (e.g., BD+17:3248 with [Fe/H] = —2.1), where a greater number of candidates exist. Detection of uranium presents an even bigger challenge, due to the weakness of the absorption lines involved, and blending with features of other species. It was not possible to measure even the strongest uranium line in the optical, U II 3859.57 A , in the carbon-enhanced star CS 22892-

113 052, due to blending with a CN line. Other lines (such as from Fe) can cause potential problems as well. The ideal star for detecting uranium would therefore be a cool giant with low carbon abundance, very low overall metallicity, but strong enhancement of the r-process elements. It would ideally be a bright star, because high signal-to-noise (S/N) ratios as well as high spectral resolving power (R = X/SX > 60,000) are required to measure the strength of the U II 3859.57 A line accurately. Note that in CS 31082-001, this line has an equivalent width of only a few mA. In order to identify new r-process enhanced stars, we adopt a twopronged approach (for a complete description, see Ref. 21). The first step consists of identification of a large sample of metal-poor giants with [Fe/H] < —2.5 in the HES, by means of moderate-resolution (~ 2 A ) follow-up spectroscopy of several thousand cool (0.5 < B — V < 1.2) metal-poor candidates selected in that survey. In the second step, "snapshot" spectra (S/N > 20 per pixel at 4100 A ; R « 20,000) of confirmed metal-poor stars are obtained with UVES on the VLT. Such spectra can be secured for a B = 15.0 star with a 8m-class telescope in exposure times of only 900 seconds, during unfavorable observing conditions in terms of seeing, bright moonlight, cloud coverage, and airmass. The weak constraints on the observing conditions makes it feasible to observe large samples of stars in queue mode, a popular choice for many large telescopes presently. Given the large number of spectra to be processed, it is mandatory that we employ automated techniques for abundance analysis. Such techniques are described in detail by Ref. 22. Fig. 1 illustrates how snapshot spectra allow one to easily identify stars with enhancements of r-process elements, using the Eu II 4129.73 A . We have adopted the snapshot spectroscopy approach in a Large Programme (170.D-0010, P.I. Christlieb) approved by ESO. A total of 376 stars (including four comparison stars) are scheduled to be observed; most of them are from the HES. These observations are expected to yield 7-10 new r-II stars, about twice as many r-I stars, and perhaps some additional r-s stars. As a by-product, our program will provide the opportunity to measure abundances of a— elements such as Mg, Ca, and Ti, and of iron-peak elements such as Cr, Mn, Fe, Co, Ni, and Zn, as well as others depending on the S/N of each spectrum, for nearly entire set of stars that we plan to observe in snapshot mode. This will result in, by far, the largest sample of very metal-poor stars with homogenously-measured abundances of a significant number of individual elements. Fig. 2 shows several examples.

114

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115

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116

3. Understanding the Nature of the r-Process The numbers of stars in each recognized class of r-process-enhanced objects are so few that astronomers speculate about the astrophysical origins for all of these classes, and the possible inter-relationships between them. Upon completion of HERES, we expect to be in a position to resolve a number of critical questions concerning the astrophysical processes involved in the formation of these elements. These questions include: (1) What is the frequency of r-II, r-I, and r-s stars as a function of metallicity ? The two r-II stars reported in the literature both have [Fe/H] « —3.0. Is the lack of r-II stars with [Fe/H] > —3.0 real, or just a result of the small samples obtained to date? If real, it may reflect the possibility that these large enhancements are only associated with the earliest r-process-generating events. Similar questions must be answered about the r-I and r-s stars, which apparently include objects of higher [Fe/H]. (2) What is the distribution of r-process enhancements for r-II, r-I, and r-s stars ? Although for simplicity we have separated the classes of r-II and r-I stars, it is possible that this distinction has no physical basis, and that there exists a continuum of the level of r-process-enhancement amongst MP stars in the Galaxy. Or, could the distribution be bimodal, as the present data suggests ? This question (combined with the one above) is essentially the same as put forward by Ref. 23 and Ref. 24, who sought to test phenomenological models for the origin of the r-process. Its resolution clearly requires much larger samples, so that consideration of the range of r-process enhancements may be studied in detail. (3) How stable is the pattern of r-process-element abundances in the range 56 < Z < 76 ? The r-II and r-I stars exhibit abundance patterns that are wellmatched to the scaled solar r-process pattern in this range. Although this piece of information is clearly fundamental, it would be of interest to better quantify it by consideration of the scatter about the solar pattern on an element-by-element basis. This would

117 provide a testable target for models of the astrophysical production of r-process elements. A first attempt at just such a quantification was made by Ref. 17, albeit for a very small sample of stars. (4) What is the range of abundances exhibited by r-process elements in the range 40 < Z < 50 ? It has been suggested that a number of r-I and r-II stars exhibit different star-to-star abundances of their light r-process elements, such as Zr, Mo, Pd, and Ag, even at similar metallicity. To better constrain the origin of these elements, and to establish whether or not their production is consistent with a hypothesized "weak" rprocess, we require a sufficiently large sample from which the level of variation might be confidently established. (5) What is the range of r-process-enhancement for the third r-processpeak elements, Z > 76, and the actinides Th and U ? This question goes to the very heart of the application of cosmochronometers involving the actinides, as well as their decay products. 4. F u t u r e Survey Efforts Our hope and expectation is that, in the near future, application of a similar approach to even larger numbers of targets will expand of these classes further, and/or lead to the identification of new classes of r-processenhanced MP stars. Discussion are now underway, for example, to couple medium-resolution spectroscopic surveys (such as the proposed extension to the Sloan Digital Sky Survey, SEGUE: Sloan Extension for Galactic Understanding and Evolution) to high-resolution follow-up with the HobbyEberly Telescope (HET). It is expected that SEGUE will discover some 10,000 giants with [Fe/H] < —2.5, at least a subset of which will be bright enough for the required high-resolution follow-up to commence. While waiting for SEGUE, we are hoping to conduct a exploratory HET program, using brighter (northern-hemisphere) HK-survey candidates. Acknowledgments T.C.B. acknowledges support received for this work from grants AST 0098508 and AST 00-98549, as well as from grant PHY 02-16783: Physics

118 Frontiers Center/Joint Institute for Nuclear Astrophysics (JINA), awarded by the U.S. National Science Foundation. N . C . acknowledges support received from a Henri Chretien Internation Research G r a n t administered by the American Astronomical Society, and a Marie Curie Fellowship of the European Community, H P M F - C T - 2 0 0 2 - 0 1 4 3 7 . P.S.B. acknowledges support received for this work from the Swedish Research Council.

References 1. J.W. Chamberlain and L.H. Aller Astrophys J., 114, 52 (1951) 2. T.C. Beers, G.W. Preston, and S.A. Shectman, Astron. J., 103, 1987 (1992) 3. T.C. Beers, in Third Stromlo Symposium: The Galactic Halo, eds. B. Gibson, T. Axelrod, and M. Putman (ASP: San Francisco) 165, p. 67 (1999) 4. N. Christlieb and T.C. Beers, in Subaru HDS Workshop on Stars and Galaxies: Decipherment of Cosmic History with Spectroscopy, eds. M. Takada-Hidai and H. Ando (NAO: Mitaka), p. 255 (2000) (astro-ph/0001378) 5. N. Christlieb, Rev. Mod. Ast, 16, 191 (2003) 6. N. Christlieb, M. Bessell, T.C. Beers, B. Gustafsson, A. Korn, P. Barklem, T. Karlsson, M. Mizuno-Wiedner, and S. Rossi, Nature, 419, 904 (2002) 7. N. Christlieb, B. Gustafsson, A.J. Korn, P S . Barklem, T.C. Beers, M.S. Bessell et al, Astrophys. J., 603, 708 (2004) 8. C. Sneden, G.W. Preston, A. McWilliam, and L. Searle Astrophys. J., 431, L27 (1994) 9. C. Sneden, A. McWilliam, G.W. Preston, J.J. Cowan, and D.L. Burris, Astrophys. J. 467, 819 (1996) 10. C. Sneden, J.J. Cowan, J.E. Lawler, I.I. Ivans, S. Buries, T.C. Beers et al, Astrophys. J., 591, 936 (2003) 11. R. Cayrel, V. Hill, T.C. Beers, B. Barbuy, M. Spite, F. Spite et al., Nature, 409, 691 (2001) 12. V. Hill, B. Plez, R. Cayrel, T.C. Beers, B. Nordstrom, J. Andersen et al, Astron. Astrophys., 387, 560 (2002) 13. H. Schatz, R. Toenjes, B. Pfeiffer, T.C. Beers, J.J. Cowan, V. Hill et al., Astrophys. J., 579, 626 14. S. Honda, W. Aoki, T. Kajino, H. Ando, T.C. Beers, T . C , H. Izumiura et al., Astron. J., in press (astro-ph/0402298) 15. J. Westin, C. Sneden, B. Gustafsson, and J.J. Cowan, Astrophys. J. 530, 783 (2000) 16. J.J. Cowan, C. Sneden, S. Buries, I. Ivans, T.C. Beers, J.W. Truran et al., Astrophys J., 572, 861 (2002) 17. J.A. Johnson and M. Bolte, Astrophys. J., 554, 888 (2001) 18. J.J. Cowan and C. Sneden, in Observatories Astrophysics Series, Vol. 4: Origin and Evolution of the Elements, ed. A. McWilliam and M. Rauch (Cambridge: Cambridge Univ. Press), in press (2003) (astro-ph/0309802) 19. G.J. Wasserburg, M. Busso, M., and R. Gallino, Astrophys. J., 466, L109 (1996)

119 20. J.G. Cohen, N. Christlieb, Y.-Z. Qian, and G.J. Wasserburg, Astrophys. J., 588, 1082 (2003) 21. N. Christlieb, T.C. Beers, P. Barklem, M. Bessell, J. Holmberg, A. Korn et al., Astron. Astrophys., submitted (2004) 22. P.S. Barklem, N. Christlieb, T.C. Beers, and V. Hill, Astron. Astrophys., submitted (2004) 23. G.J. Wasserburg and Y.-Z. Qian, it Astrophys. J., 538, L99 (2000) 24. B.D. Fields, J.W. Truran, and J.J. Cowan, Astrophys. J., 575, 845 (2002)

THE /--PROCESS RECORD IN METEORITES ANDREW M. DAVIS Chicago Center for Cosmochemistry, Department of the Geophysical Sciences and Enrico Fermi Institute, University of Chicago, 5640 South Ellis Avenue, Chicago IL 60637-1433, USA

The /--process record in bulk meteorites and components of primitive meteorites (including refractory inclusions and presolar grains) is reviewed. Small /--process excesses are seen in bulk meteorites and refractory inclusions. Large /--process enhancements have only been observed in presolar diamond. The unique properties and formation conditions of presolar diamond, high purity and high surface-to-volume ratio, may allow it to preserve an r-process signature. It is suggested that the conditions under which r-process matter is ejected from a nascent neutron star dictate that apart from diamonds, strong r-process enhancements are not to be expected in larger presolar grains and other solar system components.

1.

Introduction

Since the Sun is not capable of heavy element nucleosynthesis, the isotopic compositions of solar system materials provide a record of nucleosynthesis in previous generations of stars. The isotopic composition of the solar system is well mixed, but there are some exceptions. The terrestrial planets have been extensively melted and reprocessed, destroying any direct isotopic record of their formation. Achondritic meteorites, which come from asteroids melted early in solar system history, contain evidence for the presence of some short-lived radionuclides. Chondritic meteorites are aggregates of a variety of components: (1) chondrules—mm-size droplets that were melted in the solar system [1]; (2) refractory calcium-, aluminum-rich inclusions (CAIs)—0.1 mm to 1 objects enriched in refractory elements and also made in the solar system [1,2]; and (3) presolar grains—grains of SiC, graphite and diamond that are genuine Stardust, condensed in individual stars (principally AGB stars and Type II supernovae) [3]. There are variations of a few parts in 104 in the isotopic compositions of a few elements among bulk meteorites, which sample Mars and the asteroid belt. There are variations of a few parts in 103 in the isotopic compositions of a rare type of CAI that preserved heterogeneities in the early solar system. There are variations of up to factors of several hundred in presolar grains, which reflect nucleosynthesis conditions of individual AGB stars and supernovae. In this paper, stable isotopic anomalies due to the r-process, as well as the inferred presence of unstable r-process radionuclides will be discussed.

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121 2.

Bulk Meteorites

2.1. Stable Isotopes The isotopic compositions of only five rock-forming elements are known to vary among bulk meteorites: oxygen, titanium, chromium, molybdenum, and ruthenium. Oxygen isotopic variations among solar system materials have been known since the discovery of excess 16 0 in refractory inclusions in meteorites [4]. Relative to a mass fractionation line describing all terrestrial rocks, bulk meteorites have a range from a 6%o deficit to a 2%o excess in 16 0 [5]. These effects were initially thought to reflect isotopic heterogeneity of nucleosynthetic origin among the presolar materials that formed the solar system [4,5]. Since 16 0-enriched grains are virtually unknown among presolar grains [3], the variations within the solar system are now thought to be due to chemical processes, either: (1) photochemical self-shielding that may have operated near the Sun [5,6] within the context of the X-wind model for the solar nebula [7], at the surface of the accreting solar nebula [8], or in molecular clouds [9]; or (2) gas-phase mass independent fractionation reactions involving symmetric molecules [10]. Isotopic anomalies in titanium were discovered in CAIs and were subsequently found in bulk carbonaceous chondrites [11]. These anomalies are restricted to excesses of less than \%c in 50Ti, the most neutron-rich isotope of titanium, which is made by neutron-rich statistical equilibrium (the e-process) in Type IA supernovae [12]. No titanium isotopic anomalies have been found in any other meteorite groups besides the carbonaceous chondrites. There are also nucleosynthetic anomalies in 54Cr in bulk carbonaceous chondrites [13] and in leachates from stepwise dissolution of carbonaceous chondrites [14,15]. Like 50Ti, 54Cr is made by the e-process in Type IA supernovae. Isotopic anomalies in molybdenum have been found in bulk carbonaceous chondrites [16,17,18] and in iron meteorites [16,18]. The molybdenum anomalies correspond to small excesses in r- and p-process isotopes (or small deficits in ^-process isotopes). These excesses are up to 0.3%e and differ in different meteorite groups [19]. Leaching experiments, in which primitive carbonaceous chondrites are dissolved in increasingly harsh reagents, reveal larger molybdenum isotopic anomalies, covering a range from a 4%c excess to a l%o deficit in s-process molybdenum [20], The bulk solar system, by definition,

122 has no isotopic anomalies, but the bulk solar system molybdenum was made from a variety of components. One of these components, presolar SiC, is known be enriched in ^-process molybdenum (see section 4, below), so by mass balance, there must be a complementary component enriched in r- and p-process molybdenum. The maximum extent of this r+p-process component revealed in the leaching experiments corresponds to only \%o and there is no convincing evidence for decoupling of the r- and p-process molybdenum isotopic anomalies [16,20]. Finally, there are variations in ruthenium isotopic composition among bulk meteorites, including iron meteorites [18,21]. These anomalies are well correlated with molybdenum isotopic anomalies when data are grouped according to meteorite classification [19] and reinforce the idea that there is some heterogeneity in s- and r+p-process components among meteorite parent bodies. 2.2. Radioactive isotopes Bulk meteorites contain evidence for the in situ decay of twelve now-extinct short-lived radionuclides (T1/2=0.1-103 My) that were present when the solar system formed [22,23], as well as ten extant long-lived species. Only a few of these are dominantly or completely of r-process origin: 107Pd (Tm=6.5 My), 129I (15.7 My), 147Sm (108 Gy), 182Hf (9 My), 187Re (43 Gy), 232Th (14 Gy), 235U (704 My), 238U (4.47 Gy), and 244Pu (82 My). The low solar system abundances 1 t\*j

}0Q

1 ft*?

of Pd and I and high abundances of Hf and actinides appear to require two r-processes, one for A-130 to 195 and another for A-195 and above [24,25]. 3.

Refractory Inclusions

CAIs can be divided into two groups, normal ones and so-called FUN inclusions (for their Fractionation and Unidentified Nuclear isotopic effects) [2,26]. Normal CAIs have up to 5% excess 16 0, but as discussed earlier, this is likely of chemical origin. Large CAIs have \%c excesses of 48Ca [27] and 50Ti [28] and small CAIs made of the mineral hibonite (CaMgxTixAl12_2xOi9) have much larger effects, ranging from a 7% deficit in 50Ti [29] and a 6% deficit in 48Ca [30] to a 10% excess in 48Ca [30] and a 30% excess in 50Ti [30]. 48Ca and 50Ti are made by the e-process in Type IA supernovae. The only other isotopic anomalies commonly found in normal CAIs are excesses of up to 5%o in p-process 138La [31]. The FUN inclusions are quite unusual: they have isotopic anomalies in every element measured, with effects of a few %c. The isotopic compositions of a

123 large number of elements have only been measured in three FUN CAIs, Allende EK-1-4-1 and C-l and Vigarano 1623-5. The two Allende CAIs have very different patterns (summarized in [32]), but C-l and 1623-5 have identical isotopic compositions for all eleven elements measured, even though the two CAIs are from different meteorites [33]. EK-1-4-1 generally has larger isotopic anomalies than the other two FUN CAIs. In CAIs, it is necessary to normalize data to a pair of isotopes, because of isotopic mass fractionation in the mass spectrometer used to make the measurements. Normalized to 86Sr and 88Sr, the FUN CAIs have deficits in p-process 84Sr [32,33]. Normalized to 134Ba and 138 Ba, EK-1-4-1 has excesses in 135Ba and 137Ba and C-l and 1623-5 have a small deficit in I35Ba. The pattern in EK-1-4-1 is suggestive of an r-process addition, with 137Ba/133Ba~1.6. Only EK-1-4-1 has neodymium isotopic anomalies and these are consistent with an r-process addition. EK-1-4-1 has samarium isotopic anomalies consistent with enrichment in the r-process as well as in p-process 144Sm. CI and 1623-5 only have excesses in 144Sm. The general conclusion from heavy element isotope anomalies in FUN CAIs is that they show enrichments in the r- and p-processes, but that the two processes are decoupled and the p-process anomalies are not consistent among different elements [32]. This behavior in FUN inclusions is in contrast to the molybdenum data on bulk meteorites, where the p- and r-processes do not appear to be decoupled [16,20]. 4.

Presolar Grains

Nature has been kind, in the sense that both SiC and graphite Stardust grains contain concentrations of heavy elements that are high enough to be measured on individual /im-sized grains. Each such grain provides a nucleosynthetic record of a single star [3]. Approximately 90% of SiC grains are classified as mainstream and appear to have formed around AGB stars. Through the use of high sensitivity mass spectrometry using laser resonant ionization of laser-desorbed atoms [34], the isotopic compositions of strontium [35], zirconium [36,37], molybdenum [38], ruthenium [39], and barium [40] have been measured in individual SiC grains and in all cases the grains are enriched in ^-process isotopes. The data are entirely consistent with formation in AGB stars of 1.5-3 solar masses with approximately solar metallicity [41]. The isotopic compositions of these elements have also been measured in SiC X-grains, which have a number of isotopic characteristics indicating formation in Type II supernovae [3]. The isotopic composition of molybdenum is quite peculiar [37,42,43] and is enriched in 95Mo and 97Mo relative to the other molybdenum isotopes. These are normally considered to be s-process

124

isotopes with some /--process contribution. Mo, an r-only isotope does not show significant enrichments relative to s-only 96Mo. This isotopic pattern can be reproduced by the neutron-burst that occurs when the shock from the supernova explosion passes though the region of the envelope where abundances are appropriate to drive the 22Ne(a,n)25Mg reaction [44]. The neutron burst is also clearly seen in recent models that follow the full stellar evolution of massive stars through the supernova explosion with a complete nuclear network [45]. The latter models are particularly compelling in that no special effort was made to produce a neutron burst: it just happened as a natural consequence of following the physics as closely as possible. The other elements measured in single Xgrains, zirconium [43], ruthenium [46] and barium [43], are entirely consistent with the neutron burst model. Thus, presolar grains from supernovae have isotopic signatures of the envelope that is ejected in the supernova explosion and the only r-process signature in these grains was likely inherited from a previous generation of stars (as is the case for presolar grains from AGB stars). The isotopic compositions of zirconium and molybdenum have also been measured in presolar graphite [47]. Most graphite grains have s-process signatures and likely formed in AGB stars, but two grains have 96Zr excesses. These excesses can arise from the r-process, but can also be produced in the sprocess. The neutron exposure in AGB stars comes from two reactions, 13 C(a,n)160 during the interpulse period and 22Ne(cc,n)25Mg during thermal pulses. The neutron density during the latter reaction is high enough to drive the neutron capture channel at the 95Zr branch point. In solar metallicity models, 96Zr is depleted in the interpulse exposure and enriched again in the thermal pulse, but with a net depletion in %Zr in dredged-up material [41]. Under conditions of low metallicity, the 22Ne neutron source is more important and 96Zr excesses are predicted [48]. Presolar graphite and SiC grains with ^-process patterns are characterized by large %Zr deficits and smaller deficits in ^Zr, 91Zr, and 92Zr relative to 94Zr [37,47]. Under low metallicity conditions, models predict 6Zr excesses accompanied by deficits in ^Zr, 91Zr, and 92Zr relative to 94Zr [48]. Such a pattern is seen in one graphite grain, but the %Zr/94Zr ratio is ten times solar [47], higher than can be produced by low metallicity j-process models [48]. A second graphite grain has somewhat less excess 96Zr (%Zr/94Zr ratio is 2.5 times solar), within the range that can be produced in low metallicity AGB stars, but it has small excesses in ^Zr, 91Zr, and 92Zr relative to 94Zr. The light zirconium isotope pattern is complementary to that of other grains, which is not characteristic of the ^-process. Thus, both grains are candidates for r-process patterns. Unfortunately, no other elements were measured in one grain and molybdenum in the other grain appears to be a solar system contaminant [47]. Although an r-process origin is possible for these zirconium patterns, it is more

125 likely that they result from a neutron-burst nucleosynthesis during Type II supernova explosions, since similar zirconium isotopic patterns are seen in SiC X-grains [43]. Thus, although there are hints of r-process patterns in graphite, they need to be confirmed by measurements of elements with r-only isotopes. Presolar diamond from carbonaceous chondrites is enriched in both the heavy and light isotopes of xenon [50]. The heavy component, Xe-H, could be a signature of the r-process or could be due to neutron burst nucleosynthesis [51]. The isotopic composition of tellurium in presolar diamonds appears to have resolved this issue [52]. Diamond from the Allende meteorite were placed on the filament of a thermal ionization mass spectrometer and gradually heated. The tellurium released was quite variable in isotopic composition with data points covering the entire range between solar system composition and a component that contained only the two r-only isotopes 128Te and 130Te. This component was free of p-only 120Te and j-only 122Te, 123Te and 124Te. 125Te and 126Te are of mixed r- and ^-process origin, but are also missing from the r-component. These isotopes are shielded by the long-lived isotopes 125Sb (Ti/2=2.76 y) and 126Sn (250 ky). This implies that diamond trapped tellurium, but no antimony and tin, before decay of 125Sb and 126Sn [52]. Another possibility is that tin, antimony and tellurium are implanted but the daughters of 125Sb and 126Sn are lost by recoil from the tiny 10 nm diamonds [53,54]. 5.

Conclusions

Although more than 100 individual presolar grains have been measured for isotopic compositions of various heavy elements, no unambiguous r-processenriched grain has been found. r-Process enrichments have been found in one CAI, but the enrichments are only about l%c. r-Process enrichments of similar magnitude have also been found in leaching of carbonaceous chondrites, but they are accompanied by p-process enrichments and the pattern is likely to be the complement of s-process-enriched presolar SiC grains, a known component of the matter that accreted to form the solar system. Presolar grains with up 20-fold enrichment in s-process isotopes are known, so why have no individual presolar grains with a clear r-process enrichment been found? Diamonds appear to contain implanted r-process tellurium and xenon [50,52], but no r-process signature has been detected in Type X SiC that is clearly of Type II supernova origin. The preferred model for the r-process is that a neutrino wind drags matter out from a nascent neutron star. This must occur at high speed and the r-process freeze-out matter will overtake grains that condense from the expanding envelope after the explosion and will be implanted in them. Diamond may have special properties that allow it to preserve this signature. First, the crystal

126 structure of diamond is such that the concentration of trace elements in diamond condensed at high temperature will be very low. Second, the small average size of diamonds, -10 nm, means that they have very high surface to volume ratios. The grains of Type X SiC that have been analyzed for heavy elements are much larger, with diameters of 2-3 fim. Furthermore, refractory elements such as zirconium, molybdenum and barium readily condense into SiC, so that the isotopic signature of envelope material may overwhelm any implanted r-process component. It is likely that most of the r-process matter dragged away from nascent neutron stars does not condense and does not get implanted into diamond or SiC from the parent supernova. Rather, it likely enters the interstellar medium and condenses or is implanted into cold interstellar grains atom by atom. This would explain why only very modest r-process enhancements have been found in solar system materials. Acknowledgments This work was supported by the National Aeronautics and Space Administration through grant NAG5-12997. References 1. E. R. D. Scott and A. N. Krot, In Meteorites, Planets, and Comets (Ed. A. M. Davis), Vol. 1 Treatise on Geochemistry (Eds. H. D. Holland and K. K. Turekian), Elsevier-Pergamon, Oxford, 143 (2003). 2. G. J. MacPherson, In Meteorites, Planets, and Comets (Ed. A. M. Davis), Vol. 1 Treatise on Geochemistry (Eds. H. D. Holland and K. K. Turekian), Elsevier-Pergamon, Oxford, 201 (2003). 3. E. K. Zinner, In Meteorites, Planets, and Comets (Ed. A. M. Davis), Vol. 1 Treatise on Geochemistry (Eds. H. D. Holland and K. K. Turekian), Elsevier-Pergamon, Oxford, 17 (2003). 4. R. N. Clayton, L. Grossman and T. K. Mayeda, Science 182, 485 (1973). 5. R. N. Clayton, In Meteorites, Planets, and Comets (Ed. A. M. Davis), Vol. 1 Treatise on Geochemistry (Eds. H. D. Holland and K. K. Turekian), Elsevier-Pergamon, Oxford, 129 (2003). 6. R. N. Clayton, Nature 415, 860 (2002). 7. F. H. Shu, H. Shang and T. Lee, Science 271, 1545 (1996). 8. J. R. Lyons and E. D. Young, In Lunar Planet Sci. XXXV, #1970, Lunar and Planetary Institute, Houston (CD-ROM) (2004). 9. H. Yurimoto and K. Kuramoto, Meteorit. Planet. Sci. 37, A153 (2002). 10. M. H. Thiemens, Science 283, 341 (1999).

127 11. S. Niemeyer and G. W. Lugmair, Geochim. Cosmochim. Acta 48, 1401 (1984). 12. G. Wallerstein, I. Iben Jr., P. Parker, A. M. Boesgaard, G. M. Hale, A. E. Champagne, C. A. Barnes, F. Kappeler, V. V. Smith, R. D. Hoffman, F. X. Timmes, C. Sneden, R. N. Boyd, B. S. Meyer and D. L. Lambert, Rev. Mod. Phys. 69, 995 (1997). 13. A. Shukolyukov and G. W. Lugmair, Science 282, 927 (1998). 14. M. Rotaru, J. L. Birck and C. J. Allegre, Nature 358, 465 (1992). 15. F. A. Podosek, U. Ott, J. C. Brannon, C. R. Neal, T. J. Bernatowicz, P. Swan and S. E. Mahan, Meteorit. Planet. Sci. 32, 617 (1997). 16. N. Dauphas, B. Marty and L. Reisberg, Ap. J. 565, 640 (2002). 17. Q.-Z. Yin, S. B. Jacobsen and K. Yamashita, Nature 415, 881 (2002). 18. J. H. Chen, D. A. Papanastassiou, G. J. Wasserburg and H. Ngo, In Lunar Planet Sci. XXXV, #1431, Lunar and Planetary Institute, Houston (CDROM) (2004). 19. N. Dauphas, A. M. Davis, B. Marty and L. Reisberg, Earth Planet. Sci. Lett., submitted (2004). 20. N. Dauphas, B. Marty and L. Reisberg, Ap. J. 569, L139 (2002). 21. J. H. Chen, D. A. Papanastassiou and G. J. Wasserburg, In Lunar Planet Sci. XXXIV, #1789, Lunar and Planetary Institute, Houston (CD-ROM) (2003). 22. K. D. McKeegan and A. M. Davis, In Meteorites, Planets, and Comets (Ed. A. M. Davis), Vol. 1 Treatise on Geochemistry (Eds. H. D. Holland and K. K. Turekian), Elsevier-Pergamon, Oxford, 431 (2003). 23. Y. Lin, Y. Guan, L. A. Leshin, Z. Ouyang and D. Wang, In Lunar Planet Sci. XXXV, #2084, Lunar and Planetary Institute, Houston (CD-ROM) (2004). 24. G. J. Wasserburg, M. Busso and R. Gallino, Ap. J. 466, L109 (1996). 25. Y.-Z. Qian, P. Vogel and G. J. Wasserburg, Ap. J. 494,285 (1998). 26. G. J. Wasserburg, T. Lee and D. A. Papanastassiou, Geophys. Res Lett. 4, 299 (1977). 27. F. R. Niederer and D. A. Papanastassiou, Geochim. Cosmochim. Acta 48, 1279 (1984). 28. F. R. Niederer, D. A. Papanastassiou and G. J. Wasserburg, Geochim. Cosmochim. Acta 49, 835 (1985). 29. R. W. Hinton, A. M. Davis and D. E. Scatena-Wachel, Ap. J. 313, 420 (1987). 30. T. R. Ireland, Geochim. Cosmochim. Acta 54, 3219 (1990). 31. J. J.-S. Shen and T. Lee, Ap. J. 596, L109 (2003). 32. G. J. Wasserburg, D. A. Papanastassiou and T. Lee, In Early Solar System Processes and the Present Solar System, Soc. Italiana di Fisica, Bologna, 144 (1980) 33. R. D. Loss, G. W. Lugmair, A. M. Davis and G. J. MacPherson, Ap. J. 436, L193 (1994).

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34. M. R. Savina, M. J. Pellin, C. E. Tripa, I. V. Veryovkin, W. F. Calaway and A. M. Davis, Geochim. Cosmochim. Acta 67, 3215 (2003). 35. G. K. Nicolussi, M. J. Pellin, R. S. Lewis, A. M. Davis, R. N. Clayton and S. Amari, Phys. Rev. Lett. 81, 3583 (1998). 36. G. K. Nicolussi, A. M. Davis, M. J. Pellin, R. S. Lewis, R. N. Clayton and S. Amari, Science 277, 1281 (1997). 37. A. M. Davis, M. Lugaro, R. Gallino, M. J. Pellin, R. S. Lewis and R. N. Clayton, Mem. Soc. Astron. Ital. 72, 413 (2001). 38. G. K. Nicolussi, M. J. Pellin, R. S. Lewis, A. M. Davis, S. Amari and R. N. Clayton, Geochim. Cosmochim. Acta 62, 1093 (1998). 39. M. R. Savina, A. M. Davis, C. E. Tripa, M. J. Pellin, R. Gallino, R. S. Lewis and S. Amari, Science 303, 649 (2004). 40. M. R. Savina, A. M. Davis, C. E. Tripa, M. J. Pellin, R. N. Clayton, R. S. Lewis, S. Amari, R. Gallino and M. Lugaro, Geochim. Cosmochim. Acta 67, 3201 (2003). 41. M. Lugaro, A. M. Davis, R. Gallino, M. J. Pellin, O. Straniero and F. Kappeler, Ap. J. 593,486 (2003). 42. M. J. Pellin, A. M. Davis, R. S. Lewis, S. Amari and R. N. Clayton, In Lunar Planet. Sci. XXX, #1969, Lunar and Planetary Institute, Houston (CD-ROM) (1999). 43. M. J. Pellin, W. F. Calaway, A. M. Davis, R. S. Lewis, R. N. Clayton and S. Amari, In Lunar Planet. Sci. XXXI, #1917, Lunar and Planetary Institute, Houston (CD-ROM) (2000). 44. B. S. Meyer, D. D. Clayton and L.-S. The, Ap. J. 540, L49 (2000). 45. T. Rauscher, A. Heger, R. D. Hoffman and S. E. Woosley, Ap. J. 576, 323 (2002). 46. M. R. Savina, A. M. Davis, C. E. Tripa, M. J. Pellin, R. Gallino, R. Lewis and S. Amari, Geochim. Cosmochim. Acta 67, A418 (2003). 47. G. K. Nicolussi, M. J. Pellin, R. S. Lewis, A. M. Davis, R. N. Clayton and S. Amari, Ap. J. 504,492 (1998). 48. A. M. Davis, R. Gallino, O. Straniero, I. Dominguez and M. Lugaro, In Lunar Planet Sci. XXXIV, #2043, Lunar and Planetary Institute, Houston (CD-ROM) (2003). 49. A. M. Davis, G. K. Nicolussi, M. J. Pellin, R. S. Lewis and R. N. Clayton, In Nuclei in the Cosmos V (Eds. N. Prantzos & S. Harissopulos), Editions Frontieres, Paris, 563 (1999). 50. R. S. Lewis, M. Tang, J. F. Wacker, E. Anders and E. Steel, Nature 326, 160 (1987). 51. W. M. Howard, B. S. Meyer and D. D. Clayton, Meteoritics 27,404 (1992). 52. S. Richter, U. Ott and F. Begemann, Nature 391, 261 (1998). 53. U. Ott, Ap. J. 463, 344 (1996). 54. Y.-Z. Qian, P. Vogel and G. J. Wasserburg, Ap. J. 513, 956 (1999).

I N H O M O G E N E O U S CHEMICAL EVOLUTION A N D T H E SOURCE OF R-PROCESS ELEMENTS

DOMINIK ARGAST

E-mail:

Institut fur Physik Klingelbergstrasse 82 CH-4056 Basel Switzerland [email protected]

In this work, neutron star mergers, lower-mass (in the range 8 —10 M Q ) and highermass core-collapse supernovae (with masses > 20 MQ) are assessed as dominant sources of r-process elements. I conclude that it is not possible at present to distinguish between the lower-mass and higher-mass supernovae scenarios within the framework of inhomogeneous chemical evolution. However, neutron-star mergers seem to be ruled out as the dominant r-process source, since their low rates of occurrence would lead to r-process enrichment that is not consistent with observations.

1. Introduction Heavy elements beyond the iron peak are formed in part by r-process nucleosynthesis, i.e. the rapid capture of neutrons on seed nuclei. Yet, although the physical requirements for the occurrence of r-process nucleosynthesis are well understood, the astrophysical nature of the dominant r-process site is still unknown. The abundance pattern of neutron capture elements heavier than Ba (Z > 56) in ultra metal-poor stars matches the scaled solar system r-process abundances remarkably well.1""3 This suggests that the synthesis of r-process elements started early in Galactic evolution and that the r-process is robust for elements heavier than Ba, i.e. it originates from a single astrophysical site or at least occurs under well defined physical conditions. A number of possible astrophysical sites responsible for the robust rprocess were put forth in the past. It has been suggested that r-process elements might be formed during the prompt explosion of a massive star in the range 8 — 10 M© and that the amount of r-process matter ejected may be consistent with observed Galactic r-process abundances. 4 However, there 129

130 are major objections to the prompt explosion mechanism from detailed corecollapse supernova (SN II) studies. 5 - 6 . Another promising r-process site are neutrino-driven winds from nascent neutron stars. 7 ~9 On the other hand, r-process yields consistent with observed r-process abundances in stars may be obtained in this scenario only for extreme assumptions such as massive neutron stars of 2 M© or more, which makes this not a very likely scenario. Recently, detailed r-process calculations for neutron star mergers (NSM) have been presented. 10-12 Coalescing neutron stars potentially can provide in a natural way the large neutron fluxes required for the build-up of heavy elements through rapid neutron capture. Yet, it remains to be seen if their low occurrence rate is consistent with observations of r-process elements in ultra metal-poor stars.

2. Treatment of r-Process Sources in the Model An ideal tracer of the r-process enrichment of the ISM is the pure r-process element europium. Unfortunately, only a small sample of Eu abundances at very low metallicities (i.e. [Fe/H] < —2.5) are available to date. In order to trace the r-process enrichment at lower metallicities, the well studied element barium is also used in this investigation. Note that Ba abundances in stars are dominated by the s-process and only sa 15% of the solar Ba abundance was formed by rapid neutron capture. 13 However, the r-process fraction [Ba r /Fe] of Ba abundances can be computed by removing the sprocess contribution to Ba in stars with [Fe/H] > —2.5 if Eu abundances have also been determined. For stars with metallicities [Fe/H] < —2.5, it is assumed that the whole Ba inventory is of pure r-process origin. Care has been taken to remove known carbon stars from the sample. Such stars mostly show unusually large Ba abundances, which are thought to originate from mass transfer of s-process enriched matter in binary systems. In the following, r-process yields of Eu and Ba are estimated under the assumption of a robust r-process for nuclei more massive than Ba, i.e. only one source is responsible for the enrichment of the ISM with r-process elements beyond Z=56. The yields were chosen in such a way that the whole range of r-process abundances and its average in metal-poor halo stars are reproduced in the model. Note that r-process yields have in essence been treated as free parameters and are tuned to match the observations. In model SN810, r-process nucleosynthesis is assumed to occur in SNe II with progenitors in the mass range 8—10 M© with constant Ba and Eu yields over the whole mass range. The yields are then deduced from the average

131 [Eu/Fe] and [Ba r /Fe] ratios (both pa 0.5) of metal-poor halo stars. Furthermore, I assume that the amount of a and iron peak elements synthesised in these SN II events is negligible. As an alternative to model SN810, I also calculated the chemical evolution of the ISM with r-process yields from SNe II in the mass range 20 - 50 M 0 (model SN2050). The r-process yield of the 20 M 0 is chosen so that it reproduces the largest [Eu/Fe] and [Ba r /Fe] ratios of metal-poor halo stars observed. Since this requires a large amount of ejected r-process matter, the yields have to decrease sharply with increasing progenitor mass to account for the average [Eu/Fe] and [Ba r /Fe] abundance ratios of metalpoor halo stars. Constraints on the properties of the Galactic NSM population are controversial. Coalescence timescales for neutron star mergers are typically estimated to be of the order 100 — 1000 Myr, but a dominant population of short lived neutron star binaries with merger times less than 1 Myr has also been suggested. 14-15 Galactic NSM rates are estimated to lie in the range of (7.5 x 10~ 7 - 3 x 10 - 4 ) yr - 1 . 1 5 ~ 1 7 The amount of r-process matter ejected in a NSM event is of the order of 10~ 5 - 10~ 2 M 0 . n ' 1 8 To account for these large uncertainties, four models, with average NSM rates of 2 x 10~ 3 yr" 1 , 2 x 1 0 - 4 yr _ 1 , 2 x 1 0 - 5 yr _ 1 , and 2 x 10" 6 y r " \ have been calculated. In all coalescence timescale of 1 Myr has been adopted. The amount of ejected r-process matter is 1 0 _ 4 M Q , 10~ 3 M Q , 10~ 2 M Q , and 1 0 _ 1 M Q , respectively. The NSM rate and the amount of ejected r-process matter are tightly correlated, since the total amount of r-process matter in the Galaxy has to be reproduced. 19 Thus, higher NSM rates require that less r-process matter is ejected in each event, and vice versa. 3. E n r i c h m e n t of t h e I S M w i t h r-Process E l e m e n t s 3.1. SN II as Dominant

r-Process

Sites

The results of models SN810 and SN2050 are shown in Figs. 1 and 2, respectively. The figures show the evolution of [Eu/Fe] and [Ba r /Fe] as functions of metallicity [Fe/H]. Note that the [Ba r /Fe] plots only show the r-process contribution to the total Ba abundances of halo stars. The evolution of r-process elements shown in Figs. 1 and 2 are qualitatively very similar. At very low metallicities ([Fe/H] < —2.5), a large scatter in abundances of model stars is visible. This scatter is due to chemical inhomogeneities in the early ISM. 20 The scatter decreases as the mixing

132

-2 [Fe/H]

[Fe/H]

Figure 1. Evolution of [Bu/Fe] and [Bar/Fe] abundances as functions of metallicity [Fe/H]. Lower-mass SNe II (Model SN810) are assumed to be the dominant r-process sources. Black dots denote model stars; observations are marked by filled squares. Average ISM abundances are marked by a continuous line.

^ ° r ; •*

[Fe/H]

Figure 2. Evolution of [Eu/Fe] and [Bar/Fe] abundances as functions of metallicity [Fe/H]. Higher-mass SNe II (Model SN2050) are assumed to be the dominant r-process sources. Symbols are'as in Fig. 1.

of the ISM Improves and finally reaches the initial mass function averaged mean. At this stage, the ISM can be considered well mixed and the further

133 evolution is comparable to the one of classic chemical evolution models. In the following, I point out some important features of the ISM enrichment resulting from models SN810 and SN2050. (1) In both models, r-process elements appear very early in the enrichment of the ISM. Some model stars with r-process abundances exist even at metallicities [Fe/H] < - 4 , which is in agreement with observed Ba abundances in ultra metal-poor stars. (2) For metallicities [Fe/H] > - 2 , the scatter in [Eu/Fe] and [Ba r /Fe] abundances of model stars is comparable to that seen in observations. (3) Model SN810 fails to reproduce the two metal-poor stars with the highest Eu abundances ([Eu/Fe] > +2.0 at [Fe/H] « -2.5). The existence of such ultra r-process enhanced stars might pose a serious problem for the SN scenario, since an unusual large amount of ejected r-process matter (> 10~ 4 M Q ) is required to reproduce these observations in chemical evolution models. (4) The models also predict some stars with very low [Eu/Fe] and [Ba r /Fe] ratios at [Fe/H] < —2, which are not observed to date. However, if stars with [r/Fe] < — 1 exist in the Galactic halo, their Eu and Ba lines may be too weak to be detectable. In summary, core-collapse SNe seem to be a valid source of r-process elements from the point of view of chemical evolution, since the enrichment of the ISM in the cases discussed above is in qualitative, if not necessarily quantitative, agreement with observations. 3.2. NSMs

as Dominant

r-Process

Sites

For the NSM scenario, four model-runs were carried out, assuming NSM rates ranging from 2 x 10~ 3 y r _ 1 to 2 x 10~ 6 y r - 1 and a coalescence timescale of 1 Myr. A condensed overview of all models displaying the evolution of [Ba r /Fe] is shown in Fig. 3. The evolution of r-process abundances is strikingly different from the case in which r-process nucleosynthesis occurs in SNe II. All models with NSMs as r-process sources fail to reproduce observations. The upper left panel of Fig. 3 gives the best fit to observations in the NSM case, although model stars with r-process contributions at [Fe/H] < —3 are still somewhat scarce. However, a NSM rate of 2 x 10~ 3 y r _ 1 is one order of magnitude larger than the most optimistic estimate of the

134

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Figure 3. [Bar/Fe] vs [Fe/H] for the NSM rates 2 x 10~ 3 yr~\ 2 x l O ^ y i T 1 , 2 x l O ^ y r " 1 , and 2 x l O ^ y r " 1 (from left to right and top to bottom). The coalescence timescale adopted in these cases is 106 yr. Symbols are as in Fig. 1.

galactic NSM rate. As a representative example of the remaining models with consistent NSM rates, the model shown in the upper right panel of Fig. 3 is discussed in the following. The following qualitative differences are immediately visible, if the upper right panel of Fig. 3 is compared to Figs. 1 and 2: (1) r-Process nuclei appear at the earliest around [Fe/H] « - 2 . 5 , whereas r-process elements such as Eu are observed at [Fe/H] = - 3 and probably even down to [Fe/H] = - 4 in the case of Ba. The

135

reason for this late injection of r-process matter in the model is the low NSM rate. (2) There is a prominent tail of model stars with very low [Ba r /Fe] ratios at [Fe/H] = —2. Such model stars are also present in Figs. 1 and 2. In this case, however, the tail does not develop until [Fe/H] > —2. Since the tail develops at higher metallicities, it cannot be dismissed as unobservable. (3) Even late in the enrichment of the ISM ([Fe/H] > — 1), the scatter in possible [r/Fe] ratios is of the order 1.5 — 2.0 dex, whereas observations of [Eu/Fe] and [Ba r /Fe] abundances show a scatter of approximately 0.2 — 0.3 dex. These aspects strongly argue against NSMs as the dominant r-process source, especially since the parameters used for the model in discussion are at the upper limit set by theoretical and observational constraints. Lower NSM rates and, consequently, larger ejecta masses, only aggravate the problems mentioned above. The dramatic changes in the distribution of r-process abundances occurring with decreasing NSM rate are clearly visible in the sequence of plots in Fig. 3. In the upper left panels of Fig. 3 (NSM rate 2 x 10~ 3 yr _ 1 ), a few model stars with r-process abundances first appear around [Fe/H] » —3.5, in contrast to [Fe/H] « - 1 in the panels at the lower right (NSM rate 2 x 1 0 ~ 6 y r - 1 ) . Simultaneously, the scatter in [Ba r /Fe] and [Eu/Fe] at solar metallicity, which is of the same order as that observed in the upper left panel, increases to almost 3 dex in the lower right panel, clearly not consistent with observations. Furthermore, the tail of model stars with low [r/Fe] abundances becomes more pronounced and concentrated and is shifted to higher metallicities. 4. Conclusions In this work, I study the enrichment of the ISM with r-process elements in the framework of inhomogeneous chemical evolution. I present a detailed comparison of the impact of lower-mass SNe II (8 — 10 M Q ), higher-mass SNe II (> 20M Q ), and NSMs as major r-process sites on the enrichment history of the early Galaxy. In both SNe II scenarios, the model results are qualitative similar to the pattern of r-process abundances in ultra metal-poor stars. However, we conclude that, due to the large uncertainties inherent in the progenitor mass dependence of iron yields of SNe H 2 0 - 2 1 it is not possible to clearly rule out

136

either lower-mass SNe II or higher-mass SNe II as dominant r-process sites from the point of view of inhomogeneous chemical evolution. Additional uncertainties are introduced by the fact that reliable r-process yields from SNe II are unavailable as yet. Here, they were deduced in such a way that the average [r/Fe] abundances in metal-poor halo stars are reproduced. On the other hand, NSMs seem to be ruled out as major r-process sources for the following reasons:

(1) Estimates of the Galactic NSM rate are two to three orders of magnitude lower than estimates of the Galactic SNe II rate. Thus, the injection of r-process nuclei into the ISM by NSMs would occur late during Galaxy formation ([Fe/H] w —2.5), whereas r-process elements are already observed at [Fe/H] = —3 and probably even at [Fe/H] = - 4 . (2) The late injection of r-process elements furthermore leads to prominent tails in the distribution of r-process abundances down to very low [r/Fe] ratios at [Fe/H] > —2, which are not consistent with observations. (3) Since NSMs occur at a lower rate than SNe II, their r-process yield has to be about two orders of magnitude higher than the r-process yield of typical SNe II. Due to this large r-process yield, considerable chemical inhomogeneities in the ISM are expected to be present even at solar metallicity. The scatter in [r/Fe] is predicted to be of the order 2.0 — 2.5 dex, whereas a scatter of only 0.2 — 0.3 dex is observed.

Thus, I conclude that the exact astrophysical nature of r-process sites still remains a mystery, since it is not possible to clearly distinguish between neutron capture element abundance patterns resulting from lower-mass SNe II ( 8 - 1 0 M Q ) and those from higher-mass SNe II (> 20 M Q ) in the framework of inhomogeneous chemical evolution. However, the present investigation suggests that core-collapse SNe are much more likely to be the dominant rprocess sites than coalescing neutron star binaries, if the present estimates of the galactic NSM rate will not be revised considerably in future investigations. However, it remains to be seen how SNe II can actually produce the required r-process yields. An extended discussion of these results can be found in Ref. 22.

137 Acknowledgements This work was supported by the Swiss National Science Foundation. References 1. Sneden, C , Cowan, J.J., Ivans, I.I., Puller, G.M., Buries, S., Beers, T.C., & Lawler, J.E. 2000, ApJ, 533, L139 2. Westin, J., Sneden, C , Gustafsson, B., & Cowan, J.J. 2000, ApJ, 530, 783 3. Cowan, J.J., et al. 2002, ApJ, 572, 861 4. Wheeler, J.C., Cowan, J.J., & Hillebrandt, W. 1998, ApJ, 493, L101 5. Bruenn, S.W. 1989a, ApJ, 340, 955 6. Bruenn, S.W. 1989b, ApJ, 341, 385 7. Thompson, T.A., Burrows, A., & Bradley, S.M. 2001, ApJ, 562, 887 8. Wanajo, S., Toshitaka, K., Mathews, G.J., & Otsuki, K. 2001, ApJ, 554, 578 9. Terasawa, M., Sumiyoshi, K., Yamada, S., Suzuki, H., & Kajino, T. 2002, ApJ, 578, L137 10. Freiburghaus, C , Rosswog, S., & Thielemann, F.-K. 1999, ApJ, 525, L121 11. Rosswog, S., Liebendorfer, M., Thielemann, F.-K., Davies, M.B., Benz, W., & Piran, T. 1999, A&A, 341, 499 12. Rosswog, S., Davies, M.B., Thielemann, F.-K., & Piran, T. 2000, A&A, 360, 171 13. Burris, D.L., Pilachowski, C.A., Armandroff, T.E., Sneden, C , Cowan, J.J., & Roe, H. 2000, ApJ, 544, 302 14. Fryer, C.L., Woosley, S.E., & Hartmann, D.H. 1999, ApJ, 526, 152 15. Belczynski, K., Kalogera, V., & Bulik, T. 2002, ApJ, 572, 407 16. van den Heuvel, E., & Lorimer, D. 1996, MNRAS, 283, L37 17. Kalogera, V., & Lorimer, D.R. 2000, ApJ, 530, 890 18. Oechslin, R., Rosswog, S., & Thielemann, F.K. 2002, PhRvD, 65, 103005 19. Wallerstein, G., et al. 1997, RvMP, 69, 995 20. Argast, D., Samland, M., Gerhard, O.E., & Thielemann, F.-K. 2000, A&A, 356, 873 21. Argast, D., Samland, M., Thielemann, F.-K., & Gerhard, O.E. 2002, A&A, 388, 842 22. Argast, D., Samland, M., Thielemann, F.-K., & Qian, Y.Z. 2004, A&A, 416, 997

GO U P S T R E A M OF T H E "MILKY WAY": ORIGIN OF HEAVY ELEMENTS I N F E R R E D F R O M GALACTIC CHEMICAL EVOLUTION

Y. I S H I M A R U 1 , S. W A N A J O 2 , N. P R A N T Z O S 3 , W . A O K I 4 , S. G. R Y A N 5 Department of Physics, Ochanornizu University, 2-1-1 Otsuka, Bunkyo, Tokyo 102-8554, Japan; E-mail: [email protected] Department of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan. Institut d'Astrophysique de Paris, 98 bis, Boulevard Arago, 75014, Paris, France. National Astronomical Observatory, Mitaka, Tokyo 181-8588 Japan. Department of Physics and Astronomy, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK.

Observed large star-to-star scatters in chemical abundances of metal-poor stars may indicate that the inter-stellar gas was not fully mixed at the early epoch of the Galactic evolution. We construct an inhomogeneous chemical evolution model, and compare predicted stellar abundance distributions with observations, using statistical method. We take several supernova yields; the data of Nomoto et al. (1997) and Woosley & Weaver (1995), and discuss consistency of these yield sets with observations. In particular, we discuss the origin of r-process, from the point of view of enrichment of europium. Using the Subaru HDS, we have estimated Eu abundances of three extremely metal-poor stars with [Fe/H] < —3. Comparison with our Galactic evolution model implies the dominant source of Eu to be the low-mass end of the supernova mass range.

1. Introduction Recent abundance analysis of metal-poor halo stars reveals the presence of large dispersions in heavy elements. This may be interpreted as a result of incomplete mixing of the interstellar medium (ISM) at the beginning of the Galaxy 1 . Each type of element shows a unique dispersion, which cannot be simply explained by spatial inhomogeneity of the ISM 2 . One of the possible explanations is that the ISM was not mixed well, and metalpoor stars contain products of only one or a few supernovae (SNe). If star formations are mainly triggered by SNe, the composition of the formed star must be a mixture of the ISM and the individual SNe ejecta, and the 138

139 scatter possibly reflects variation in the yields of SNe from different mass progenitors. In particular, the abundances of neutron-capture elements like Sr, Ba, and Eu show large dispersions in excess of observational errors 3 ' 4 . This implies that r-process yields are highly dependent on the masses of SN progenitors. However, the origins of r-process elements are still uncertain. Although a few scenarios such as neutrino winds 5 in core-collapse supernovae (SNe), the collapse of O-Ne-Mg cores resulting from 8 — 10M© stars 6 , and neutron star mergers 7 show some promise, no consensus has been achieved. In this study, we construct a Galactic chemical evolution model, taking into account of inhomogeneous gas mixing. We take several known SN yields and examine their consistency with observational dispersions in stellar chemical compositions. Especially, we discuss the enrichment of europium, using an inhomogeneous chemical evolution model based on induced star formations. In addition, we report on three extremely metalpoor stars which we show to have very low Eu abundances. These data are compared with our chemical evolution models to distinguish between the proposed r-process sites.

2. Inhomogeneous Chemical Evolution We have constructed a Galactic chemical evolution model, assuming star formations are induced by individual SNe. Since a new star is formed from a mixture of a supernova remnant (SNR) and the ISM gathered by expansion of the SNR, its chemical composition can be calculated from the mass average of that of the SNR and the ISM. We take two sets of yields given by known SN models; Nomoto et al. 8 (hereafter N97) and Woosley & Weaver9 (hereafter WW95). The yields of WW95 take into account dependency of yields on stellar metallicity, whereas N97 assumes constant yields irrespective of metallicity. Thus, differences in predictions by two SN models must reveal effect of metallicity dependency of yields on chemical evolution and scatters in [X/Fe] a of metal-poor stars.

140 i i | i i i i J "i—mr—r | "i i i i | i i T—T

Figure 1. [Mg/Fe] vs. [Fe/H] relations predicted from N97 (left panel) and WW95 (right panel). Predicted distributions of stellar fraction (gray scales) are compared to observational data (small circles). Large symbols indicate stars formed from the SNe of the first generation stars (N97) and from SNe of 1 0 " 4 Z Q stars(WW95). The numbers in the circles indicate progenitor masses in a unit of the solar mass. The average lines and 50% confidence regions of observations are given by thick solid and thin dashed lines, respectively. Those of model predictions are also given by gray thick solid, sold, and thin thin (90%) lines.

2.1. [X/Fe] V8« [Fe/H] predicted

by different SN

models

We calculate stellar distributions on diagrams of relative abundance ratios of [O-Zn/Fe] vs. [Fe/H], and compare dispersions predicted from both two models with observational data by statistical method. Figure 1 shows examples of [Mg/Fe] vs. [Fe/H] relations predicted by N97 and WW95. a

[Xi/Xj] Xi.

EE log(N{/Nj)

— log(JVj/JVj)0, where Ni indicates abundance of t-th element

141

Obviously, we can see the predicted number density of stars per unit area (gray-scales) shrinks with increasing of metallicity. We also put several stars formed via SNe of the first generation stars (large symbols). It is shown that the widths of stellar distributions are determined by variations in yields of different progenitor mass. Stellar distribution shows extremely large dispersion, if SN products of the first generation stars are mixed with zero-metal gas (large squares in N97). But if ISM is already enriched efficiently by higher mass stars when lower mass progenitors explode (large circles in N97), a predicted scatter is smaller. Thus, since the efficiency of gas mixing has some uncertainties, actual stars can distribute between these two extreme cases. A similar result is obtained also by WW95 (right panel), which shows stars formed by SNe of 10~ 4 ZQ stars. We also put the average stellar abundance distributions (thick solid gray lines) and the 50% and 90% confidence intervals (solid and thin-solid gray lines). They are compared with observational values of average (thick solid lines) and 50% confidence intervals (solid lines) 2 .

2.2. Statistical

analysis

of dispersions

and SN

yields

Concerning the average trends of [X/Fe], several elements such as Na, Al, Sc, Cu, Zn, etc. are already known to show clear differences between two yield sets, while some elements such as a-elements are believed to be rather stable and show similar trends irrespective of models. However, as shown in Fig. 1, the width of scatters in metal-poor stars shows clear difference of two models even in a-elements. Thus, we take 50% confidence intervals and compare them with observational values. Figure 2 shows the ratios of predictions over observations of width of 50% confidence intervals. Although both of two models seem to predict underestimated dispersions in [Fe/H]> —2, it can be understood if we take into account observational errors which are comparable to dispersions in higher metallicity stars. On the other hand, dispersions by N97 seem small especially in [Fe/H]< —3, since few stars are predicted in this area. The distributions of lower metallicity stars are affected also by the efficiency of gas mixing. In our model, a parameter for gas mixing is given by the expansion radius of SNR, which is calculated from an analytical function of density of the ISM 10 . If SNR radius has 1.5cr uncertainty in logarithmic scale, some stars are formed from the gas more diluted by the ISM. As a result, stellar dispersions are elongated towards lower metallicity and show better agreements with observations. However, the maximum width of 50% confidence interval is affected little.

142

[Fe/H]

Figure 2. Relation between [Fe/H] and width of scatters. The upper and lower panels are given by N97 and WW95, respectively. Gray thick solid and thin solid lines indicate predicted 50% and 90% intervals, respectively. Black dotted lines are given from observations of Norris et al. (2001).

Therefore, if predicted dispersion exceeds observational value significantly, the inconsistency comes from the SN model rather than gas dynamics. Figure 2 shows overestimates of dispersions in Mg and Al of WW95 and in Ca and Co in N97. Both models predict too large dispersions in Sc. These elements suggest problems in supernova models. 3. The site of r-process inferred from Eu abundances 3.1. Enrichment

of Eu in the Halo

We investigate the enrichment of Eu, as a representative of r-process elements, in the Galactic halo 11 . The r-process elements are supposed to be produced only in Type II SNe. We examine the following two cases in which the r-process elements are produced from the stars: (a) 8 — 10M Q , and (b) > 30M©. Yields for Type II and Type la SNe are taken from Nomoto et al. 8 12 ' . The 8 — IOMQ stars are assumed to produce no iron, since their contri-

143

bution to the enrichment of iron-peak elements in the Galaxy is negligible6. The mass of produced Eu is assumed to be constant over the stellar mass range. The requirement that the model reproduces the solar values [Eu/Fe] = [Fe/H] = 0 implies ejected Eu masses 3.1 x 10~ 7 and 7.8 x 10~ 7 M o for cases (a) and (b), respectively. Figures 3a and 3b show the enrichment of Eu in the halo by cases a and b, respectively. The observable differences between the cases appear at [Fe/H]< —3. In case (b), most of the stars are expected to have [Eu/Fe]> 0, owing to Eu production solely by massive, short-lived stars. In cases (a), significant numbers of stars having [Eu/Fe] < 0 are predicted at [Fe/H] < —3 owing to the delayed production of Eu by lower mass SN progenitors. However, most previous observational data (small circles) distribute between the 90% confidence lines for both cases, which has made it difficult to determine the mass range of the r-process site.

3.2. Detection

of low Eu

abundances

Although [Ba/Fe] in metal-poor stars decreases towards lower metallicity, it has been uncertain whether [Eu/Fe] shows a similar trend, because almost no data of Eu abundance has been available for such low metallicity stars. Thus we selected three very metal-poor ([Fe/H] < —3) giants, HD 4306, CS 22878-101, and CS 22950-046, which were known from previous studies 3 ' 13 to have [Ba/Fe] ~ —1, typical for their metallicities. Observations were made with the High Dispersion Spectrograph (HDS) of the 8.2m Subaru Telescope in 2001 July, at a resolving power R = 50,000. The detailed analysis and estimated abundances are seen in Ishimaru et al. 14 . The newly obtained data are represented by large double circles in Fig. 3ab. Our data add the lowest detections of Eu, at [Fe/H] < —3, and help distinguish between the two cases. The best agreement can be seen in case (a), in which the three stars, and most other stars from previous observations are located between the 50% confidence lines at [Fe/H] < —3. On the other hand in case (b), these stars are located outside the 90% confidence region. We suggest, therefore, that case (a) is most likely to be the r-process site, i.e. SNe from low-mass progenitors such as 8 — 10M© stars. Our analysis gives [Ba/Eu] values consistent with the solar r-process 15 when estimated errors are included (see Table 3 of Ishimaru et al. 2004). Hence our result may hold for heavy r-process elements with Z > 56, not just Z ~ 63. The values of [Sr/Ba], however, are significantly higher than

144

h

i

-4

i

-3

i

-2 -1 [Fe/H]

log Ufar

1

0

Figure 3. Comparison of the observed data of [Eu/Fe] with the model predictions. The r-process site is assumed to be SNe of (a) 8—lOM© and (b) > 30M© stars. The predicted number density of stars per unit area is gray-scaled. The average stellar abundance distributions are indicated by thick-solid lines with the 50% and 90% confidence intervals (solid and thin-solid lines, respectively). The average abundances of the ISM are denoted by the thick-dotted lines. The current observational data are given by large double circles, with other previous data (small circles).

for the solar r-process, implying that these three stars exhibit light r-process elements (Z < 56) produced in more-massive SNe (> IOMQ). The discussion above suggests that the production of the r-process elements is associated with a small fraction of SNe near the low-mass end of the range. Neutrino winds in the explosions of massive stars may face difficulties in being a dominant source of the r-process elements. Wanajo et al. 16 have demonstrated that an r-process in the neutrino winds proceeds from only very massive proto-neutron stars, which might result from massive progenitors such as > 20 — SOM© stars. Hypernovae (> 20 — 25M©)17

145 or pair-instability supernovae (140 — 260M©) 18 , resulting from stars near the high mass-end of the SN progenitors, similar to case (b), are clearly excluded as the major r-process site. We suggest, therefore, that the dominant r-process site is SN explosions of collapsing O-Ne-Mg cores from 8 - 10M Q stars 19 . Recently, Wanajo et al. 6 have demonstrated that the prompt explosion of the collapsing O-NeMg core from a 9M Q star reproduces the solar r-process pattern for nuclei with A > 130, and is characterized by a lack of a-elements and only a small amount of iron-peak elements. This clearly differs from more massive SNe with iron cores (> IOMQ) that eject both these elements, and is consistent with the fact that the abundances of heavy r-process elements in stars with [Fe/H] ~ —3 are not related with those of iron-peak elements or of elements with lower atomic numbers 20 . This study shows the importance of detecting Eu in extremely metalpoor stars to explore the origin of r-process elements. Further observations are needed to confirm the origin.

4. Conclusions We constructed a chemical evolution model, assuming SN induced star formation. Predicted dispersions in [O-Zn/Fe] are compared with observational data. The differences between two sets of yields; N97 and WW95, clearly appear in dispersions. The widths of 50% and 90% confidence regions are determined by stellar mass dependency of SN yields, but are not affected significantly by the mixing length of SNR. Thus, the overestimate in dispersions suggests problems for SN models; Mg and Al for WW95, Ca and Co for N97, and Sc for both models. The abundances of neutron-capture elements like Sr, Ba, and Eu show large dispersions in excess of observational errors. This implies that rprocess yields are highly dependent on the masses of SN progenitors. Using the Subaru HDS, we have estimated Eu abundances of three extremely metal-poor stars with [Fe/H] < — 3 to determine the r-process site. All are found to have sub-solar values of [Eu/Fe]. Comparison with our chemical evolution model of the Galactic halo implies the dominant source of Eu to be the low-mass end of the supernova mass range. Future studies of stars with low Eu abundances will be important to determine the r-process site.

146

References 1. Gilroy, K. K., Sneden, C , Pilachowski, C. A., & Cowan, J. J. 1988, ApJ, 327, 298 2. Norris, J. E., Ryan, S. G., & Beers, T. C. 2001, ApJ, 561, 1034 3. McWilliam, A., Preston, G. W., Sneden, C., & Searle, L. 1995, AJ, 109, 2757 4. Ryan, S. G., Norris, J. E., & Beers, T. C. 1996, ApJ, 471, 254 5. Woosley, S. E., Wilson, J. R., Mathews, G. J., Hoffman, R. D., & Meyer, B. S. 1994, ApJ, 433, 229 6. Wanajo, S., Tamamura, M., Itoh, N., Nomoto, K., Ishimaru, I., Beers, T. C., & Nozawa, S. 2003, ApJ, 593, 968 7. Freiburghaus, C., Rosswog, S., & Thielemann, F. -K. 1999, ApJ, 525, L121 8. Nomoto, K., Hashimoto, M., Tsujimoto, T., et al. 1997a, Nucl. Phys. A, 616, 79 9. Woosley, S. E. & Weaver, T. A. 1995, ApJS, 101, 181 10. Cioffi, D. F., McKee, C. F., & Bertschinger, E. 1988, ApJ, 334, 252 11. Ishimaru, Y. & Wanajo, S. 1999, ApJ, 511, L33 12. Nomoto, K., et al. 1997b, Nucl. Phys. A, 621, 467 13. McWilliam, A. 1998, AJ, 115, 1640 14. Ishimaru, Wanajo, Aoki, & Ryan, 2004, ApJ, 600, L47 15. Arlandini, C., Kappeler, F., Wisshak, K., Gallino, R., Lugaro, M., Busso, M., & Straniero, O., 1999, ApJ, 525, 886 16. Wanajo, S., Kajino, T., Mathews, G. J., & Otsuki, K. 2001, ApJ, 554, 578 17. Maeda, K. & Nomoto, K. 2003, ApJ, in press 18. Heger, A. & Woosley, S, E. 2002, ApJ, 567, 532 19. Wheeler, J. C., Cowan, J. J., & Hillebrandt, W. 1998, ApJ, L493, 101 20. Qian, Y. -Z. & Wasserburg, G. J. 2003, ApJ, 588, 1099

THE

fl-PROCESS:

CURRENT UNDERSTANDING AND F U T U R E TESTS*

YONG-ZHONG QIAN School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA E-mail: [email protected]

Current understanding of the r-process is summarized in terms of the astrophysical sites, the yield patterns, and the role of neutrinos. The importance of observational and experimental tests is emphasized. A number of future tests regarding the above three aspects of the r-process are discussed.

1. Introduction The goal of this contribution is to present a summary of current understanding of the r-process and to suggest a number of observational and experimental tests that can lead to further progress. Three aspects of the r-process will be discussed: the astrophysical sites, the yield patterns, and the role of neutrinos. A more detailed review of recent progress in understanding the r-process can be found in [1]. 2. Astrophysical Sites Despite decades of studies, we still do not have a self-consistent model that can produce the conditions for r-process nucleosynthesis. On the other hand, two major categories of candidate sites have been proposed: corecollapse supernovae (e.g. [2-7]) and neutron star mergers (e.g. [8-12]). A simple argument was made in [13] to favor core-collapse supernovae over neutron star mergers as the major site for the r-process based on observations of abundances in metal-poor Galactic halo stars. This argument was borne out by a detailed numerical study on the chemical evolution of ' T h i s work is supported in part by the US Department of Energy under grants DEFG02-87ER40328 and DE-FG02-OOER41149.

147

148

the early Galaxy [14], which calculated r-process abundances in stars for both core-collapse supernova and neutron star merger models and compared them with data. The basic conclusions from these studies are that observations of metal-poor stars are consistent with r-process enrichment by core-collapse supernovae (see also [15]) but are in conflict with neutron star mergers being the major r-process site. The conclusion regarding neutron star mergers is quite robust so long as the Galactic rate of these events is much lower than that of core-collapse supernovae. For example, with a typical Galactic rate of ~ (100 y r ) _ 1 for core-collapse supernovae and of ~ (105 y r ) - 1 for neutron star mergers, the Fe enrichment of the interstellar medium (ISM) by core-collapse supernovae would be much more frequent than the r-process enrichment by neutron star mergers if the latter were the major r-process site. In this case, stars with very low Fe abundances formed from an ISM where only a few core-collapse supernovae had occurred would have received no contributions from neutron star mergers and therefore, would have no r-process elements such as Eu. This is in strong conflict with the substantial Eu abundances observed in stars having Fe abundances as low as ~ 1 0 - 3 times solar and also with the substantial Ba abundances observed in stars having Fe abundances as low as ~ 1 0 - 4 times solar a (e.g. [16]). These observations can be accounted for only if neutron star mergers could make major r-process contributions at a rate close to that of Fe enrichment by core-collapse supernovae. Such a high neutron star merger rate is very unlikely and it is much more probable that core-collapse supernovae are responsible for both the r-process and Fe enrichment of metal-poor stars. A firm upper limit on the rate of neutron star mergers may be provided by LIGO that is being built to detect gravitational wave signals from such events. In the rest of the discussion, it will be assumed that core-collapse supernovae are the major r-process site. 2.1. Diverse

r-Process

Sources

Assuming that core-collapse supernovae are sources of the r-process elements and Fe, we still have to answer the following questions: (1) Does r-process production vary from event to event? (2) How does r-process production correlate with Fe production? (3) How does r-process and Fe production depend on the progenitors of core-collapse supernovae? These questions will be addressed mostly from the observational side below. a

A t such low metallicities corresponding to early times, only the r-process associated with fast-evolving massive progenitors can contribute to the Ba in the ISM.

149 Several observations support that there are at least two distinct kinds of r-process sources. Meteoritic data on extinct radioactivities in the early solar system indicate that at least some r-process events produce 182Hf but not 1 2 9 I (e.g. [17]). In addition, observations of the metal-poor star CS 22892-052 [18] show that while the elements Ba and above with mass numbers A > 130 closely follow the solar r-process pattern, the elements Rh and Ag with A < 130 fall below the extension of this pattern to the region of A < 130 (see Fig. 1). The r-process pattern in this star is rather close to that in another metal-poor star CS 31082-001 [19] (see Fig. 4). Both the meteoritic data and observations of metal-poor stars indicate that in order to obtain the overall solar r-process pattern, there should be a source producing mainly the heavy r-process nuclei with A > 130 and another producing mainly the light r-process nuclei with A < 130.

_2 1 • i ' I t i 40

I 50

I 60

I 70

I 80

Atomic Number ( Z ) Figure 1. The observed abundances in CS 22892-052 (filled circles with error bars: [18]) compared with the solar r-process pattern (solid curve: [20]) that is translated to pass through the Eu data. The data on the heavy r-process elements from Ba to Ir are in excellent agreement with the translated solar r-process pattern. However, the data on the light r-process elements Rh and Ag clearly fall below this pattern. The abundance of element E is given in the spectroscopic notation log e(E) = log(E/H) + 12, where E / H is the number ratio of E to H atoms in the star.

The relation between production of the heavy r-process nuclei and that of Fe can be inferred by comparing the abundances in the metal-poor stars CS 31082-001 [19], HD 115444, and HD 122563 [21] (see Fig. 2). While

150 the heavy r-process elements closely follow the solar r-process pattern for all three stars, the absolute abundances of these elements differ by a factor of ~ 100. However, the absolute abundances of the elements from 0 to Ge with A < 75 are approximately the same for these stars. This clearly demonstrates that the source for the heavy r-process nuclei in these stars cannot produce any of the elements from O to Ge including Fe (e.g. [22]). The core-collapse supernovae associated with this source may have progenitors of ~ 8-10 MQ, which develop O-Ne-Mg cores with very thin shells before collapse [23, 24]. The supernova shock produces essentially no nucleosynthesis as it propagates through the thin shells. So no elements from 0 to Ge are made. However, production of the heavy r-process nuclei could occur in the material ejected from the newly-formed neutron star (e.g. [25]). This can then explain why these nuclei are not produced together with the elements from O to Ge. In addition, the source for the heavy r-process nuclei in the stars shown in Fig. 2 can also be associated with accretioninduced collapse (AIC) of a white dwarf into a neutron star in binaries [26] as no elements from O to Ge are produced in this case, either.

Atomic Number

Atomic Number

Figure 2. Comparison of the observed abundances in CS 31082-001 (asterisks: [19]), HD 115444 (filled circles), and HD 122563 (squares: [21]). (a) The data on CS 31082-001 are connected with solid line segments as a guide. Missing segments mean incomplete data. The downward arrow at the asterisk for N indicates an upper limit. Note that the abundances of the elements from O to Ge are almost indistinguishable for the three stars, (b) The data on CS 31082-001 to the left of the vertical line are again connected with solid line segments as a guide. In the region to the right of the vertical line, the solid, dot-dashed, and dashed curves are the solar r-process pattern translated to pass through the Eu data for CS 31082-001, HD 115444, and HD 122563, respectively. Note the close description of the data by these curves. The shift between the solid and the dashed curves is ~ 2 dex.

151 Observations show that the late-time light curves of some core-collapse supernovae were powered by decay of 56 Ni to 56 Fe (e.g. [27]). These supernovae have progenitors of > 10 M Q , which develop Fe cores with extended shells before collapse. The supernova shock in this case produces 56 Ni and lighter nuclei through explosive burning in the inner shells. This explosive burning and the hydrostatic burning in the outer shells during the presupernova evolution lead to production of the elements from O to Ni by core-collapse supernovae with progenitors of > 10 M Q . Such supernovae may be associated with the source responsible for mainly the light r-process nuclei (e.g. [22]).

2.2. Tests for r-Process

Sources

The association of r-process sources with different progenitors of corecollapse supernovae can be tested in a number of ways. First, it needs to be shown that a substantial fraction of core-collapse supernovae result from progenitors of ~ 8-10 MQ and AIC events. There are ongoing efforts to identify supernova progenitors by examining the archival images taken with the Hubble space telescope [28, 29]. In one case, a progenitor of ~ 8-10 MQ has been demonstrated [30, 31]. With sufficient statistics to be built up in the future, these efforts will be able to determine the fraction of core-collapse supernovae with low-mass progenitors. Identification of AIC events is more difficult as such events are not expected to have the usual optical display associated with regular supernovae. A firm upper limit on the rate of AIC events may be provided by super Kamiokande and Sudbury Neutrino Observatory, which are capable of detecting the neutrino signals from these events. The strongest evidence so far for association of r-process nucleosynthesis with AIC events was provided by observations of the metal-poor star HE 2148-1247 [32]. The abundances of Fe and lower atomic numbers in this star are typically ~ 10~ 2 times solar. However, the abundances of the neutron-capture elements Ba and above in the star are at the solar level (see Fig. 3). Such high neutron-capture abundances cannot represent the composition of the ISM from which HE 2148-1247 was formed. Instead, they must have resulted from contamination of the surface of this star. As abundances of Ba and above at the solar level must consist of contributions from both the r-process and the s-process (most of the solar Ba came from the s-process while essentially all the solar Eu came from the r-process), the explanation for the observed abundances in HE 2148-1247 requires coordi-

152

nated contamination by both an r-process source and an s-process source. This coordination may be achieved as follows [26]. If HE 2148-1247 had a more massive binary companion of ~ 3-8 M Q , this companion would have produced s-process elements during its evolution and contaminated the surface of HE 2148-1247 with these elements through mass transfer. The companion eventually became a white dwarf, which then collapsed into a neutron star [33] after accreting some material back from HE 2148-1247. The ejecta from the AIC event would again contaminate the surface of this star, but this time with r-process elements. The extremely high contributions from both the s-process and the r-process to HE 2148-1247 can then be accounted for. IIIIIIIIII|IIIIIIIII|IIIIIIIII|IIIIIIIII|IIIIIIIII|IIMIIIII |iiiiiiMi|iiiiinii|iiiy

'Zr

Sr«

Pb

J

I

1

ftr

I

\

Eu 1 CSiml

I

'

'

I

•"!

Th '•'' 70

' 80

|

•••in.'a 90

Atomic Number Figure 3. The observed abundances in HE 2148-1247 (squares with error bars: [32]) compared with the solar abundances (solid curve: [34]). The abundances of Fe and lower atomic numbers in HE 2148-1247 are typically ~ 1 0 - 2 times solar but those of the elements Ba and above are at the solar level. Variations in the radial velocity of HE 2148-1247 have been observed so this star is in a binary [32].

The above AIC scenario has two possible outcomes. If the binary was disrupted by the AIC event, then a single metal-poor star with extremely high neutron-capture abundances would be produced. Indeed, a number of such stars have been observed [35]. On the other hand, if the binary survives, then the metal-poor star with extremely high neutron-capture abundances has a neutron star companion today. The neutron star companion may be revealed through X-ray emission due to its accretion. A number of

153

metal-poor stars with extremely high neutron-capture abundances, including HE 2148-1247, are known to be in binaries. Some loose upper limits on the X-ray emission due to possible neutron star companions of several stars were obtained from archival all-sky data [36]. It would be very interesting to see if dedicated X-ray searches can provide support for the AIC scenario. The best tests for r-process production by core-collapse supernovae would be direct observations of newly-synthesized r-process nuclei in these events. One possibility is to examine the spectra of an event for atomic lines of r-process elements. The lines of Ba were observed in SN 1987A [37-39]. Combined with Fe production inferred from the light curve, this appears to indicate that SN 1987A produced both Fe and Ba. As mentioned in Sec. 2.1, Fe producing core-collapse supernovae may be responsible for mainly the light r-process nuclei with A < 130. So the Ba observed in SN 1987A may represent the heaviest r-process element produced by such supernovae [40]. Clearly, optical observations of supernovae can provide very valuable information on the r-process. Perhaps the most direct test for r-process production is detection of 7-rays from the decay of the unstable progenitor nuclei that are initially produced by the r-process. A number of such nuclei have significant 7-ray fluxes for recent or future supernovae in the Galaxy (e.g. [42, 43]). The most interesting nucleus is 126 Sn with a lifetime of ~ 105 yr. If the Vela supernova that occurred ~ 104 yr ago produced 126 Sn, the 7-ray flux from the decay of this nucleus in the Vela supernova remnant may be close to the detection limit of INTEGRAL [42]. Hopefully, some information on 126 Sn production by the Vela supernova will be provided by INTEGRAL in the near future.

3. Yield Patterns and Role of neutrinos The extensive r-process patterns observed in the metal-poor stars CS 22892052 [18] and CS 31082-001 [19] are shown in Fig. 4. These two rather close patterns cover the elements from Sr to Cd with A = 88-116 and the elements Ba and above with A > 130. Unfortunately, the elements Te and Xe with A ~ 130 cannot be observed in stellar spectra. On the other hand, Te and Xe isotopes have been found in presolar diamonds. It is extremely important to understand the Te and Xe patterns in these diamonds (e.g. [44, 45]) as they may be the only data outside the solar system on r-process production in the region of A ~ 130. According to the meteoritic data, at least some r-process events produce

154 I I I I I I I rTTTt I I I I 1 I I I I I I I

111111111

Os

Ba

Pb

(I

=d

I Nd f e e l Gd-rEr I JDyf YbT

"

*

Ho Rh

Ag

^

Eu

i-i

i i

F

Tb Tm

lu Th

1 , 1

40

• I • i •

50

i

I

60

70

T: 80

Atomic Number ( Z ) Figure 4. The observed abundances in CS 22892-052 (filled circles: [18]) compared with those in CS 31082-001 (open circles: [19]). The open circle for P b is shifted slightly for clarity. Downward arrows indicate upper limits.

182

Hf but not 1 2 9 I. If these events were responsible for the r-process patterns shown in Fig. 4, they must produce the nuclei with A = 88-116 and A > 130 but skip those with A ~ 130. A fission scenario was proposed in [46] to achieve this. In this scenario, the r-process produces a freeze-out pattern covering A > 190 with a peak at A ~ 195 and fission of progenitor nuclei during their decay towards stability produces the nuclei with A < 130 and A > 130 but very little of those with A ~ 130. In addition, fission may be significantly enhanced through excitation of the progenitor nuclei by interaction with the intense neutrino flux in core-collapse supernovae [46, 47]. The above fission scenario also accounts for the difference in the Th/Eu ratio between CS 22892-052 and CS 31082-001 (see Fig. 4) that is difficult to explain by the possible difference in the stellar age [46]. In this scenario, Th represents the progenitor nuclei surviving fission whereas Eu represents the nuclei produced by fission. The Th/Eu ratio would then depend on the fraction of the progenitor nuclei undergoing fission, which would in turn depend on, for example, the extent of neutrino interaction in a specific r-process event. Neutrino interaction can also result in emission of neutrons [48, 49]. In fact, it was shown that the solar r-process abundances of the nuclei with A = 183-187 can be completely accounted for by neutrino-induced neutron

155 emission from the progenitor nuclei in the peak at A ~ 195 [48, 50]. Clearly, to test neutrino-induced nucleosynthesis associated with the r-process requires a lot of nuclear physics input, such as branching ratios of fission and neutron emission for excited neutron-rich nuclei and the associated fission yields. Perhaps some of this input could be studied at future rare isotope accelerator facilities. 0.6

| I I I 1| I I I I | I I I I | I I I I | I I I I | I I I I

0.05 0.5 -

0.03

- 0.02

I_

0.3

111111111

0.01

1

1

ill!

0.4

.

1 '

0.04 E-

0.0 182

,'

f

i

^z

>1 —I 184

0.2

r-- f — i 186

J

188 f i I

t 0.1

I • i i • I i i i i I i i • i I i i i i I

170

175

180

Figure 5. Effects of neutrino-induced neutron emission for the region near the abundance peak at A ~ 195 [48, 50]. The abundances before and after neutrino-induced neutron emission (following freeze-out of the r-process) are given by the solid and dashed curves, respectively. The filled circles (some with error bars) give the solar r-process abundances. The region with A = 183-187 is highlighted in the inset.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

Y.-Z. Qian, Prog. Pari. Nucl. Phys. 50, 153 (2003). S. E. Woosley and E. Baron, Astrophys. J. 391, 228 (1992). S. E. Woosley and R. D. Hoffman, Astrophys. J. 395, 202 (1992). B. S. Meyer et a l , Astrophys. J. 399, 656 (1992). J. Witti, H.-T. Janka, and K. Takahashi, Astron. Astrophys. 286, 841 (1994). K. Takahashi, J. Witti, and H.-T. Janka, Astron. Astrophys. 286, 857 (1994). S. E. Woosley et al., Astrophys. J. 433, 229 (1994). J. M. Lattimer and D. N. Schramm, Astrophys. J. 192, L145 (1974). J. M. Lattimer and D. N. Schramm, Astrophys. J. 210, 549 (1976).

156 10. E. Symbalisty and D. N. Schramm, Astrophys. Lett. 22, 143 (1982). 11. B. S. Meyer, Astrophys. J. 343, 254 (1989). 12. C. Freiburghaus, S. Rosswog, and F.-K. Thielemann, Astrophys. J. 525, L121 (1999). 13. Y.-Z. Qian, Astrophys. J. 534, L67 (2000). 14. D. Argast et al., Astron. Astrophys. 416, 997 (2004). 15. Y. Ishimaru and S. Wanajo, Astrophys. J. 511, L33 (1999). 16. A. McWilliam et al., Astron. J. 109, 2757 (1995). 17. G. J. Wasserburg, M. Busso, and R. Gallino, Astrophys. J. 466, L109 (1996). 18. C. Sneden et al., Astrophys. J. 533, L139 (2000). 19. V. Hill et al., Astron. Astrophys. 387, 560 (2002). 20. C. Arlandini et al., Astrophys. J. 525, 886 (1999). 21. J. Westin et al., Astrophys. J. 530, 783 (2000). 22. Y.-Z. Qian and G. J. Wasserburg, Astrophys. J. 567, 515 (2002). 23. K. Nomoto, Astrophys. J. 277, 791 (1984). 24. K. Nomoto, Astrophys. J. 322, 206 (1987). 25. S. Wanajo et al., Astrophys. J. 593, 968 (2003). 26. Y.-Z. Qian and G. J. Wasserburg, Astrophys. J. 588, 1099 (2003). 27. J. Sollerman, New Astron. Rev., 46, 493 (2002). 28. S. D. Van Dyk, W. Li, and A. V. Filippenko, Pub. Astron. Soc. Pac. 115, 1 (2003). 29. S. J. Smartt et a l , Mon. Not. R. Astron. Soc. 343, 735 (2003). 30. S. D. Van Dyk, W. Li, and A. V. Filippenko, Pub. Astron. Soc. Pac. 115, 1289 (2003). 31. S. J. Smartt et al., Science 303, 499 (2004). 32. J. G. Cohen et al., Astrophys. J. 588, 1082 (2003). 33. K. Nomoto and Y. Kondo, Astrophys. J. 367, L19 (1991). 34. E. Anders and N. Grevesse, Geochim. Cosmochim. Acta 53, 197 (1989). 35. G. W. Preston and C. Sneden, Astron. J. 122, 1545 (2001). 36. E. M. Schlegel, Astron. J. 125, 1426 (2003). 37. R. E. Williams, Astrophys. J. 320, L117 (1987). 38. R A. Mazzali, L. B. Lucy, and K. Butler, Astron. Astrophys. 258, 399 (1992). 39. P. A. Mazzali and N. N. Chugai, Astron. Astrophys. 303, 118 (1995). 40. Y.-Z. Qian and G. J. Wasserburg, Astrophys. J. 559, 925 (2001). 41. T. Tsujimoto and T. Shigeyama, Astrophys. J. 561, L97 (2001). 42. Y.-Z. Qian, P. Vogel, and G. J. Wasserburg, Astrophys. J. 506, 868 (1998). 43. Y.-Z. Qian, P. Vogel, and G. J. Wasserburg, Astrophys. J. 524, 213 (1999). 44. U. Ott, Astrophys. J. 463, 344 (1996). 45. S. Richter, U. Ott, and F. Begemann, Nature 391, 261 (1998). 46. Y.-Z. Qian, Astrophys. J. 569, L103 (2002). 47. E. Kolbe, K. Langanke, and G. M. Fuller, Phys. Rev. Lett. 92, 111101 (2004). 48. Y.-Z. Qian et al., Phys. Rev. C55, 1532 (1997). 49. K. Langanke and E. Kolbe, Atom. Data Nucl. Data Tables 79, 293 (2001). 50. W. C. Haxton et a l , Phys. Rev. Lett. 78, 2694 (1997).

N U C L E A R R E A C T I O N RATES A N D T H E P R O D U C T I O N OF LIGHT P-PROCESS ISOTOPES IN FAST E X P A N S I O N S OF P R O T O N - R I C H M A T T E R

G. C. J O R D A N , IV*AND B . S. M E Y E R Department

of Physics and Astronomy, Clemson University, Clemson, SC 29634-0978, USA E-mail: [email protected]

We study nucleosynthesis in rapid expansions of proton-rich matter such as might occur in winds from newly-born neutron stars. For rapid enough expansion, the system fails to maintain an equilibrium between neutrons and protons and the abundant 4 He nuclei. This leads to production of quite heavy nuclei early in the expansion. As the temperature falls, the system attempts to re-establish the equilibrium between free nucleons and 4 He. This causes the abundance of free neutrons to drop and the heavy nuclei to disintegrate. If the disintegration flows quench before the nuclei reach the iron group, a distribution of p-process nuclei remains. We briefly discuss the possibility of this process as the mechanism of production of light p-process isotopes (specifically 9 2 Mo, 9 4 M o , 9 6 R u , and 9 8 R u ) , and we provide a qualitative assessment of the impact of nuclear reaction rates of heavy, proton rich isotopes on the production of these astrophysically important nuclides.

1. Introduction The precise mechanism for the production of the light p-process nuclei, 92 94 ' Mo and 96 ' 98 Ru, remains mysterious. The heavier p-process nuclei are typically only ~ 1% as abundant as their s-process and r-process counterparts. They are successfully accounted for by the "gamma-process", which occurs when pre-existing heavy nuclei are heated to TQ — T/(10 9 K) of between 2-3 and cooled rapidly 1 . Disintegration flows drive the nuclei to iron, but, if the expansion is sufficiently rapid, quench before reaching their target. This leaves a distribution of proton-rich isotopes. If ~ 1% of heavy nuclei have been exposed to such a processes, we may understand •http://www.ces.clemson.edu/~gjordan

157

158 the abundance of the heavy p-process nuclei. By contrast, any process that successfully produces the heavy p-process nuclei will underproduce the light ones. This is because, unlike the heavy pprocess nuclei, the light p-process isotopes are nearly as abundant as their r-process and s-process counterparts. This suggests some other process than the "gamma-process" may be responsible for their origin (although questions remain about the need for an exotic site 2 ). Suggested other sites or processes are thermonuclear supernovae 3 , alpha-rich freezeouts in corecollapse supernovae 4,5 , or the rp-process 6 . Each of these processes or sites has its own difficulties in either producing the right isotopes or actually ejecting them into interstellar space, and the question of the site of origin of the light p-process nuclei remains. In this paper we explore the possibility that the light p-process isotopes may be made in very fast expansions of proton-rich matter. Although other sites may be possible, the setting we envision is a neutrino-driven wind from a high-mass proto-neutron star early in its epoch of Kelvin-Helmholtz cooling by neutrino emission. Some calculations find wind expansion timescales (which we here define as the density expansion timescale |^^f | _ 1 ) as short as a millisecond7. The Ye, that is, the electron-to-baryon ratio, in these winds is set by the interaction of neutrinos and antineutrinos with free nucleons. While the antineutrino spectrum from the neutron star is considerably harder than the neutrino spectrum at late times, which tends to make the wind neutron rich, it is possible that the two spectra are more nearly equal earlier. This could allow for proton-rich (that is, Ye > 0.5) matter since the lower mass of the proton would favor the reaction ue+n -» p + e~ over the reaction ue + p —> n + e+. Normally, fast expansions of proton-rich matter would simply undergo an alpha-rich freezeout and produce iron-group isotopes. For sufficiently fast expansions with high enough entropy, however, the nucleosythesis enters a new regime in which free neutrons and protons are not in equilibrium with the abundant 4 He nuclei. Such expansions can produce neutron-rich nuclei heavier than iron and nickel even in matter with Ye very close to or even exceeding 0.5 8 . In the present paper, we demonstrate the possibility of producing p-process nuclei in such expansions and explore the effect of nuclear reaction rate changes on the resulting yields. We will present a much more complete discussion of these ideas elsewhere9. In section 2 we define the details of our calculations. We present the results of our calculations in section 3 and an analysis of the nucleosynthesis and the effect of reaction rates in 4. We finish with some concluding remarks

159 in section 5. 2. Calculations Our model of the expansion of matter occurring in the fast winds is based on the previous fast expansion calculations of Meyer 8 and similarly uses the Clemson Nucleosynthesis Code 10 with NACRE u and NON-SMOKER 12 rate compilations. In our calculations, material expands adiabatically from high temperature and density. In the expansion, the density initially declines exponentially with a timescale of r = 0.001 s and then merges over to a flow in which the density falls off as the inverse square of the time. To a reasonable approximation, such an expansion models a neutrino driven wind initially accelerating as it leaves the surface of a nascent neutron star and then evolving to a constant outflow velocity. The material was given an initial temperature of Tg — 10.0 and an initial density consistent with an entropy per baryon of s/fcg = 150. Each calculation began with a mixture of neutrons and protons giving an initial value of Y e =0.510. The calculations were allowed to run until the neutron abundance fell below 1.0 • 1 0 - 2 5 . For the purposes of demonstrating the importance of the reaction rates between heavy nuclei in fast expansions, we also performed a crude reaction rate study on our model. Our study consisted of four calculations. The first was a calculation using the standard set of reaction rates. The second calculation uniformly increased (at all temperatures) all of the Strong and Electromagnetic reaction rates by 3/2 for nuclei with atomic number, Z, greater than 27. The third calculation increased the standard values of the same set of reaction rates as in the the second calculation (Strong and EM rates of nuclei with Z greater than 27) by a factor of 2/3. Finally, the fourth calculation multiplied all of the Strong and Electromagnetic reaction rates for nuclei with Z greater than 39 by factor of 3/2. We will refer to these calculations as A), B), C), and D) respectively. 3. Results Table 1 presents the top ten overproduction factors in each of our four calculations. Column A) lists the overproduction factors from calculation A). The bulk of the yields from this calculation, as seen in Figure 1, panel A), are nuclei having a mass number, A, up to 120, and with the most overproduced isotopes between A « 100 to 110. Notice that two the isotopes of interest, 9 8 Ru and 94 Mo, were overproduced by factors of 106 and 10 5 . Though they did not make the list, 96 Ru was overproduced by a factor 104

160 Table 1.

List of top 10 overproductions in our calculations

A A

Z

1

102pd

2

108

3

98

4

106

5

104pd

6

112

Cd

Ru Cd

B

A

z

Cl

C

A

1.28 • 10 6

5.12- 10 1

96

Ru

8.78' 10 5

3.40- 10

1

95

Mo

3.21 • 10 5

Co

1.88- 10

1

92

Mo

7.58' 10 4

°Cr

1.82- 10 1

84

Sr

3.30 10 4

1.41- 10

1

93

Nb

1.58' •10 4

1

78

Kr

1.55 •10 4

Xe

1.37- 10

4.56- 10 6

124

Xe

6.54. 10 6

49Ti

1.84- 10

6

132

Ba

6.27. 10

6

60Ni

1.65- 10

6

130

Ba

5.59. 10

6

s9

9.21- 10 s

138

Ce

5.55- 10 6

112

Sn

6

4.57- 10

3.70. 10 3.18' 10

5

136

Ce

2.17 • 10

8

110

Cd

3.07 •10 5

128

Xe

1.38 •10 6

9

94

Mo

1.97' 10

5

113

1.95 •10

5

10

Mo

126

Sn iooRu

113In

O

6

5

7

z

45

7

144

In

Sm

2.23- 10

1.16 • 10 9.90 •10

5

5

A 94

z

CI

D

63

Sc

Cu

CI 1.31- 10

2

6

46Ti

1.25- 10

48Ti

7.18 • 10°

97

Mo

8.54 •10 3

6

44

6.85- 10°

98

Ru

4.56 •10 3

6.32 10°

91

43

Ca Ca

Zr

3.58 •10 3

Note: Column A contains the top 10 overproduced isotopes from the calculation using the standard set of reaction rates. Column B and C contain data from the calculations using the set of reaction rates in which Strong and Electromagnetic rates for isotopes with Z greater than 27 are multiplied by 2/3 and 3/2 respectively. Column D contains data from the calculation with the standard reaction rates are multiplied by 3/2 for isotopes with Z greater than 39.

while 92 Mo was only overproduced by a factor of 100. This calculation is intriguing because of the large overproduction factors of the light p-process isotopes (except for 92 Mo in this calculation). Panel B) of Figure 1 shows the results of calculation B), where the Strong and Electromagnetic rates for isotopes with Z greater than 27 are multiplied by a factor of 2/3. In this Figure we see that heavier nuclei (up to A of 150) are produced in calculation B) than in calculation A). Column B) of Table 1 shows this as well. The most overproduced isotopes have A w 120 to 140. The light p nuclei are produced in this calculation as well and have overproduction factors between 100 and 10 4 , though they are by no means the most overproduced isotopes. The key point of this calculation is that by forcing the reactions involving the heavy nuclei above the iron group to take a little longer, heavier nuclei are produced than when compared with the calculation using the standard set of reaction rates. Comparing the yields of calculation C) in panel C) of Figure 1 to the yields of the other three calculations reveals that calculation C) produces considerably lighter nuclei. It is interesting to note that calculation C)

161 B) Z > 27 Strong and EM Rotes X 2 / 3

A) Standard Rates

-

O"5

-10

-15

1I T ' I W

\ :

1 . V \ {Atomic Moss Number)

C) Z > 27 Strong ond EM Rates X 3 / 2

100 A (Atomic Mass Number)

A {Atomic Moss Number)

Figure 1. Abundance vs. A for the four calculations.

closely resembles an alpha-rich freezeout given the concentration of nuclei around the iron peak. In fact, C) has no significant yield of isotopes over A « 60. Panel C) of Figure 2 is also revealing in the lack of production of isotopes above Z as 32, which is close to our reaction rate modification line of Z = 28. We thus see that by increasing the reaction rates for nuclei above the iron peak, the resulting calculation produces an alpha-rich freezeout type abundance pattern with no nuclei above mass 60 and a sharp decline in the production of nuclei with Z > 30. Finally, the best results for the light p-process isotopes came from calculation D). Panel D) of Figure 1 shows a pronounced mass peak between A of 90 and 100, which is where the light p isotopes of interest (or their progenitors) are produced. We also point out the drop at A = 100, after which, no nuclei are produced. Panel D) of Figure 2 tells the same story. We see a build up of nuclei, reaching a maximum at Z = 44, then a sharp decline. By Z = 50, the number of nuclei produced is negligible. Again, we see that by increasing the reaction rates among the heavier nuclei (in this case, those with Z > 39) dramatically reduces the yield of those nuclei.

162 A) Standard Rates

B) Z > 27 Strong and EM Rotes X 2 / 3

Z (Atomic Number)

Z (Atomic Number)

Figure 2. Abundance vs. Z for the four calculations.

4. Discussion Drawing from the observations of section 3 we discuss the process by which nuclei are produced in these fast expansions as well as summarize the effects of the reaction rate modifications on this process. The mechanism that produces heavy nuclei in these fast expansions is best explained in terms of a system descending the hierarchy of statistical equilibria. All four of the calculations begin with Tg = 10. At such a high temperature, reaction rates are much faster than the expansion, and the nuclei arrange themselves into a nuclear statistical equilibrium (NSE) population. As the matter expands and the temperature falls, reaction rates slow. In this case, one would normally expect an expansion to produce a smooth transition from NSE to a QSE in which the only restriction is the conservation of the total number of heavy nuclei (henceforth referred to as QSE/j). This is because the first reactions to become too slow to maintain NSE are the three body reactions that produce heavy nuclei. In the present calculations, however, the entropy is so high and the expansion so fast that the abundances of the light nuclei 3 H and 3 He are very low. In this case, because the initial buildup of 4 He in the system is via reaction flows through these isotopes, the system is unable to maintain an equilibrium between neutrons and protons and 4 He.

163 Figure 3 shows this clearly. When the ratio in the Figure is equal to 1, the protons, neutrons, and 4 He are in equilibrium with each other. As the temperature falls below T9 « 9, the system is expanding too quickly to keep pace with the equilibrium amount of 4 He. Because the neutrons and protons are not getting locked into 4 He as quickly as equilibrium demands, there is an excess of free neutrons and protons over the equilibrium (NSE or QSE/i) abundances. In this way, the expansion is more reminiscent of big bang nucleosynthesis than of typical stellar freezeout expansions.

'

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Figure 3. R a / R p R ^ vs. Tg for the four calculations. Note that all four lines overlap down to Tg of 5.

As 4 He is produced in the attempt by the system to reach equilibrium, the system is also converting the 4 He into heavier isotopes. Because of the oversupply of neutrons and protons, these isotopes have large values of A relative to NSE or QSE^ expectations. As the temperature falls to near T9 = 5, however, the abundance of heavy nuclei begins to become large enough to catalyze the equilibrium between neutrons and protons and 4 He via reaction cycles such as 56 Ni(n, 7) 57 Ni(n, 7) 58 Ni(p, 7) 5 9 Cu(p, a) 5 6 Ni. This drives the neutron and proton abundances back toward equilibrium with the 4 He abundance, which leads to a dramatic reduction in abundance of free neutrons. Once this happens, heavy nuclei are no longer

164 supported against rapid disintegration, and nuclear flows carry them back down towards iron-group nuclei. This phase is reminiscent of "gamma process" nucleosynthesis1; however, in the present case, the seed nuclei for the disintegration were built up at an earlier stage of the expansion. The disintegration flow will reach the iron-group nuclei if it begins early enough. Otherwise, the flow will stop with an appreciable abundance of intermediate-mass, proton-rich nuclei. The final phase of the process involves the capture of free protons on the heavy nuclei. Due to the large abundance of protons at the end of the expansion, they are able to capture onto the heavy nuclei produced earlier in the expansion. These proton captures play two roles towards the end of the calculation. First, they provide an upward "pressure" keeping the nuclei from flowing down to the iron peak. Second, many (p,7)-(7,p) equilibria are set up, increasing the final Y e of the heavy nuclei produced. The effect of the proton captures can be either large or small depending on the initial parameters (entropy, expansion time-scale, Y e ) of the expansion. We begin our comparisons of the four calculations at Tg = 5. This is the point at which the equilibrium between the neutrons and protons and 4 He is being re-established and at which the system attempts to move all of its heavy nuclei down to the iron peak. Calculation C) comes closest to achieving this. Because of the enhanced rates for the reaction cycles, the equilibrium between neutrons and protons and 4 He (and the concomitant QSEft) is fully restored; thus, disintegration flows almost fully convert the very heavy nuclei to nuclei near the iron peak in C). The opposite effect is seen in calculation B). In this case, the reaction rates have been reduced, which delays the effect of the reaction cycles in restoring the QSE/j until the temperature is too low for this restoration to be fully effective. As a consequence of the slowed reaction rates, the abundance of heavy nuclei is spread up to a mass number of 150, close to the abundance pattern before the disintegration flows began in earnest. Remarkably, although there is less than an order of magnitude difference in this set of reaction rates and that in C), the effects on the final yields is very pronounced. Calculations A) and D) are in between the two extremes of B) and C). These calculations are able to transport their heavy nuclei closer to iron group, but do not quite make it. Calculation A) is similar to B) in that it never reaches QSE . It is able, however, to move its heavy nuclei below A — 135. Calculation D) is more effective at moving its nuclei than A). Though D) never reaches QSE/j either, Figure 3 shows an increase in the

165 ratio Ra/RlR2n from T9 of 4 to 3. This signals the system's attempt to reach QSE/j accompanied by the disintegration of nuclei towards the iron group. The fact that the flow of nuclei towards the iron peak stalls at N — 50 allows for the overproduction the of light p-process isotopes and makes these isotopes the most overproduced by the system. Notice that increasing the reaction rates above Z = 39 helped move the nuclei down towards the iron group more effectively than the standard set of reaction rates alone could do. This is because the disintegration flows begin at a higher temperature with the faster rates.

5. Conclusion To summarize, we see that fast expansions can produce heavy nuclei and that the character of the yield of these expansions is very sensitive to reaction rates. The method by which these expansions produce heavy nuclei begins with the system achieving NSE after which, the temperature rapidly falls removing the system from NSE and simultaneously begins to produce heavy nuclei. As the temperature reaches Tg » 5, the system attempts to establish QSE/j. If it is successful, the expansion produces an alpharich freezeout type abundance pattern. If the system is not successful, the yields are more or less evenly spread over a wide range of mass numbers. If the system manages to move the nuclei close to the iron group but stalls, the nuclei can pile up at the stall point. As we saw, this is crucial in the production of the light p-process nuclei. Further work on this scenario is clearly needed. First, we must establish its astrophysical plausibility and setting. In particular, it remains to be seen whether supernovae attain the requisite entropies, timescales, and Ye 's. Interestingly, because winds from proto-neutron stars may evolve from slightly proton rich to neutron rich with time, p-process and r-process nucleosynthesis may occur in the same site with the former preceding the latter by a few tenths of a second, the timescale on which the neutrino and antineutrino spectra are changing 7 . Second, it is evident that the wide range of abundance patterns produced for such modest changes in the reaction rate values means that the yields from this process are sensitive to many reaction rates between heavy nuclei on the proton rich side of stability. A full reaction rate study will be needed to identify reaction rates important to the production of light p isotopes in this process. We hope that both theoretical efforts will motivate many new experiments with proton-rich radioactive ion beams.

166 Acknowlegdment s This work was support by N S F grant AST98-19877 and by grants from NASA's Cosmochemistry P r o g r a m and D O E ' s SciDAC program. References 1. S. E. Woosley and W. M. Howard, Astrophys. J. Suppl., 36, 285 (1978). 2. V. Costa, M. Rayet, R. A. Zappala, and M. Arnould, Astron. Ap, 358, 67 (2000). 3. W. M. Howard, B. S. Meyer and S. E. Woosley, Astrophys. J. Lett, 373, 5 (1991). 4. G. M. Fuller and B. S. Meyer, Astrophys. J., 453, 792 (1995). 5. R. D. Hoffman, S. E. Woosley and B. S. Meyer, Astrophys. J., 460, 478 (1996). 6. H. Schatz et al., Phys. Rev. Lett, 86, 3471 (2001). 7. T. A. Thompson, A. Burrows and B. S. Meyer, Astrophys. J., 562, 887 (2001). 8. B. S. Meyer, Phys. Rev. Lett, 89, 231101 (2002). 9. G. C. Jordan, IV. and B. S. Meyer, Astrophys. J. Lett, in preparation (2004). 10. B. S. Meyer, Astrophys. J. Lett, 449, 55 (1995). 11. C. Angulo et al., Nucl. Phys. A, 656, 3 (1999). 12. T. Rauscher and F.-K. Thielemann, At. Dat Nucl. Dat Tables, 75, 1 (2000).

r-PROCESS N U C L E O S Y N T H E S I S IN PROTO-MAGNETAR WINDS

T O D D A. T H O M P S O N * Astronomy Department & Theoretical Astrophysics Center The University of California, Berkeley, Ca, 94720 E-mail: [email protected]. edu

The astrophysical origin of the r-process nuclei is unknown. Because of their association with supernovae and intrinsic neutron-richness, protoneutron star winds are considered as a likely candidate site for production of the r-process nuclei. However, most models of winds from "canonical" neutron stars with mass of 1.4 M Q and radius of 10 km fail to generate the heaviest r-process nuclei. In this proceedings we provide a brief review of the protoneutron star wind scenario and discuss the emergence of these outflows in the context of fully dynamical models of successful core-collapse supernovae. That standard models fail motivates an exploration of more extreme neutron star environments. We address some issues surrounding winds from highly magnetic (Bo •> 10 15 G) protoneutron stars ('proto-magnetars'), including magnetic trapping of wind material and entropy amplification. We further speculate on the role of rapid rotation in this context and the resulting nucleosynthesis.

1. Introduction The rapid neutron capture (r-)process is a mechanism for heavy element nucleosynthesis that accounts for roughly half of all nuclei above the iron group, with characteristic abundance peaks at A ~ 80, 130, and 195 [1,2]. Although the nuclear physics of r-process nucleosynthesis is well understood, the site in nature for production of these nuclides, the astrophysical seat of the r-process, is unknown (for a review, see Ref. 3). The post-explosion Kelvin-Helmholtz cooling phase of protoneutron star (PNS) evolution, lasting tens of seconds after explosion [4,5], is accompanied by a neutrino-driven outflow [6,7]. Neutrino interactions in the tenuous outer layers of the hot, extended PNS atmosphere drive a wind analogous to the thermally-driven Parker wind model for the Sun [8]. Because of its * Hubble Fellow

167

168 intrinsic neutron richness, characteristic mass loss rates, and association with supernovae, this outflow has been considered a leading candidate as the astrophysical site for production of the r-process nuclei [6,9-15].

2. P r e l i m i n a r i e s In the r-process, seed nuclei capture neutrons on timescales shorter than those for /? decay. Nucleosynthesis proceeds well to the neutron-rich side of the valley of /? stability. For large enough neutrino-to-seed ratio (n/s ~ 100/1) the r-process succeeds and nuclei up to and beyond the third abundance peak (A ~ 195) may be formed. In a given astrophysical environment, the r-process subsides as the neutron flux abates, and the very neutron-rich nuclei formed decay to their primary stable isobar. The n/s ratio at the start of the r-process in a given astrophysical environment depends on three quantities at the start of seed formation: the electron fraction (the number of electrons per baryon, Ye), the entropy (5), and the dynamical timescale (TDyn) [16,17]. All else being equal, higher S, lower Ye, and shorter TDyn imply larger n/s ratio (for a review, see Ref. 18). The standard picture for r-process nucleosynthesis in PNS winds is as follows. The supernova explodes, driving a ~ 10 51 erg explosion into the massive progenitor star within ~ 0.1 — 0.5 seconds after core collapse. The newly-born PNS cools and contracts, radiating its gravitational binding energy in neutrinos. The pressure in the region between the PNS and the supernova shock decreases as the shock moves outward and the wind, powered by neutrino heating, emerges into the post-shock ejecta. The PNS surface (Rv > 10 km, the radius of neutrino decoupling, defined by the condition r„ ~ 2/3, where TV is the neutrino optical depth, an energy- and species-dependent quantity) is hot (temperatures of ~ 5 MeV) and has a low electron fraction (Ye(Ru) ~ 0.1) and entropy (S(Rl/) ~ 10 ks baryon - 1 ). The matter there is composed of relativistic charged leptons, free nucleons, and trapped photons. As the wind is driven outward by neutrino heating, the matter descends a gradient in density and temperature. The wind material is heated only within the first ~50km, primarily via the chargedcurrent absorption processes on free nucleons ven —> pe~ and uep —» ne+, and its entropy increases concomitantly. As the temperature of the matter drops below ~ 1 MeV, nucleons combine into alpha particles, neutrino heating ceases, and the material expands adiabatically with entropy SQQ. These charged-current processes also set the electron fraction as the seed nuclei form. As the matter expands away from the PNS surface and the chemical

169 equilibrium between ve and De neutrinos obtained near the neutrinosphere (Rv) is broken, the flux and energy density of the electron-type neutrino species determine the electron fraction [10]. Typically, within 10 km of the PNS surface Ye asymptotes to Ye°°. At a temperature of ~0.5 MeV (a radius in most spherical models of ~100km) a particles combine with the remaining free neutrons in an a-process to form seed nuclei [19]. At this location in the temperature profile, the dynamical timescale is determined by Trjyn = r/v\T=Q 5 M e V , where v is the wind velocity. Simply stated, short TDyn is favored for the r-process because for faster expansion there is less time to build seed nuclei, and, hence, the n/s ratio is preferentially larger, all else being equal. When the wind material finally reaches a temperature of ~0.1 MeV (at a radius of several hundred kilometers) the r-process may begin if the n/s ratio, as set by Y£°, Soo, and TDyn, is sufficiently high. 3. Wind Emergence In Ref. 6, models of supernovae were calculated including collapse, explosion, and the Kelvin-Helmholtz phase. Their calculations generated a very subsonic outflow and, at late times, the necessary thermodynamical conditions for robust r-process nucleosynthesis. The fact that the flow was subsonic increased both TDyn and Soo of the outflow material, relative to a transonic solution. Subsequent models of winds find much lower S ^ (typically a factor of ~ 3 — 5) and conditions unfavorable for r-process nucleosynthesis [9-15, but see Ref. 21]. The difference between the steadystate models typified by Ref. 10 and those of Ref. 6, is that the former tacitly assumed a transonic wind, a whereas the latter attained only very subsonic velocities. The issue is one of pressure. If a wind attempts to emerge into a region with large asymptotic thermal pressure, only a subsonic breeze can be obtained, not a fully transonic wind. Conversely, for vanishing asymptotic pressure and time-independent boundary conditions, if an outflow forms at all, it uniquely picks out the transonic solution, the matter flowing smoothly through the sonic point (iconic where v = cs and cs is the local adiabatic sound speed) . b The emergence of the wind on a timescale of just a fraction of a second a A transonic wind is an outflow whose velocity profile contains a sonic point, where the matter velocity is equal to the local adiabatic sound speed. This characteristic distinguishes a wind solution and a breeze solution, the latter being a flow that is subsonic everywhere. For a review of stellar wind theory, see Ref. 22.

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after the supernova has attained positive velocities, into the post-shock matter is a problem that can be addressed with dynamical models [6,7]. Before appealing to our numerical solution, let us first identify the relevant scales. We define a boundary pressure, Pbound, which represents the thermal pressure of the matter behind the shock at a given point in time as it attains positive velocities in a successful supernova model. We further define the thermal pressure at the sonic point, PSOnic, in a transonic neutrino-driven wind solution that ignores Pbound entirely. We assert that the relevant dimensionless quantity that determines whether or not a given Outflow b e c o m e s t r a n s o n i c is t h e r a t i o P S O nic/Abound- If Psonic/Pbound ^

1,

then the boundary pressure is negligible and a transonic wind obtains. If Psonic/Pbound i$ 1> then only a subsonic outflow is possible. The early evolution of Pbound as the supernova shock is launched can be estimated. Assuming adiabatic expansion of the just-post-shock matter between radii P i and R2, Pbound, 1 /Pbound, 2 ~ (P2/P1) 3 4, where the exponent depends on whether free nucleons or relativistic leptons dominate the pressure. Shock velocities in our exploding models are typically > 109 cm s _ 1 at 1000 km. Thus, the timescale for the shock to move by a factor two, which implies a decrease in Pbound by an order of magnitude, is < 100 ms. This timescale is short compared to the timescale required for the neutrino luminosity and neutrinosphere to change significantly (the Kelvin-Helmholtz timescale, TKH, which in this early phase is close to ~ 1 second). Because Psonic evolves on TKH, it is roughly constant on the timescale for Pbound to decrease. This allows for the ratio PSOnic/Pbound to increase dramatically on a timescale short compared to TKH and it is for precisely this reason that a transonic or near-transonic wind should develop robustly in successful models of core-collapse supernovae. In Fig. 1 we provide two snapshots of the velocity profile (solid lines) in a representative exploding model taken from the simulations of Ref. 20. This simulation includes rapid rotation in an approximate way and viscous dissipation of shear energy. In this model inclusion of this additional source of energy deposition is sufficient to generate an explosion [20]. For comparison, in Fig. 1 we also include the sound speed profile. The two snapshots are separated by ~100 ms in time, the shock moving from approximately 750 km to 2000 km. The large dot at ~850 km marks the sonic point and wind emergence. Profiles of entropy, mass loss rate, and electron fraction all show that a quasi-steady-state solution, quantitatively similar to that expected from the models of Ref. 15 and the analytic estimates of Ref. 10 is obtained. The estimates for the evolution of Pbound and Psonic and the

171 condition for wind emergence, that Psonic/ftound > 1, are borne out in all of the successful exploding models of Ref. 20. At the end of this calculation, just 100 ms after the second snapshot in Fig. 1, the mechanical power of the wind is > 1050 erg s _ 1 . Unfortunately, we are only able to follow the wind and shock evolution for a short period of time in these calculations. Wind calculations that follow the evolution of the PNS during the entire Kelvin-Helmholtz cooling phase must be constructed to understand the full dynamics.

I—I-£J

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Figure 1. Matter velocity and adiabatic sound speed at two snapshots during explosion. Note the development of the sonic point on a timescale of ~ 100 ms. This figure has been reproduced here from Ref. 20.

4. Magnetic Fields & Rotation Non-rotating non-magnetic (NRNM) models of winds from 1.4 M Q 10 km PNSs fail to generate the heaviest r-process nuclei [9-15] (but, see R,efs. 6 and 21). For this reason we are motivated to consider some issues potentially important to winds from highly magnetic (B0 > 10 15 G) and rapidly rotating (P ~ 1 ms) PNSs (or, 'proto-magnetars') [23,24,25].

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4.1. High Magnetic

Fields

In NRNM models, higher entropy is obtained for higher PNS mass and smaller PNS radius. This is because, all else being equal, as the depth of the gravitational well increases a given mass element composing the wind spends more time in the heating region. This leads to higher entropy and more favorable conditions for the r-process. Magnetic fields may behave analogously, forcing matter to dwell longer in the heating region as a result of magnetic trapping [26]. Simple comparisons between the thermal pressure of NRNM PNS winds and magnetic energy density show that for magnetar-strength surface fields (B0 ~ 10 15 G), the wind is magnetically dominated [26]. Although the wind is asymptotically dominated by the kinetic energy of the outflow, very near the surface of the PNS, within several PNS radii, the field may form closed magnetic loops, trapping material that would otherwise escape. The material trapped in these closed or tangled loops is not trapped permanently; the material continues to be heated by the neutrino radiation field and its thermal pressure increases. The trapped matter's thermal pressure eventually exceeds the local magnetic energy density and it escapes dynamically. For specific neutrino heating rate qu, the trapping timescale is Ttrap ~ (B2/8ir — P)/(pqv). The increase in pressure via energy deposition is accompanied by an increase in entropy (As ~ qvT~trap/T). For Bo ~ 1015 G, estimates show that this increase in entropy from magnetic trapping is large enough to yield 3 rd -peak r-process nucleosynthesis; the factor of ~ 3 — 5 in entropy lacking in NRNM models might be attained [26]. This argument implies that magnetars, or neutron stars born with magnetar-like surface field strengths, may be responsible for the production of the r-process nuclides. We must then consider the birth rate of such objects and the amount of r-process material ejected per event. The magnetar birth rate is as yet very uncertain [27], but may be as high as tens of percent of the total neutron star birth rate. This is of particular importance when considering the total r-process budget and the relative scatter of representative r-process nuclei in calculations of galactic chemical evolution [28,29]. There are host of other effects in proto-magnetar winds that might effect their nucleosynthesis. For example, any phenomenon that disrupts closed magnetic loops on a timescale shorter than Ttrap will undermine the entropy amplifications estimated above [26]. Convection below the PNS surface, driving a magnetic dynamo and the emergence of magnetic flux

173 from the PNS surface may do just that [23,24]. Any MHD instabilities or shearing motions caused by, for example, rotation, may disrupt these closed field lines as well. In addition to neutrino heating, protomagnetar winds may have other wind driving mechanisms, including energy deposition via magnetic reconnection and momentum deposition by Alfven waves launched at the protomagnetar surface. Lastly, and perhaps most importantly, there are theoretical grounds for believing that neutron stars with magnetar fields must be borne with rapid rotation [23,24]. How are the dynamics of protomagnetar winds affected when spin periods approach ~ 1 ms? 4.2. Rapid

Rotation

The basic physics of the evolution of winds from rapidly rotating highly magnetic neutron stars has recently been explored [30]. The combination of magnetic and centrifugal forces can have important consequences for the wind dynamics and the rotational evolution of the protomagnetar as in analogous models for stellar winds [31,32,30]. Strong magnetic fields force wind mass elements to corotate with the neutron star surface out to the Alfven point RA- If fi = P/2ir is the angular velocity of the protomagnetar and vu is the asymptotic velocity attained in NRNM wind models, magneto-centrifugal slinging dominates neutrino energy deposition as a driving mechanism if RA& > vv. If the surface magnetic field is strong enough so that RA is greater than the sonic radius, iconic, and if RVQ, > cs(R„), then the mass loss rate, the asymptotic energy, and the momentum flux of the wind increase dramatically. As in models of magnetocentrifugally dominated stellar winds [31,32], the combined action of rapid rotation and magnetic fields changes the basic physics of the wind and the rotational evolution of the star itself. The effect of magnetocentrifugal slinging on the nucleosynthetic conditions has yet to be quantified, although the inclusion of the centrifugal force in the wind equations should decrease both Tuyn and SOQ. 5. Summary, Conclusions, &; Implications The problem of the production of the r-process nuclei is unsolved. Much work remains. A number of theoretical efforts are needed. First, fully dynamical models following collapse, bounce, explosion, wind emergence, and the whole Kelvin-Helmholtz cooling epoch are needed to understand the dynamics of the wind evolution on long timescales [6]. Second, although

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the results of Refs. 6 and 21 indicate otherwise, there is some consensus that the entropy in standard models of PNS winds is too low by a large factor for the dynamical timescales and electron fractions derived [9-15]. This prompts consideration of 'non-standard' models that might include strong magnetic fields, rotation, or jets [26,33,34]. Other recent calculations suggest some r-process nuclei may be synthesized in the accretion disks of collapsars [35]. More sophisticated modeling is required to understand the importance of magnetic fields in the PNS context fully, but their importance will be primary in determining the dynamics of winds from nascent magnetars or neutron stars with magnetar-like surface fields, even if small-scale. The combination of strong fields and millisecond rotation periods further complicates the picture, but leads to interesting magnetocentrifugal effects. Along with observational efforts that place limits on the birth fraction of magnetars, theoretical efforts must address these processes in detail in order to ascertain the importance of magnetar birth in shaping the chemical evolution of the galaxy. Acknowledgments I thank Eliot Quataert, Phil Chang, Adam Burrows, Stan Woosley, and Al Cameron for helpful conversations. T.A.T. is supported by NASA through Hubble Fellowship grant #HST-HF-01157.01-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. References 1. Burbidge, E. M., Burbidge, G. R., Fowler, W. A., & Hoyle, F. 1957, Rev. Mod. Phys., 29, 547 2. Cameron, A. G. W. 1957, PASP, 69, 201 3. Wallerstein, G. et al. 1997, Rev. Mod. Phys., 69, 995 4. Burrows, A. & Lattimer, J. M. 1986, ApJ, 307, 178 5. Pons, J. A., Reddy, S., Prakash, M., Lattimer, J. M., k, Miralles, J. A. 1999, ApJ, 513, 780 6. Woosley, S. E., Wilson, J. R., Mathews G. J., Hoffman, R. D., & Meyer, B. S. 1994, ApJ, 433, 209 7. Burrows, A., Hayes, J., & Fryxell, B. A. 1995, ApJ, 450, 830 8. Duncan, R. C., Shapiro, S. L., & Wasserman, I. 1986, ApJ, 309, 141 9. Takahashi, K., Witti, J., & Janka, H.-T. 1994, A&A, 286, 857 10. Qian, Y.-Z. & Woosley, S. E. 1996, ApJ, 471, 331 11. Cardall, C. Y. & Fuller, G. M. 1997, ApJL, 486, 111 12. Sumiyoshi, K., Suzuki, H., Otsuki, K., Teresawa, M., & Yamada, S. 2000, PASJ, 52, 601

175 13. Otsuki, K., Tagoshi, H., Kajino, T., & Wanajo, S.-Y. 2000, ApJ, 533, 424 14. Wanajo, S., Kajino, T., Mathews, G. J., & Otsuki, K. 2001, accepted to ApJ 15. Thompson, T. A., Burrows, A., & Meyer, B. S. 2001, ApJ, 562, 887 16. Meyer, B. S. & Brown, J. S. 1997, ApJS, 112, 199 17. Hoffman, R. D., Woosely, S. E., & Qian,Y.-Z. 1997, ApJ, 482, 951 18. Meyer, B. S. 1994, Ann. Rev. Astron. Astrophys., 32, 153 19. Woosley, S. E. & Hoffman, R. D. 1992, ApJ, 395, 202 20. Thompson, T. A., Quataert, E., & Burrows, A. 2004, submitted to ApJ, Astro-ph/0403224 21. Terasawa, M., Sumiyoshi, K., Yamada, S., Suzuki, H., & Kajino, T. 2002, ApJL, 578, L137 22. Lamers, H. J. G. L. M. & Cassinelli, J. P., Introduction to Stellar Winds (Cambridge University Press, Cambridge, 1999) 23. Duncan, R. C. & Thompson, C. 1992, ApJL, 392, 9 24. Thompson, C. & Duncan, R. C. 1993, ApJ, 408, 194 25. Kouveliotou, C , Strohmayer, T., Hurley, K., van Paradijs, J., Finger, M. H., Dieters, S., Woods, P., Thompson, C , Duncan, R. C. 1999, ApJL, 510, 115 26. Thompson, T. A. 2003, ApJL, 585, L33 27. Kaspi, V. M. & Helfand, D. J. 2002, Neutron Stars in Supernova Remnants, ASP Conference Series, Vol. 271, Edited by P. O. Slane & B. M. Gaensler 28. Qian, Y.-Z. 2000, ApJL, 534, 67 29. Argast, D., Samland, M., Thielemann, F.-K., & Qian, Y.-Z. 2004, A&A, 416, 997 30. Thompson, T. A., Chang, P., & Quataert, E. 2004, submitted to ApJ, Astroph/0401555 31. Weber, E. J. & Davis, L. 1967, ApJ, 148, 217 32. Mestel, L. 1968, MNRAS, 138, 359 33. Nagataki, S. & Kohri, K. 2001, PASJ, 53, 547 34. Cameron, A. G. W. 2001, ApJ, 562, 456 35. Pruet, J., Thompson, T. A., & Hoffman, R. 2004, accepted to ApJ, Astroph/0302132

.R-PROCESS NUCLEOSYNTHESIS IN N E U T R I N O - D R I V E N W I N D S : T R E A T M E N T OF T H E INJECTION R E G I O N A N D R E Q U I R E M E N T S ON N E U T R I N O EMISSION*

A. W . S T E I N E R A N D Y.-Z. Q I A N School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA E-mail: [email protected]

During the Kelvin-Helmholtz cooling phase of a protoneutron star, the intense neutrino flux of the protoneutron star drives a wind by depositing energy in the overlying material. It has been proposed that this neutrino-driven wind is a likely site for the r-process. We reexamine the physical conditions in the wind by paying particular attention to the injection region. We emphasize that the inner boundary of the wind is physically determined by treating the injection region and derive an approximate criterion for this boundary. We also study the dependence of a key parameter for the r-process, the neutron-to-seed ratio obtained in the wind, on the characteristics of neutrino emission. The neutrino luminosities and average energies required for successful r-process nucleosynthesis in the wind are explored.

1. Introduction The protoneutron star (PNS) produced in a core-collapse supernova radiates neutrinos over a period of ~ 10 s. During this Kelvin-Helmholtz cooling phase, neutrinos deposit energy in the material above the PNS mainly through the absorption reactions ve+n -*p+e~ and ve+p —> n + e+. This neutrino heating drives a mass outflow termed the "neutrino-driven wind" [1], which has been proposed as a possible site for the r-process (e.g. [2, 3]). However, with the exception of the supernova model in [4], the relevant physical conditions obtained from both numerical supernova models (e.g. [5-7]) and detailed studies of the wind (e.g. [8, 9]) appear to fall short of those required for a robust r-process (e.g. [10-12]). Proposed remedies to produce more favorable conditions for r-process nucleosynthesis in the wind "This work is supported in part by the US Department of Energy under grants DEFG02-87ER40328 and DE-FG02-OOER41149.

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177 include general relativistic effects of a massive and/or compact PNS (e.g. [8, 9, 13-15]), effects of neutrino oscillations (e.g. [16, 17]), and effects of strong PNS magnetic fields [18]. A recent paper [19] reported that wind conditions for a robust r-process were obtained with standard PNS and neutrino physics, but no numerical details have been published yet. By definition, a wind is a steady-state outflow described by a set of ordinary differential equations with no time dependence. In the case of a spherically symmetric neutrino-driven wind, these equations are: M = 4nr2pv, dv _ ldP GM dr p dr r2 q I de P dp\ mjv \dr p2 dr J dYe v— = (A„en + \e+n)Yn — (ApeP + \e-p)Yp ,

(1) (2) (3) (4)

where M is the constant mass outflow rate, r is the radius from the center of the PNS, p is the matter density, v is the velocity, P is the pressure in the wind material, M is the mass of the PNS, q is the net heating rate per nucleon, m^ is the nucleon rest mass, e is the energy per gram of the wind material, Ye, Yn, and Yp are the electron, neutron, and proton number fractions, respectively, of this material, and A„e„, \e-p, APeP, and Ae+„ represent the rates for the reactions ve + n ^ p + e~ and ve + p ^ n + e+. For the regime where the physical conditions in the wind are determined, the wind material can be treated as in nuclear statistical equilibrium (NSE), for which the nuclear composition can be determined as functions of Ye, p, and the temperature T. For example, Yn + Yp w 1 and Yp w Ye at T > 1 MeV. In addition, the equations of state give P and e as functions of p, T, and the composition. Thus, we can choose v, p, T, and Ye as a set of basic variables for the wind and solve them as functions of r from equations (l)-(4). In order to solve the wind equations, we need the rates q, Aj,e„, A e - p , ApeP, and Ae+„ associated with neutrino processes above the PNS. These can be calculated as functions of PNS neutrino emission characteristics and/or material conditions above the PNS (e.g. [8]). In addition, we need the values of v, p, T, and Ye at the inner boundary near the PNS. With the above input, the wind is obtained as the transonic solution to equations (l)-(4). The mass outflow rate M is obtained from the critical condition at the sonic point (e.g. [8]). A simple prescription for the inner boundary is to

178 adopt the conditions at the neutrinosphere (e.g. [9]), where neutrinos cease to diffuse and start to freestream with fixed luminosities and energy spectra. In this contribution, we discuss a physical approach to determine the inner boundary for the neutrino-driven wind by paying particular attention to the injection region, where the conditions at any radius are determined by approximate hydrostatic equilibrium and approximate equilibrium between heating and cooling. An effective criterion for the inner boundary of the wind is derived. We also study the dependence of a key parameter for the r-process, the neutron-to-seed ratio obtained in the wind, on the characteristics of neutrino emission. The neutrino luminosities and average energies required for successful r-process nucleosynthesis in the wind are explored.

2. Description of the Injection Region A steady-state wind starting from the neutrinosphere is clearly a mathematical idealization of the neutrino-heated ejecta from the PNS. Realistically, the velocity of the ejecta must increase from zero at the neutrinosphere to finite values implied by the mass outflow rate M in the wind over a finite injection region. The term 47rr2/w increases with r in the injection region and stays constant in the wind region. The radius at which this term first reaches the constant M for the wind is then the inner boundary of the wind. Ideally, a numerical study of the neutrino-heated ejecta from the PNS should be a natural extension of any supernova model that can produce a successful explosion. In practice, the quasi-steady state nature of this ejecta makes its description insensitive to the details of the explosion mechanism so long as an explosion is obtained. An effective approach to model the neutrino-heated ejecta from the PNS is to follow the time development of some initial configuration of matter above the PNS with a hydrodynamic code. Eventually, the initial configuration will be relaxed into a steady-state configuration that automatically includes an injection region and a wind region. This approach was adopted for the numerical analyses of the wind in [8]. The existence of an injection region is clearly shown by Figs. 1 and 2 in [8]. We here present an approximate treatment of the injection region without using the time relaxation approach in [8]. We also derive an effective criterion for the inner boundary for the wind. We show that the wind equations (l)-(4) along with the approximate treatment of the injection region give conditions in the wind that are in very good agreement with the nu-

179 merical models in [8]. Our approximate treatment takes advantage of the small velocity of matter in the injection region. To zeroth order, the velocity can be ignored and we assume hydrostatic equilibrium in this region. Further, the dynamic timescale Tdyn = r/v at a given radius r is sufficiently long so that a kinetic equilibrium between heating and cooling [20] can be assumed. Likewise, an equilibrium between the reactions changing n and p can also be assumed. With the above approximations, the conditions (e.g. p, T, and Ye) in the injection region can be obtained from

qvN + qve

1 dP GM p ar rz + <2W = qeN + qe-e+ , y e

~

\

*ven J- \

i ^e+n _L \_ 4- X

(6) '

/~\ { '

where qVN, qve, and qvv are the heating rates per nucleon due to neutrino absorption on nucleons, neutrino scattering on e~ and e + , and neutrino pair annihilation, respectively, while qen and qe-e+ are the cooling rates per nucleon due to e~ and e + capture on nucleons and pair annihilation, respectively. Equation (7) can be obtained from equation (4) by setting v — 0, Yp — Ye, and Yn = 1 — Ye for the injection region. Starting from the neutrinosphere, we can solve p, T, and Ye as functions of r from equations (5)-(7) for the injection region. For the models presented in [8], we find that the injection region ends when the specific energy (per gram) erei of relativistic particles (e~, e + , and 7) becomes approximately equal to the specific energy ejv of nonrelativistic nucleons: ^ ~ 1. (8) ejv Equation (8) can then be taken as an effective criterion for the inner boundary of the wind. This criterion can be understood as follows. Near the neutrinosphere, the pressure P is dominated by the contribution Pjv oc pT from nucleons. In addition, the dominant heating rate q„N decreases slowly with r but the dominant cooling rate qeN is a steep function of T. Kinetic equilibrium then results in T staying approximately constant near the neutrinosphere. This requires p to drop exponentially with r by Eq. (5) for hydrostatic equilibrium. Consequently, the importance of the contribution Prei oc T 4 to P from relativistic particles increases with r. When P re i ~ P/v or eTei/eN ~ 1 is reached, kinetic equilibrium that requires little change in T cannot be maintained together with hydrostatic equilibrium anymore. The injection region then ends and a dynamic wind regime starts.

180

3. Physical Conditions in the Neutrino-Driven Wind We now describe our numerical treatment of the neutrino-driven wind. Starting from the neutrinosphere, we integrate equations (5)-(7) for the injection region until erei/ew ~ 1 is reached. The conditions at this point are then used as those for the inner boundary of the wind. Starting from the inner boundary, we pick a value for M and solve equations (l)-(4). If the solution meets the critical condition at the sonic point, then it is accepted as a description of the wind with the corresponding M. Otherwise, we repeat the procedure for another value of M until the wind solution is obtained. The physical parameters of the wind that are important to nucleosynthesis include M, the final entropy per baryon S, and a typical dynamic timescale fd yn evaluated for example, at T' = 0.5 MeV. These parameters are calculated from the above approach for a number of cases with different PNS radii and neutrino luminosities. The results are compared with those from the numerical models of [8] in Table 1. It can be seen that the agreement is very good (within ~ 15%). We also calculate the physical parameters of the wind taking the neutrinosphere as the inner boundary and present the results in Table 2. It can be seen that ignoring the injection region has large effects on M and fd yn at early times when the PNS has a larger radius (Model 30B). The difference from the numerical models of [8] is almost a factor of 2 in this case. Table 1.

Comparison of wind results.

Model

MQW (M0/S)

10A

9.7xl0"6

8.8X10" 5

10B

1.4xl0~

5

5

IOC

5.6X10"

6

10D

4.6xl0"6

10E

6.8xl0~6

10F

2.8xl0~

6

2.64X10"

30A

7.6xl0"

2

2

24

30B

l.lxlO"2

l.lxKT2

26

30C

3

3

4.2xlCr

M (MQ/S)

1.3X10"

6

SQV/

S

fdyn]QW (s)

fdyn (s)

74

77

2.4xl0"2

2.0xl0"2

91

6.6X10"

2

5.6xl0-2

1

9.3xl0~2

86 94

99

l.lxlO"

4.4xl0~5

109

111

2.4xl0"2

2.0xl0"2

6.5xl0"6

127

132

6.6xl0"2

5.8xl0"2

143

l.lxlO-

1

9.7xl0-2

24

3.2X10"

2

3.1xl0"2

27

7.5X10" 2

6.6X10" 2

29

1

l.OxlO"1

5.2xlO"

8.4xl0~ 4.0xl0~

6

140

28

1.2X10"

Note: The results denoted with the subscript "QW" are taken from [8].

To check that our approximate prescription for the inner boundary of the wind is physically sound, we compare two timescales of interest based

181 Table 2. Model

Effects of the injection region.

M (MQ/S)

S

10B

1.4xl0-5

lOBi

5

1.3X10-

-2

30B

l.lxlO

30Bi

6.0X10-3

86 95 26 32

fdyn

(s)

Notes

6.6xl0"2

(a)

4.4xl0-2 7.5X10"2

(b) (a)

4.0X10"2

(b)

Note: (a) The results are taken from [8]. (b) The results are obtained by ignoring the injection region.

on the wind solution. These are the dynamic timescale Tdyn = r/v and the thermodynamic timescale r t h = £/qVN- For kinetic equilibrium to hold in the injection region, r t h < Tdyn. In contrast, we expect r t h > Tdyn for the wind region. These two timescales are shown as functions of r in Figure 1. It can be seen that r t h becomes comparable to Tdyn at the inner boundary of the wind and quickly increases above Tdyn for larger radii.

-

1

1,

"•-....

T,

102 10' 10'

Figure 1. The dynamic (Ta yn ) and thermodynamic (r t h) timescales for early (left panel) and late (right panel) configurations of the PNS. The vertical line indicates the inner boundary of the wind.

As concluded by earlier studies (e.g. [8, 11]), the parameters Ye, S, and fdyn in the wind do not typically lead to a successful r-process. One possibility is that the assumed neutrino emission characteristics of the PNS have large uncertainties. These uncertainties will be carried into the calculation of q. To examine the effects of uncertainties in q on the conditions in the

182 wind, we multiply qVN and qeM by constant factors C\ and C2, respectively. The results for M, S, and fd yn corresponding to different values of C\ and C2 are compared in Table 3. These results show that uncertainties within a factor of 2 in qVN and qeM will not cause sufficient changes in S and fdyn to yield favorable conditions for the r-process. On the other hand, the uncertainties in the neutrino emission characteristics have a large effect on Ye. This effect is examined in detail in Sec. 4. Table 3.

Effects of uncertainties in q.

Model

M

10B

1.3X10" 5

91

5.6X10" 2

(1.0,1.0)

5

78

4.2X10- 2

(2.0,0.5)

S

T

dyn

(Ci,C2)

lOBd

3.8xl0~

lOBe

3.2xl0-6

115

7.3X10- 2

(0.5,2.0)

lOBf

1.6xlO"

B

94

4.0X10" 2

(2.0,2.0)

lOBg

7.2X10" 6

94

8.2x10-2

(0.5,0.5)

4. Neutrino Emission Characteristics and r-Process Nucleosynthesis in the Wind The electron fraction Ye is a crucial parameter for nucleosynthesis. A necessary condition for an r-process to occur in the wind is Ye < 0.5 at the beginning of nucleosynthesis. The evolution of Ye in the wind has been studied extensively (e.g. [8, 21-23]). At T ~ 1 MeV, A„e„ and APeP are much larger than Ae+„ and A e - p . In addition, (A„en + ^pep)Tdyn 3> 1 so that Eq. (4) gives Ye « A„e„/(A„,,n + A PeP ). As T drops below ~ 1 MeV, free nucleons begin to combine into a particles and heavier nuclei. The evolution of Ye then must be obtained from Eq. (4) by taking into account the change of nuclear composition. Note that as a significant Yn must exist in the wind to enable an r-process, the effect of ve + n —> p + e~ on Ye is especially important (e.g. [22]). The rates A„e„ and XPeP are determined by the luminosities and energy spectra of ve and ve, and therefore, are subject to the uncertainties in these neutrino emission characteristics. In view of possible uncertainties in the neutrino emission characteristics as calculated from current supernova models, we carry out a simple parametric study of the effects of these characteristics on nucleosynthesis in the neutrino-driven wind. We consider three snapshots during the evolution of a PNS of 1.4 M 0 . (1) Near the beginning of the Kelvin-Helmholtz cooling

183 phase, the PNS has a radius of R = 30 km and a luminosity of ~ 1052 erg/s for each neutrino species. We assume LVe = LPe and an average ve energy of ( £ „ J = 14 MeV. (2) The PNS has a radius of R = 10 km and a luminosity of ~ 10 51 erg/s for each neutrino species. We assume L„e = LDa and an average ve energy of (E„e) = 9 MeV. (3) Same as (2) but now LVc/(EVe) = Lpc/(EPe) is assumed instead. Case (3) corresponds to a fully-deleptonized PNS for which the number fluxes for ve and 9e are equal. In all three cases, we assume LVi = LPe and (EVi) = 28 MeV, where vx stands for v^, vT, z/M, or 9T. For each of the above three cases, we calculate v(r), p(r), T(r), and Ye(r) of the wind for a range of Lpe and (Epe). In addition, when T drops below ~ 0.5 MeV, we follow the production of seed nuclei by the a-process [3] using the analytic prescription of [11]. We then calculate the neutron-toseed ratio n/s at T ~ 0.25 MeV corresponding to the end of the a-process. As the typical seed nuclei have mass numbers A ~ 90, n/s ~ 40 and 105 are required to produce the peaks at A ~ 130 and 195, respectively, in the solar r-process abundance pattern. We find that for case (1), n/s is too small to give any significant r-process nucleosynthesis for reasonable values of LPe and (Epe). The contours of fixed n/s are shown as functions of Lpe and {EPe) for cases (2) and (3) in Fig. 2. The electron fraction Ye at the beginning of the a-process is roughly constant for a fixed {EPc). The strong dependence of n/s on this Ye is evident in Fig. 2. The primary difference between cases (2) and (3) can also be traced to the difference in Ye. For the same Lpe and (Epe), the larger LVe in case (2) gives a larger Aj/e„ and hence, a larger Ye. For both cases (2) and (3), the steepening of the contours at low Lpc can be traced to an increase in fdyn- The contours for n/s ~ 40 and 105 give the required Lpe and (Epe) for producing the r-process abundance peaks at A ~ 130 and 195, respectively.

5. Discussion a n d Conclusions We have provided an approximate procedure to determine the inner boundary of the neutrino-driven wind by including the injection region. We have shown that the wind equations with the inner boundary determined this way give conditions that are in very good agreement with those obtained from the numerical models of [8]. In addition, we have carried out a parametric study of the dependence of r-process nucleosynthesis on the neutrino emission characteristics of the PNS. The neutrino luminosities and average energies required to produce different neutron-to-seed ratios in the

184 105.0

22

OO

(MeV)

20

^

\40.0

~~\^

\_I5J)

1 , ,

14

:\

12 :

0.5

10

: 0.5

1

1.5

2 , 2.5

3

3.5

Figure 2. Contours of fixed n/s for cases (2) (left panel) and (3) (right panel). The horizontal axis is Lae in units of 10 5 1 erg/s. The contours for n/s ~ 40 and 105 give the required Lpe and (Eae) for producing the r-process abundance peaks at A ~ 130 and 195, respectively.

wind have been derived for two different evolutionary stages of the PNS. Whether these parameters are actually achieved for a PNS remains to be demonstrated by either detailed neutrino transport calculations with new nuclear physics input (e.g. new equation of state for hot and dense matter) or more preferably detection of neutrino signals from a future supernova. Based on the results obtained here, the most promising case for r-process nucleosynthesis appears to be associated with a PNS that is fully deleptonized when the neutrino luminosity is still high. The deleptonization timescale depends sensitively on the symmetry energy of the nuclear equation of state [24]. This dependence certainly merits further studies. On the other hand, the deleptonization timescale may depend on the initial configuration of the collapsing core. Most supernova models focus on the collapse of Fe cores associated with progenitors of > 1OM 0 . However, observations of metal-poor stars strongly suggest that supernovae from collapse of O-Ne-Mg cores (associated with progenitors of ~ 8-10 M Q ) and accretion-induced collapse of white dwarfs are the sources for the heaviest r-process nuclei [25]. Detailed models of these kinds of supernovae and the associated neutrino emission are much needed. References 1. R. C. D u n c a n , S. L. Shapiro, a n d I. W a s s e r m a n , Astrophys. J. 3 0 9 , 141 (1986). 2. S. E. Woosley a n d E. Baron, Astrophys. J. 3 9 1 , 228 (1992).

185 3. S. E. Woosley and R. D. Hoffman, Astrophys. J. 395, 202 (1992). 4. S. E. Woosley et al, Astrophys. J. 433, 229 (1994). 5. B. S. Meyer et al, Astrophys. J. 399, 656 (1992). 6. J. Witti, H.-T. Janka, and K. Takahashi, Astron. Astrophys. 286, 841 (1994). 7. K. Takahashi, J. Witti, and H.-T. Janka, Astron. Astrophys. 286, 857 (1994). 8. Y.-Z. Qian and S. E. Woosley, Astrophys. J. 471, 331 (1996). 9. T. A. Thompson, A. Burrows, and B. S. Meyer, Astrophys. J. 562, 887 (2001). 10. B. S. Meyer and J. S. Brown, Astrophys. J. Suppl. Ser. 112, 199 (1997). 11. R. D. Hoffman, S. E. Woosley, and Y.-Z. Qian, Astrophys. J. 482, 951 (1997). 12. C. Freiburghaus et al, Astrophys. J. 516, 381 (1999). 13. C. Y. Cardall and G. M. Fuller Astrophys. J. 486, L l l l (1997). 14. K. Otsuki et al, Astrophys. J. 533, 424 (2000). 15. S. Wanajo et al, Astrophys. J. 554, 578 (2001). 16. G. C. McLaughlin et al, Phys. Rev. C59, 2873 (1999). 17. D. O. Caldwell, G. M. Fuller, and Y.-Z. Qian, Phys. Rev. D 6 1 , 123005 (2000). 18. T. A. Thompson, Astrophys. J. 585, L33 (2003). 19. M. Terasawa et al, Astrophys. J. 578, L137 (2002). 20. A. Burrows and T. J. Mazurek, Astrophys. J. 259, 330 (1982). 21. Y.-Z. Qian et al, Phys. Rev. Lett. 71, 1965 (1993). 22. G. M. Fuller and B. S. Meyer, Astrophys. J. 453, 792 (1995). 23. G. C. McLaughlin, G. M. Fuller, and J. R. Wilson, Astrophys. J. 472, 440 (1996). 24. J. A. Pons et al, Astrophys. J 513, 780 (1999). 25. Y.-Z. Qian and G. J. Wasserburg, Astrophys. J. 588, 1099 (2003).

GENERAL RELATIVITY AND NEUTRINO-DRIVEN SUPERNOVA WINDS*

C. Y. C A R D A L L Physics Division Oak Ridge National Laboratory Oak Ridge, TN 37831-6354, USA Email: [email protected] Department of Physics and Astronomy University of Tennessee Knoxville, TN 37996-1200, USA

To date, detailed core-collapse supernova simulations have not succeeded in elucidating the explosion mechanism. But whatever the mechanism turns out to be, there will be a neutrino-heated outflow between the hot, newly-born neutron star and the outgoing supernova shock wave whose neutron richness, low density, and high temperature could provide promising conditions for the synthesis of heavy nuclei via rapid neutron capture (the r-process). General relativistic effects improve the prospects for this outflow as an r-process site. Among relativistic effects, the enhanced "gravitational potential" is more important than the gravitational redshift or trajectory bending of neutrinos.

1. Core-collapse Supernovae Core-collapse supernovae—those of Type lb, Ic, and II—result from the catastrophic collapse of the core of a massive star. For most of their existence, stars burn hydrogen into helium. In stars at least eight to ten times as massive as the Sun, temperatures and densities become sufficiently high to burn to carbon, oxygen, neon, magnesium, and silicon and iron group elements. The iron group nuclei are the most tightly bound, and here burning in the core ceases. The iron core—supported by electron degeneracy "This work was supported by Scientific Discovery Through Advanced Computing (SciDAC), a program of the Office of Science of the U.S. Department of Energy (DOE); and by Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the DOE under contract DE-AC05-00OR22725.

186

187

pressure—eventually becomes unstable. Its inner portion undergoes homologous collapse (velocity proportional to radius), and the outer portion collapses supersonically. Electron capture on nuclei is one instability leading to collapse, and this process continues throughout collapse, producing neutrinos. These neutrinos escape freely until densities and temperatures in the collapsing core become so high that even neutrinos are trapped. Collapse is halted soon after the matter exceeds nuclear density; at this point (called "bounce"), a shock wave forms at the boundary between the homologous and supersonically collapsing regions. The shock begins to move out, but after the shock passes some distance beyond the surface of the newly born neutron star, it stalls as energy is lost to neutrino emission and dissociation of heavy nuclei falling through the shock. The details of how the stalled shock is revived sufficiently to continue plowing through the outer layers of the progenitor star are unclear. Some combination of neutrino heating of material behind the shock, convection, instability of the spherical accretion shock, rotation, and magnetic fields launches the explosion. It is natural to consider neutrino heating as a mechanism for shock revival, because neutrinos dominate the energetics of the post-bounce evolution. Initially, the nascent neutron star is a hot thermal bath of dense nuclear matter, electron/positron pairs, photons, and neutrinos, containing most of the gravitational potential energy released during core collapse. Neutrinos, having the weakest interactions, are the most efficient means of cooling; they diffuse outward on a time scale of seconds, and eventually escape with about 99% of the released gravitational energy. Because neutrinos dominate the energetics of the system, a detailed understanding of their evolution will be integral to any detailed and definitive account of the supernova process. If we want to understand the explosion— which accounts for only about 1% of the energy budget of the system—we should carefully account for the neutrinos' much larger contribution to the energy budget. What sort of computation is needed to follow the neutrinos' evolution? Deep inside the newly-born neutron star, the neutrinos and the fluid are tightly coupled (nearly in equilibrium); but as the neutrinos are transported from inside the neutron star, they go from a nearly isotropic diffusive regime to a strongly forward-peaked free-streaming region. Heating of material behind the shock occurs precisely in this transition region, and modeling this process accurately requires tracking both the energy and angle dependence of the neutrino distribution functions at every point in space.

188

A full treatment of this six-dimensional neutrino radiation hydrodynamics problem remains too costly for currently available computational resources. Throughout the 1990s, several groups performed simulations in two spatial dimensions with simplified neutrino transport. One simplification allowed for neutrino transport in two spatial dimensions, but with neutrino energy and angle dependence integrated out—effectively reducing a five dimensional problem to a two dimensional one. 1 ' 2 ' 3 These simulations showed convection in two regions. First, loss of electron neutrinos from the outer layers of the neutron star caused composition gradients that could drive convection, which boosted neutrino luminosities by bringing hotter material to the surface. Second, heating decreased further from the neutron star surface, giving rise to a negative entropy gradient. The resulting convection increased the efficiency of neutrino heating by delivering heated material to the region just behind the shock. These simulations exhibited explosions, suggesting that the enhancements in neutrino heating behind the shock resulting from convection provided a robust explosion mechanism. More recent simulations in three spatial dimensions with this same approximate treatment of neutrino transport showed similar outcomes.4 A different simplification of neutrino transport employed in the 1990s was the imposition of energy-dependent neutrino distributions from spherically symmetric simulations onto fluid dynamics computations in two spatial dimensions.5 Unlike the multidimensional simulations discussed above, these did not exhibit explosions, casting doubt upon claims that convectionaided neutrino heating constituted a robust explosion mechanism. The nagging qualitative difference between multidimensional simulations with different neutrino transport approximations renewed the motivation for simulations in which both the energy and angle dependence of the neutrino distributions were retained. Of necessity, the first such simulations were performed in spherical symmetry (actually a three-dimensional problem, depending on one space and two momentum space variables). Results from three different groups are in accord: Spherically symmetric models do not explode, even with solid neutrino transport. 6 ' 7,8 Recently, one of these groups performed simulations in two spatial dimensions, in which their energy- and angle-dependent neutrino transport was made partially dependent on spatial polar angle as well as radius. 9 ' 10 Explosions were not seen in any of these simulations, except for one in which certain terms in the neutrino transport equation corresponding to Doppler shifts and angular aberration due to fluid motion were dropped.

189 This was a surprising qualitative difference induced by terms contributing what are typically thought of as small corrections. The continuing lesson is that getting the details of the neutrino transport right makes a difference. Where, then, do simulations aiming at the explosion mechanism stand? The above history suggests that elucidation of the mechanism will require simulations that feature truly spatially multidimensional neutrino transport. Development of the formalism,11 algorithms, 12 and computer code necessary to this transport capability is ongoing as part of the Terascale Supernova Initiative. This substantial collaboration—led by Anthony Mezzacappa of Oak Ridge National Laboratory and funded by the Department of Energy's Scientific Discovery through Advanced Computing (SciDAC) program—is dedicated to the elucidation of the core-collapse supernova explosion mechanism through supercomputer simulations. At least one other major development of multidimensional neutrino transport capability is underway as well.13 In addition to sophisticated neutrino radiative transfer, inclusion of magnetic field dynamics seems increasingly strongly motivated as a possible driver of the explosion, because simulations with "better" neutrino transport have failed to explode—even in multiple spatial dimensions. Work on the inclusion of magnetic fields is also part of the Terascale Supernova Initiative. 2. Relativistic Neutrino-driven Winds: Early Work It was realized in the early 1990s that whatever the explosion mechanism turns out to be, there will be an evacuated region between the hot, newlyborn neutron star and the outgoing supernova shock wave, whose neutron richness, low density, and high temperature of the region could provide promising conditions for the synthesis of heavy nuclei via rapid neutron capture (the r-process). 14 Consideration of the exploding supernova models3' of Wilson and Mayle in the late 1980s and early 1990s ls led Meyer et al. 14 to this insight, and to the related observation that the ejected amount of this "hot bubble" material—together with the Galactic supernova rate— seemed about right to account for the amount of r-process material in the "These simulations were spherically symmetric. In light of the discussion in the previous section, it may be surprising t h a t explosions were obtained. However, a prescription mocking up the multidimensional effects of a doubly-diffusive fluid instability (the socalled "neutron fingers") was included in these simulations, which boosted neutrino luminosities sufficiently for the neutrino-driven explosion mechanism to succeed. That the necessary conditions actually exist for this particular instability to operate effectively has been disputed, 1 5 ' 1 6 ' 1 7 b u t related instabilities may produce similar results. 1 7

190 Galaxy. This proposal was buttressed by subsequent work of Woosley et al.: 19 The Wilson and Mayle models were run out to several seconds past core bounce and explosion, showing that the intense neutrino fluxes emitted by the cooling neutron star did indeed drive neutron-rich matter off its surface into the evacuated region below the shock wave. This work also included nucleosynthesis calculations—performed by post-processing matter trajectories obtained in these simulations—that yielded impressive agreement with the observed solar system r-process abundance distribution. The observed r-process abundances require that ~100 neutrons be available for capture on each iron peak "seed" nucleus, and this neutron/seed ratio is determined by three parameters characterizing the astrophysical environment: the entropy per baryon S, the electron fraction Ye, and the dynamic expansion time scale Tdyn- High entropy favors the relative disorder of free nucleons, as opposed to their being locked up in heavier nuclei (high rates of photodisintegration at the high temperatures and low densities associated with large S provide the microscopic mechanism). Low electron fraction corresponds to neutron richness: Ye = np/(nn+np), where np and nn are the number densities of protons and neutrons (including those locked up in nuclei). A short dynamic expansion time scale prevents too many seed nuclei from building up, by causing the freeze-out of bottleneck three-body reactions producing 12 C from 4 He. The "hot bubble" exhibited in Woosley et al. 19 appears to be a subsonic outflow that bumps up against the shock wave sitting about 104 km from the neutron star. In these conditions, the factor most favorable to the r—process turns out to be a high entropy of S ~ 400 (in units of Boltzmann's constant); values of Ye ~ 0.4 and r^yn ~ 1 s are modest. Several factors motivate modeling this neutron-rich outflow from the neutron star surface on its own—separate from large-scale supernova simulations—in order to gauge its suitability as an r-process site. One obvious roadblock to the use of the large-scale simulations is the failure of most models to explode, as described in the previous section. Moreover, even if explosions are obtained, many of these simulation codes are not well suited to the task of running to the late times (> 10 s) needed to follow the wind. A physical justification for simple wind models is that exploding two-dimensional supernova models with convection settled down to approximately spherically symmetric and stationary conditions as the wind phase approached. 2,3 Simple models can provide physical insight, and are more amenable to parameter studies (e.g. dependence on neutron star mass

191 1000.0

800.0

600.0 Si 400.0

200.0

' 0.0

0.2

0.4

0.6

0.8

1.0

2M/R

Figure 1. The final entropy per baryon in units of Boltzmann's constant, as a function of the supernova core Schwarzschild radius divided by the core radius. The circle is from the Qian and Woosley numerical calculation of model 10B with post-Newtonian corrections.

and radius, neutrino luminosities and average energies) than the large-scale simulations. Studies of simpler models of the neutrino-driven wind began with an important paper of Qian and Woosley.20 They obtained estimates of 5, Tdyn, and mass outflow rate from analytic "wind" models based on steady-state Newtonian fluid equations describing the matter outflow. They showed that the putative high entropy 19 of the "hot bubble" was difficult to explain, even with an outer boundary pressure. Their values of S fell well short of that required for a robust r-process. They confirmed their analytic results with a hydrodynamic code that included simple input neutrino heating. In a few of their numerical runs, they employed an enhanced "gravitational force" — p > — 1_2GM/r r?~ motivated by the corresponding term in the relativistic fluid equations in Schwarzschild geometry. These cases resulted in larger values of S and smaller values of Tdyn, and it was pointed out that both went in the right direction towards more favorable conditions for the r-process. Cardall and Puller21 pursued this hint on the effects of relativity, following the Qian and Woosley20 approach, but with relativistic fluid equations. In addition to the relativistic effects in the fluid equations (e.g. enhanced

192

Figure 2. The dynamic expansion time scale as a function of the supernova core Schwarzschild radius divided by the core radius. The circle is from the Qian and Woosley numerical calculation of model 10B with post-Newtonian corrections.

0.4

0.6 2M/R

Figure 3. The mass outflow rate as a function of the supernova core Schwarzschild radius divided by t h e core radius. The circle is from the Qian and Woosley numerical calculation of model 10B with post-Newtonian corrections.

"gravitational force," Lorentz factors limiting velocities to the speed of light, internal energy density and pressure contributing to inertia), relativistic effects on the neutrino heating were taken into account, specifically

193

gravitational redshift and the bending of neutrino trajectories. These calculations affirmed that general relativistic effects make conditions in the wind more hospitable to the r-process. Figures 1, 2, and 3 show S, Tdyn, and the mass outflow rate as a function of the compactness of the neutron star (Schwarzschild radius divided by radius). b Trends of increasing S and decreasing Tdyn with increasing compactness are both favorable, though this comes at a cost of a smaller mass outflow rate, which translates into the production of less r-process material. These figures are not physically meaningful for 2^£f > 0.66, as compactness greater than this would imply an equation of state that violates causality (sound speed greater than the speed of light). Comparing Figures 1,2, and 3 with a parameter study 22 of the neutron/seed ratio as a function of S, T^ya, and Ye, Cardall and Fuller 21 concluded that suitable conditions for the r-process could just be achieved near the neutron star causality limit, but that the amount of ejected material becomes uncomfortably (though perhaps not prohibitively) small. The most important relativistic effect appears to be the enhanced "gravitational force." One way to see this is to note the good agreement between the Cardall and Fuller21 results and the single displayed Qian and Woosley20 numerical result, in which the enhanced "gravitational force" was the only relativistic effect included. This agreement is particularly striking in the case of the entropy per baryon S. Roughly speaking, the entropy per baryon is the energy a baryon acquires by neutrino heating, divided by a characteristic temperature at which the heating takes place. If a baryon is to escape the "gravitational potential," the acquired energy per baryon is roughly the baryon mass times the gravitational potential at the neutron star surface.20 In the relativistic case, the "gravitational potential" obtained from the enhanced "gravitational force" expressed above is \ In (l — ^gsr), which reduces to the Newtonian expression ^ £ for small compactness. Gravitational neutrino redshift and trajectory bending have some effect on the characteristic temperature at which the heating takes place, 21 but this effect is modest in comparison with the logarithmic dependence of the "gravitational potential." The result is that Figure 1 for S tracks the logarithmic dependence of the gravitational potential quite closely; the corresponding plot for the Newtonian case would be a straight

"This variation was actually computed by varying the neutron radius with the mass held fixed at 1.4M©. A particular prescription for the variation of neutrino luminosity was also employed.

194 line matching the relativistic curve at low compactness. It is evident that relativity makes a nontrivial difference for neutron star masses and radii.

3. Recent Work and Outstanding Issues Cardall and Fuller21 concluded that the prospects for suitable r-process conditions in the neutrino-driven wind improve from something like 'rather pessimistic' in the Newtonian case 20 to perhaps 'not inconceivable' when general relativity is taken into account—an assessment confirmed in subsequent work. 23,24,25,26 These works involved various improvements on previous semi-analytic estimates, including full numerical solution of the wind equations; comprehensive variations of neutron star mass, radius, and neutrino luminosities; tracking of the electron fraction; construction of evolutionary sequences; proper treatment of transonic winds; and r-process network nucleosynthesis calculations. The consensus emerging from these works was that suitable r-process conditions might obtain, but that it would be in the form of a modest entropy, rapidly expanding (and possibly transonic) "wind" rather than a high entropy, subsonic "hot bubble." The rather massive and compact neutron stars that seem to be required do not seem likely given current understanding of the dense nuclear matter equation of state, but new analyses of neutrino interactions with this dense matter may alleviate this problem by implying higher neutrino luminosities.27 A verdict of 'not inconceivable' is not particularly comforting, but given the apparent preference of Galactic chemical evolution models for a supernova r-process source over neutron star binary mergers, 28 fresh ideas on supernova winds are welcome. Hydrodynamic calculations have been performed in which outer boundary effects are claimed to play a significant role, allowing suitable r-process conditions for neutron stars of canonical mass; 29 perhaps the issue of "rapid wind" vs. "hot bubble" is worth another examination. A very different and interesting idea is that magnetic fields may trap matter long enough to be significantly heated before being released into the wind. 30,31 Final understanding of the suitability of the supernova neutrino-driven wind as an r-process site will probably only come in the context of an understanding of the explosion mechanism—which brings us back to the discussion of large-scale simulations in the first section. Once this understanding is achieved through detailed simulation, we will have better qualitative and quantitative understandings of neutrino heating, magnetic fields, fallback of material at late times, and other phenomena that will influence the wind.

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References 1. M. Herant, W. Benz, W. R. Hix, C. L. Fryer, and S. A. Colgate, Astrophys. J. 435, 339 (1994). 2. A. Burrows, J. Hayes, and B. A. Fryxell, Astrophys. J. 450, 830 (1995). 3. H.-T. Janka and E. Mueller, Astron. Astrophys. 306, 167 (1996). 4. C. L. Fryer and M. S. Warren, Astrophys. J. Lett. 574, 65 (2002). 5. A. Mezzacappa, A. C. Calder, S. W. Bruenn, J. M. Blondin, M. W. Guidry, M. R. Strayer, and A. S. Umar, Astrophys. J. 495, 911 (1998). 6. R. Buras, H.-T. Janka, M. T. Keil, G. G. Raffelt, and M. Rampp, Astrophys. J. 587, 320 (2003). 7. T. A. Thompson, A. Burrows, and P. A. Pinto, Astrophys. J. 592, 434 (2003). 8. M. Liebendorfer, O. E. B. Messer, A. Mezzacappa, S. W. Bruenn, C. Y. Cardall, and F.-K. Thielemann, Astrophys. J. Supp. 150, 263 (2004). 9. H.-T. Janka, R. Buras, and M. Rampp, astro-ph/0212317. 10. R. Buras, M. Rampp, H.-Th. Janka, and K. Kifonidis, Phys. Rev. Lett. 90, 241101 (2003). 11. C. Y. Cardall and A. Mezzacappa, Phys. Rev. D 68, 023006 (2004). 12. C. Y. Cardall, astro-ph/0404401. 13. E. Livne, A. Burrows, R. Walder, I. Lichtenstadt, and T. A. Thompson, astro-ph/0312633. 14. B. S. Meyer, G. J. Mathews, W. M. Howard, S. E. Woosley, and R. D. Hoffman, Astrophys. J. 399, 656 (1992). 15. S. W. Bruenn, A. Mezzacappa, and T. Dineva, Phys. Reports 256, 69 (1995). 16. S. W. Bruenn and T. Dineva, Astrophys. J. Lett. 458, L71 (1996). 17. S. W. Bruenn, E. A. Raley, and A. Mezzacappa, astro-ph/0404099. 18. J. R. Wilson and R. W. Mayle, Phys. Rep. 227, 97 (1993). 19. S. E. Woosley, J. R. Wilson, G. J. Mathews, R. D. Hoffman, and B. S. Meyer, Astrophys. J. 433, 229 (1994). 20. Y.-Z. Qian and S. E. Woosley, Astrophys. J. 471, 331 (1996). 21. C. Y. Cardall and G. M. Fuller, Astrophys. J. Lett. 486, L l l l (1997). 22. R. D. Hoffman, S. E. Woosley, and Y.-Z. Qian, Astrophys. J. 482, 951 (1997). 23. K. Sumiyoshi, H. Suzuki, K. Otsuki, M. Terasawa, and S. Yamada, Publ. Astron. Soc. Jap. 52, 601 (2000). 24. K. Otsuki, H. Tagoshi, T. Kajino, and S. Wanajo, Astrophys. J. 533, 424 (2000). 25. S. Wanajo, T. Kajino, G. Mathews, and K. Otsuki, Astrophys. J. 554, 578 (2001). 26. T. A. Thompson, A. Burrows, and B. S. Meyer, Astrophys. J. 562, 887 (2001). 27. S. Reddy, these proceedings. 28. D. Argast, these proceedings. 29. M. Terasawa, K. Sumiyoshi, S. Yamada, H. Suzuki, and T. Kajino, Astrophys. J. 578, 137 (2002). 30. T. A. Thompson, Astrophys. J. 585, 33 (2003). 31. T. A. Thompson, these proceedings.

A N UPDATE ON THE HOT SUPERNOVA BUBBLE R-PROCESS

G. J. M A T H E W S A N D K. O T S U K I Center for Astrophys.

(CANDU) and Joint Inst, for Nuclear Astrophys. University of Notre Dame, Department of Physics Notre Dame, IN 46556, USA E-mail: [email protected], [email protected]

(JINA)

J. R. W I L S O N A N D H. E. D A L H E D Lawrence

Livermore E-mail:

National Laboratory University of Livermore, CA 94550, USA [email protected], [email protected]

California

The neutrino-energized high-entropy bubble above the proto neutron star in a core-collapse supernova remains as one of the most promising sites for r-process nucleosynthesis. In this paper we briefly summarize the appealing features of this model along with its remaining difficulties. We present some new approaches to their resolution. In particular, we show first results from a new version of with Livermore supernova code with improved neutrino transport and numerics. Very high entropy per baryon {s/k ~ 600) appears within the bubble at late times. Though favorable for the r-process, seed nuclei are still over produced when neutrino-nucleus interactions are included. Even so, encouraging new results from the effects of magnetic fields, neutrino oscillations, and better nuclear physics input data are discussed.

1. Introduction Although the r-process is responsible for the abundance of about half of the nuclei heavier than iron, the precise astrophysical site for this nucleosynthesis process has remained a mystery. Nevertheless, among the many proposals 1 for its origin, core-collapse supernovae have remained the most likely site in which the necessary ejected mass and neutrons per seed can be achieved. Although schematic studies with semianalytic wind models are helpful in outlining possible parameter constraints, if one is ever to truly identify the site for the r-process it is important to explore r-process nucleosynthesis in the context of detailed supernova simulations. 2 In this 196

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regard, the analysis of Woosley et al. 3 based upon the supernova model of Wilson & Mayle 4 provided important insight into how the r-process might be achieved. This model identified for the first time the flow of neutrino heated material into the high entropy bubble above a nascent proto-neutron star in a core-collapse supernova. The r-process occurs ? in the region between the surface of the neutron star and the outward moving shock wave. In this region the entropy is so high that the nuclear statistical equilibrium (NSE) favors abundant free neutrons and alpha particles rather than heavy nuclei. This is, therefore, an ideal r-process site which satisfies the requirement from observations 6'7.8'9>10 that the yields be metallicity independent. Using this model, an excellent fit 3 was obtained to the Solar r-process abundance pattern for heavy A > 100 nuclei. The key ingredient in this model is that the large neutrino heating behind the shock generates a great deal of entropy within the bubble. It is in fact the pressure from this heated material which lifts the outer layers of the star. From a nucleosynthesis standpoint the high entropy drives the nuclei into free neutrons and alpha particles so that even with a modestly high electron fraction (Ye ~ 0.45) a large neutron-to-seed ratio can be generated. There are, however, some criticisms of the model. For one, the required high entropy has not been consistently duplicated by other numerical and semianalytic approaches. 11 ' 12 ' 13 ' 14 Another is that previous work 3 did not consider all possible neutrino-nucleus interactions 15>16>17 although they were included 5 to help to smooth the final abundance pattern. It has even been pointed out 18 that the light-element reaction network used in those calculations might have been too limited, at least for ejecta with very high neutron-to-seed ratios. Perhaps, the most glaring difficulty in the original result 3 was an embarrassing overproduction of the intermediatemass (A ~ 90) nuclei, whose abundance was so great that they would have dominated the ejecta from the simulations. Moreover, as we have heard at this workshop 19 it is difficult to get a supernova simulation to explode in spherical symmetry. Except for the lowest-mass progenitors, the Livermore code is the only model which consistently explodes in ID. Nevertheless, in view of the importance of identifying the r-process site, it is important to review the reasons why the LLNL supernova models explode and why that is important for the r-process. Indeed, the fact that other models do not explode and that they do not produce a robust r-process are intimately related as we shall see.

198

2. The LLNL Supernova Code Supernova calculations are exceedingly complex 2 and require careful integration of not only the hydrodynamics but the radiation transport as well. At the same time there is a detailed interplay among the equation of state and weak-interaction nuclear physics. Nevertheless, as to why the Livermore model explodes, can be (over)simplified to a single key ingredient. The LLNL code is optimized 2 to produce an enhanced neutrino luminosity soon after the core bounce. Specifically, the EOS is soft enough to produce a high-temperature core in which large thermal neutrino production occurs. Near the surface of the nascent neutron star, the neutrino emission is helped by the onset of a quasi-Ledoux "neutron-finger" convective instability whereby the higher temperature low-ye material is less buoyant than the cooler temperature high-y e material so that convective overturn dredges material and neutrinos to the surface. We note that this process is very equation-of-state dependent. For the purposes of this workshop it is important to point out that this instability occurs in a region which is nearly accessible experimentally, i.e T ~ 3 — 5 MeV and subnuclear density, p ~ 1 0 1 2 - 1 4 g c m - 3 . Although Ye ~ 0.1 — 0.2, perhaps appropriately designed heavy-ion reactions could help to probe this important effect. Once the neutrino flux has been enhanced, it serves to heat the material behind the shock. Indeed, the energy deposited by neutrinos in the bubble in fact provides the necessary energy to lift the outer layers of the star. The energy deposited, therefore, must be of order ~ 3 x 10 51 erg to account for both the 1.5 x 10 51 erg of kinetic energy and the binding energy of the outer envelope of ~ 2 x 10 51 erg. Indeed, many of the "wind models" to be found in the literature do not come near to the required heating of material in the bubble, and hence it is no surprise that they do not obtain high enough entropy for a successful r-process. To summarize, the key point is that a successful explosion requires strong heating and high entropy in the bubble. This leads to a successful r-process. Or conversely, a successful r-process requires a successful explosion model which sufficiently heats the bubble. The two can not be decoupled. One more remark regarding the heated bubble environment, is that it is somewhat inappropriate to necessarily interpret the bubble environment as a "wind". It is more realistically, a heated semi-hydrostatic radiationpressure dominated layer with an expanding outer boundary. Although, the initial lift off of material from the neutron-star surface approximates the inner portion of a wind solution. The material then slows to become

199 a part of the outward somewhat hydrostatic environment. This provides a long time for heating (i.e. high entropy) during the r-process. Hence, the difference between the wind models and the LLNL results should be interpreted as a break down of the wind model, not the supernova model as some have presumed. 2.1. New improved

results

In the past decade considerable effort has been invested in updating and improving the LLNL code. Among the key refinements, many more energy groups are now included in the neutrino transport scheme.2 Also, there is now a better treatment 20 of the relativistic bending of the neutrino trajectories near the neutron star (this enhances the scattering and heating). There have also been equation-of-state improvements at low Ye and T. Figure 1, illustrates a variety of new mass-cuts lifting from the neutron star during the simulation. These correspond to different refinements of the mass zoning which is why the lines show variable densities. This figure illustrates the way in which the critical last zones relevant for the r-process slow much more than the earlier material and quickly become incorporated into the slow (not wind) evolution of the bubble. Figure 2, shows the evolution of entropy per baryon of material as it enters the bubble. Note that heating within the bubble quickly drives the entropy to high values. Indeed, whereas the previous trajectories 3 achieved s/k ~ 400, the new models produce nearly s/k ~ 600. In other words, the new refinements of the model drive the heating even higher than before. Note, that in Figure 1 the matter leaving the proto-neutron star at late times rises more slowly than the early ejecta. This leads to the higher entropy for matter ejected at late times. 2.2.

Nucleosynthesis

We have made a preliminary calculation of the implied r-process abundance distribution from a sampling of the trajectories of Figures 1 & 2. As a bench mark we first repeated the previous calculation 3 without effects of neutrino-nucleus interactions. Indeed, as before this gives a good rprocess abundance distribution. The higher entropy at late times in the present work actually helps to reproduce the heavy r-process nuclei, and also the overproduction around A ~ 90 is slightly diminished. However, when we include the effects of neutrino-nucleus interactions during the rprocess 15 ' 17 the neutrino induced nucleon emission on 4 He ultimately leads

200

to the overproduction of seed which depletes the r-process of neutrons. Hence, these effects cause the yields of heavy nuclei to be a bit low even for this higher-entropy simulation. The question arises, therefore, as to whether a good r-process is still possible within the hot bubble environment. We are looking into three different possible ways in which this may be achieved. For one, these calculations 3 are based upon a slightly modified version of an old mass formula due to Hilf21 and beta decay rates due to Klapdor 22 . This mass formula has a rather large surface asymmetry term which slows the production of heavy r-process nuclei by keeping the path close to the line of stability. On the other hand, newer mass formulae tend to be softer away from stability. Newer mass formulae and beta-decay rates and may allow for a more efficient flow to heavy nuclei in spite of the fewer neutrons per seed. Another avenue which we are pursuing is the effect of magnetic fields on the neutrino luminosity and the wind. A version of the LLNL supernova code has been modified to include the evolution of an axisymmetric magnetic field (at the perturbation level) along with the spherical hydrodynamics. The angular component of a vector potential and a polar magnetic field are evolved in the simulations. During the collapse, magnetic flux and angular momentum are preserved. The angular velocity of the fluid then becomes nonuniform leading to twisted field lines and a high toroidal field. Initial conditions were selected which led to a typical 10 12 G final magnetic field above the neutron star. A very important result is that the twisting up of the magnetic field leads to magnetic bubbles beneath the neutron-star surface. The buoyancy force ~ B2/8np leads to the onset of convection which brings neutrinos to the surface. The result is that the neutrino luminosity increases enough to induce an explosion without the onset of neutron-finger convection. This may provide a new mechanism to drive the explosion and also to enhance the r-process. Fully axisymmetric MHD simulations are now being run to confirm this important result. Regarding the r-process, in addition to increasing the neutrino luminosity, the development of a polar magnetic field may also promote the development of jetting in the ejected material. This could explain the ubiquity of polarization in Type II supernova debris, and may also provide an environment for the currently popular 13>23>24>25 short timescale r-process which avoids the overproduction of both seed and the intermediate-mass elements. Finally, we comment on one more possible effect of interest. Neutrino oscillations, if present during the r-process, could affect the environment

201 in two ways. For high neutrino energies at a density ~ 105 g c m - 3 , the oscillation of muon neutrinos into electron neutrinos may help to increase the energy deposition within the bubble. At the same time, the oscillation of electron neutrinos into muon neutrinos at low energies at a density of ~ 106 g c m - 3 , may serve to lower Ye in the bubble making more neutrons available for the r-process. Calculations investigating this effect are currently under way. 3. Conclusion The hot supernova bubble environment remains the most robust environment in which the r-process could occur. A point which we emphasize here is that the search for a successful r-process environment and a successful hot-bubble supernova explosion are intimately connected. One can not have one without the other. We have also shown new supernova-model calculations which provide a somewhat better r-process environment than earlier work and shows some promise for ultimately providing a good r-process in a realistic environment. Work in progress will be to utilize modern nuclear mass formulae, and analyze the possible effects of magnetic fields and/or neutrino oscillations. Acknowledgments Work at the Lawrence Livermore National Laboratory performed in part under the auspices of the U. S. Department of Energy under contract W7405-ENG-48 and NSF grant PHY-9401636. Work at the University of Notre Dame supported by the US Department of Energy under Nuclear Theory grant DE-FG02-95ER40934. K.O. wishes to acknowledge partial support from NSF grant PHY02-16783 through the Joint Institute for Nuclear Astrophysics physics (JINA). References 1. Mathews, G. J. and Cowan, J. J. 1990, Nature, 345, 491. 2. Wilson, J. R. & Mathews, G. J., 2003, Relativistic Numerical Hydrodynamics, (Cambridge University Press, Cambridge). 3. Woosley, S. E., Wilson, J. R., Mathews, G. J., Hoffman, R. D., and Meyer, B. S. 1994, ApJ, 433, 229 4. Wilson, J. R. & Mayle, R. W. 1993, Phys. Rep., 227, 97. 5. Meyer, B.S., Mathews, G.J., Howard, W.M., Woosley, S.E., and Hoffman, R.D. 1992, ApJ, 399, 656

202 3x10

2x10

-

-a Pi 1x10

Figure 1. Evolution of radius with time for various mass shells during the new simulations. Note that material ejected at later times evolves with a semi-hydrostatic expansion of the bubble.

6. Sneden, C , McWilliam, A., Preston, G., Cowen, J. J., Burris, D., and Armosly, B. J. 1996, ApJ, 467,819 7. Sneden, C , Cowen, J. J., Debra, L. B., and Truran, J. W. 1998, ApJ, 496, 235 8. Sneden, C , Cowen, J. J., Ivans, I. I., Fuller, G. M., Buries, S., Beers, T. C , and Lawler, J. E. 2000, ApJ, 133, 139 9. Honda, S., Aoki, W., Ando, H., and Kajino, T. 2003, Nucl. Phys. A718, 674 10. Honda, S. et al. (SUBARU/HDS Collaboration), 2004, submitted to ApJ 11. Witti, J., Janka, H.-Th., and Takahashi, K. 1994, A & A, 286, 841 12. Qian, Y.Z., and Woosley, S.E. 1996, ApJ, 471, 331 13. Otsuki, K., Tagoshi, H., Kajino, T., and Wanajo, S. 2000, ApJ, 533, 424 14. Thompson, T. A., Burrows, A., & Meyer, B. S. 2001, ApJ, 562, 887 15. Meyer, B. S. 1995, ApJ. Lett., 449, 55 16. Meyer, B. S., McLaughlin, G. C , & Fuller, G. M. 1998, Phys. Rev., C58, 3696 17. Terasawa, M., Langanke, K., Kajino, T., and Mathews, G. J. 2004, ApJ, in press.

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0

5

10

15

20

time (sec) Figure 2. Evolution of entropy with time for various mass shells ejected during the new simulations. Note that at late times material evolves to very high entropy in the present simulation. 18. Terasawa, M., Sumiyoshi, K., Kajino, T., Tanihata, I., and Mathews, G. J. 2001, ApJ, 562, 470. 19. C. Y. Cardall, this Conf. Proceedings (2004). 20. J. A. Salmonson and J. R. Wilson, ApJ, 517, 859 (1999). 21. Hilf, E. R., von Groote, H. & Takahashi, K. 1976, in Proc. 3rd Int. Conf. on Nuclei far from Stability (Geneva: CERN) 76-13, p. 142. 22. Klapdor, H. V., Metzinger, J., and Oda, T., Atomic Data Nucl.Data, 31,81 (1994) 23. Wanajo, S., Kajino, T., Mathews, G.J., and Otsuki, K. 2001, ApJ, 554, 578 24. Terasawa, M., Sumiyoshi, K., Yamada, S., Suzuki, H., Kajino, T. 2002, ApJL, 578, L137 25. Meyer, B. S. 2002, Phys. Rev. Lett., 89, 1101

EJECTA F R O M P A R A M E T R I Z E D P R O M P T EXPLOSION

SHINYA W A N A J O 1 , N A O K I I T O H 1 , K E N ' I C H I N O M O T O 2 , Y U H R I I S H I M A R U 3 , A N D T I M O T H Y C. B E E R S 4 Department

of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo, 102-8554; [email protected], [email protected] Department of Astronomy, School of Science, University of Tokyo, Bunkyo-ku, Tokyo, 113-0033; [email protected] Department of Physics and Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610; ishimaru@phys. ocha. ac.jp Department of Physics/Astronomy, Michigan State University, E. Lansing, MI 48824; [email protected]

We examine r-process nucleosynthesis in a "prompt supernova explosion" from an 8 — 10M© progenitor star. We simulate energetic prompt explosions by enhancement of the shock-heating energy, in order to investigate conditions necessary for the production of r-process nuclei in such events. The r-process nucleosynthesis is calculated using a nuclear reaction network code including relevant neutron-rich isotopes with reactions among them. The highly neutronized ejecta (Ye PS 0.14 — 0.20) leads to robust production of r-process nuclei; their relative abundances are in excellent agreement with the solar r-process pattern.

1. Introduction The astrophysical origin of the rapid neutron-capture (r-process) species has been a long-standing mystery. So far, the "neutrino wind" scenario, in which the free nucleons accelerated by the intense neutrino flux near the neutrino sphere of a core-collapse supernova assemble to heavier nuclei, has been believed to be the most promising astrophysical site of the r-process 26 . Even this scenario, however, encounters some difficulties 15 3 14 21 19 22 . Hence, it is of special importance to consider alternative possibilities for the occurrence of the r-process in core-collapse supernovae. The question of whether 8 — 10M Q stars that form O-Ne-Mg cores can explode hydrodynamically is still open 25 . The possibility that these stars explode promptly remains because of the smaller iron core present at the onset of the core bounce, as well as the smaller gravitational potential of 204

205

their collapsing cores 18 . Hillebrandt et al. 7 have obtained a prompt explosion of a 9M© star with a 1.38M0 O-Ne-Mg core 13 , while others, using the same progenitor, have not 2 x. Mayle & Wilson 12 obtained an explosion, not by a prompt shock, but by late-time neutrino heating. The reason for these different outcomes is due, perhaps, to the application of different equations of state for dense matter, although other physical inputs may also have some influence. The purpose of this study is to investigate conditions necessary for the production of ^-process nuclei obtained in purely hydrodynamical models of prompt explosions of collapsing O-Ne-Mg cores, and to explore some of the consequences if those conditions are met 23 24 . The core collapse and the subsequent core bounce are simulated by a one-dimensional hydrodynamic code with Newtonian gravity (§ 2). The energetic explosions are simulated by artificial enhancements of the shock-heating energy, rather than by application of different sets of input physics, for simplicity. The r-process nucleosynthesis in these explosions is then calculated with the use of a nuclear reaction network code (§3). The resulting contribution of the r-process material created in these simulations to the early chemical evolution of the Galaxy is discussed in § 4. A summary follows in § 5.

2. Prompt Explosion A pre-supernova model of a 9M© star is taken from Nomoto 13 , which forms a 1.38 M© O-Ne-Mg core near the end of its evolution. We link this core to a one-dimensional implicit Lagrangian hydrodynamic code with Newtonian gravity. This core is modeled with a finely zoned mesh of 200 mass shells (2 x 1 0 - 2 M o to 0.8M o , 5 x HT 3 M© to 1.3MQ, and 5 x 10" 3 - 1 x 1O- 7 M 0 to the edge of the core). The equation of state of nuclear matter (EOS) is taken from Shen et al. 16 , which is based on relativistic mean field theory. The equation of state for the electron and positron gas includes arbitrary relativistic pairs as well as arbitrary degeneracy. Electron and positron capture on nuclei, as well as on free nucleons, are included, along with the use of the up-to-date rates from Langanke & Martinez-Pinedo n . The capture is suppressed above the neutrino trapping density, taken to be 3 x 10 11 g c m - 3 , since the neutrino transport process is not taken into account in this study. Nuclear burning is implemented in a simplified manner. The composition of the O-Ne-Mg core is held fixed until the temperature in each zone reaches the onset of oxygen-burning, taken to be 2 x 109 K, at which point

206

the matter is assumed to be instantaneously in nuclear statistical equilibrium (NSE). The temperature is then calculated by including its nuclear energy release. We begin the hydrodynamical computations with this pre-supernova model, which has a density of 4.4 x 1010 g c m - 3 and temperature of 1.3 x 10 10 K at its center. The inner 0.1M Q has already burned to NSE. As a result, the central Ye is rather low, 0.37, owing to electron capture. The core bounce is initiated when ~ 90 ms has passed from the start of the calculation. At this time the NSE core contains only 1.0MQ, which is significantly smaller than the cases of collapsing iron cores (> 1.3M©). The central density is 2.2 x 1014 g c m - 3 , significantly lower than that of Hillebrandt et al. 7 , although the temperature (= 2.1 x 1010 K) and Ye (= 0.34), are similar. This difference is perhaps due to the use of a relatively stiff EOS in this study. We find that a very weak explosion results, with an ejected mass of 0.008MQ and an explosion energy of 2 x 1049 ergs (model Q0 in Table 1). The lowest Ye in the outgoing ejecta is 0.45, where no r-processing is expected given the entropy of ~ lC/V^fe. This is in contrast to the very energetic explosions, with ejected masses of 0.2M Q , explosion energies of 2 x 10 51 ergs, and low Ye of ~ 0.2 obtained by Hillebrandt et al 7 . This might be a consequence of the lower gravitational energy release owing to the EOS applied in this study. Table 1.

Results of Core-Collapse Simulations

Model

/shock

£ex P (10 5 1 ergs)

M e j (MQ)

Q0...

1.0

0.018

0.0079

0.45

Q3...

1.3

0.10

0.029

0.36

Ke.min

Q5...

1.5

1.2

0.19

0.30

Q6...

1.6

3.5

0.44

0.14

In order to examine the possible operation of the r-process in the explosion of this model, we artificially obtain explosions with typical energies of ~ 10 51 ergs by application of a multiplicative factor (/shock) to the shockheating term in the energy equation (models Q3, Q5, and Q6 in Table 1). We take this simplified approach in this study, since the main difference between our result and that by Hillebrandt et al. 7 appear to be the lower central density in ours. If the inner core reached a higher density at the time of core bounce by applying, for example, a softer EOS, the matter would

207

obtain higher shock-heating energy. This is clearly not a self-consistent approach, and a further study is needed to conclude whether such a progenitor star explodes or not, taking into account a more accurate treatment of neutrino transport, as well as with various sets of input physics (like EOSs). Table 1 lists the multiplicative factor applied to the shock-heating term (/shock), explosion energy (.Eexp), ejected mass (M e j), and minimum Ye in the ejecta obtained for each model. Energetic explosions with EeKp > 1051 ergs are obtained for /shock > 1.5 (models Q5 and Q6), in which deeper neutronized zones are ejected by the prompt shock, as can be seen in Figure 1 (model Q6). This is in contrast to the weak explosions with Ee*p < 1050 ergs (models QO and Q3), in which only the surface of the core blows off. Note that the remnant masses for models Q5 and Q6 are 1.19MQ and 0.94M Q , respectively, which are significantly smaller than the typical neutron star mass of ~ IAMQ. We consider it likely that a mass of ~ 1.4M© is recovered by fallback of the once-ejected matter, as discussed in § 4. In Figure 2 the electron fraction in the ejecta of each model is shown as a function of the ejected mass point, Mej. For models QO and Q3, Ye decreases steeply with M e j, since the duration of electron capturing is long, owing to the slowly expanding ejecta (Figure 1). For models Q5 and Q6, on the other hand, Ye decreases gradually with M e j, owing to the fast expansion of the outgoing ejecta. Nevertheless, the inner regions approach very low Ye, 0.30 and 0.14 for models Q5 and Q6, respectively, owing to their rather high density (~ 10 11 g c m - 3 ) at the time of core bounce (Figure 1). Note that, for model Q6, Ye increases again for Mej > 0.3M©. This is due to the fact that the positron capture on free neutrons overcomes the electron capture on free protons when the electron degeneracy becomes less effective in the high temperature matter. The trend of the Ye — Mej relation up to Mej ~ 0.2M Q is similar in models Q5 and Q6, although it is inverted at Mej ~ 0.14M©, owing to the slightly different contribution of the positron and electron capture on free nucleons (Figure 2). Hence, the Ye — Mej relation between the surface and the innermost layer of the ejecta is expected to be similar to that of model Q6, as long as the explosion is sufficiently energetic (> 10 51 ergs). In the subsequent sections, therefore, we focus only on model Q6, which is taken to be representative of cases where r-process nucleosynthesis occurs. The ejected mass, M e j, is thus taken to be a free parameter, instead of simulating many other models by changing /shock-

208

H

0

1

1

i

1

1

0.5

1

1

1

1

f

1

t (s)

Figure 1. Time variations of (a) radius, (b) temperature, and (c) density for selected mass points (with roughly an equal mass interval) for model Q6. The ejected mass points are denoted in black, while those of the remnant are in grey.

3. The r-Process The yields of r-process nucleosynthesis species, adopting the model described in § 2 for the physical conditions, are obtained by application of an extensive nuclear reaction network code. The network consists of ~ 3600 species, all the way from single neutrons and protons up to the fermium isotopes (Z = 100). We include all relevant reactions, i.e., (n,7), (p,7), (a,7), (p,n), (a,p), {a,n), and their inverses. Reaction rates are taken from Thielemann (1995, private communication) for nuclei with Z < 46

209

0.5

0.4

>"0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

Figure 2. Ye distribution in the ejected material in models QO (open triangles), Q3 (filled triangles), Q5 (open circles), and Q6 (filled circles). The surface of the O-Ne-Mg core is at mass coordinate zero. For model Q6, selected mass points are denoted by zone numbers.

and from Cowan et al. 4 for those with Z > 47. The weak interactions, such as /3-decay, /^-delayed neutron emission (up to three neutrons), and electron capture are also included, although the latter is found to be unimportant. Each calculation is started at T9 = 9 (where T9 = T/10 9 K). The initial composition is taken to be that of NSE with the density and electron fraction at T9 = 9, and consists mostly of free nucleons and alpha particles. Table 2.

Ejected Mass (JW0) 56Ni

Fe

Eu

0.0

0.0018

0.0019

0.0

2.6 x 10~ 4

0.018

0.020

0.0

0.24

0.035

0.018

0.020

2.4 x 10~ 4

Q6c.

0.25

0.051

0.018

0.020

4.1 x 10~ 4

Q6d..

0.27

0.064

0.018

0.020

4.3 x 1 0 - 4

Q6e..

0.30

0.080

0.018

0.020

4.6 x 1 0 - 4

Q6f..

0.44

0.21

0.018

0.020

0.0020

Model

Mej

A> 120

QO ..

0.0079

Q6a..

0.19

Q6b..

The mass-integrated abundances from the surface (zone 1) to the zones 83, 92, 95, 98, 105, and 132 are compared with the solar r-process abundances in Figure 3 (models Q6a-f in Table 2). The latter is scaled to match the height of the first (^4 = 80) and third (A = 195) peaks of the abundances in models Q6a-b and Q6c-f, respectively. The ejecta masses of these

210

models are listed in Table 2. As can be seen in Figure 3, a solar r-process pattern for A > 130 is naturally reproduced in models Q6c-f, while models Q6a-b fail to reproduce the third abundance peak. This implies that the region with Ye < 0.20 must be ejected to account for production of the third r-process peak. Furthermore, to account for the solar level of thorium (A = 232) and uranium (A = 235, 238) production, the region with rather low Ye (< 0.18) must be ejected.

100

150 200 mass number

100

150 200 mass number

Figure 3. Final mass-averaged r-process abundances (line) as a function of mass number obtained from the ejected zones in (a) models Q6a, (b) Q6b, (c) Q6c, (d) Q6d, (e) Q6e, and (f) Q6f (see Table 2). These are compared with the solar r-process abundances (points), which is scaled to match the height of the first peak (A — 80) for (a)-(b) and the third peak (A = 195) for (c)-(f).

We find that, for models Q6c-e, the lighter r-process nuclei with A < 130

211

are somewhat deficient compared to the solar r-process pattern (Figure 3ce). This trend can be also seen in the observational abundance patterns of the highly r-process-enhanced, extremely metal-poor stars CS 22892-052 17 and CS 31082-001 6 . In model Q6f, the deficiency is outstanding because of large ejection of the low Ye matter (Figure 2). This is in contrast to the previous results obtained for the neutrino wind scenario, which significantly overproduce the nuclei with A sa 90 26 21 . The nuclei with A < 130 can be supplied by slightly less energetic explosions, like models Q6a-b (Figures 3a-b). It is also possible to consider that these lighter r-process nuclei originate from "neutrino winds" in more massive supernovae (> 10M Q ). The nuclei with A < 130 can be produced naturally in neutrino winds with a reasonable compactness of the proto-neutron star, e.g., 1.4M© and 10 km 21

Figure 3 implies that the production of thorium and uranium differs from model to model, even though the abundance pattern seems to be universal between the second and third r-process peaks, as seen in models Q6cf. This is in agreement with recent observational results suggesting that the ratio Th/Eu may exhibit a star-to-star scatter, while the abundance pattern between the second and third peaks is in good agreement with the solar r-process pattern 8 . Thus, the use of Th/Eu as a cosmochronometer should be regarded with caution, at least until the possible variations can be better quantified; U/Th might be a far more reliable chronometer 22 23 .

4. Contribution to Chemical Evolution of the Galaxy One of the essential questions raised by previous works is that, if prompt supernova explosions are one of the major sites of r-process nuclei, would in fact the r-process nuclei be significantly overproduced. Our result shows that more than 0.05M© of the r-process matter (A > 120) is ejected per event, which reproduces the solar r-process pattern (models Q6c-f in Table 2). This is about three orders of magnitude larger than the 5.8 x 10~5M© in the neutrino-heated supernova ejecta from a 20M© star obtained by Woosley et al 26 . It might be argued that this type of event is extremely rare, accounting for only 0.01 — 0.1% of all core-collapse supernovae. However, observations of extremely metal-poor stars ([Fe/H] ~ —3) in the Galactic halo show that at least two, CS 22892-052 and CS 31082-001, out of about a hundred studied at high resolution, imply contributions from highly r-process-enhanced supernova ejecta 6 17 . Moreover, such an extremely rare event would result

212

in a much larger dispersion of r-process elements relative to iron than is currently observed amongst extremely metal-poor stars. Ishimaru & Wanajo 9 demonstrated that the observed star-to-star dispersion of [Eu/Fe] over a range ~ — 1 to 2 dex, was reproduced by their chemical evolution model if Eu originated from stars of 8 — 10M Q . Recent abundance measurements of Eu in a few extremely metal-poor stars with [Fe/H] < — 3 by SUBARU/HDS further supports their result 10 . The requisite mass of Eu in their model is ~ 10~6MQ per event. The ejected mass of Eu in our result is more than two orders of magnitude larger (Table 2). In order to resolve this conflict, we propose that the "mixing-fallback" mechanism operates in this kind of supernova 20 . If a substantial amount of the hydrogen and helium envelope remains at the onset of the explosion, the outgoing ejecta may undergo large-scale mixing by Rayleigh-Taylor instabilities. Thus a tiny amount, say, ~ 1%, of the r-process material is mixed into the outer layers and then ejected, but most of the core material may fall back onto the proto-neutron star via the reverse shock arising from the hydrogen-helium layer interface. In this case, the typical mass of the proto-neutron star (~ 1.4MQ) is recovered. An asymmetric explosion mechanism, such as that which might arise from rotating cores, may have a similar effect as the ejection of deep-interior material in a small amount 27 5 . This "mixing-fallback" scenario must be further tested by detailed multidimensional-hydrodynamic studies. However, it may provide us with a new paradigm for the nature of supernova nucleosynthesis.

5. S u m m a r y We have examined the r-process nucleosynthesis obtained in the prompt explosion arising from the collapse of a 9M Q star with an O-Ne-Mg core. The core collapse and subsequent core bounce were simulated with a one-dimensional, implicit, Lagrangian hydrodynamic code with Newtonian gravity. We obtained a very weak explosion with an explosion energy of ~ 2 x 1049 ergs. No r-processing occurred in this model, because of the high electron fraction (> 0.45) with low entropy (~ lOAOifc). We further simulated energetic explosions by an artificial enhancement of the shock-heating energy. This resulted in an explosion energy of > 1051 ergs and an ejected mass of > Q.2MQ. Highly neutronized matter (Ye « 0.14) was ejected, which led to strong r-processing. The result was in good agreement with the solar r-process pattern, in particular for nuclei with A > 130.

213 The large ejection of r-process material (> 0.05.M© per event) conflicts with the level of dispersion of r-process elements relative to iron observed in extremely metal-poor stars. We suggest, therefore, that only a small fraction (~ 1%) of the r-processed material is ejected, while the bulk of such material falls back onto the proto-neutron star by the "mixing-fallback" mechanism. References 1. Baron, E., Cooperstein, J., & Kahana, S. 1987, ApJ, 320, 300 2. Burrows, A. & Lattimer, J. M. 1985, ApJ, 299, L19 3. Cardall, C. Y. & Puller, G. M. 1997, ApJ, 486, LI 11 4. Cowan, J. J., Thielemann, F. -K., & Truran, J. W. 1991, Phys. Rep., 208, 267 5. Fryer, C. & Heger, A. 2000, ApJ, 541, 1033 6. Hill, et al. 2002, A&A, 387, 560 7. Hillebrandt, W., Nomoto, K., & Wolff, G. 1984, A&A, 133, 175 8. Honda, et al. 2004, ApJ, in press 9. Ishimaru, Y. & Wanajo, S. 1999, ApJ, 511, L33 10. Ishimaru, Y., Wanajo, S., Aoki, W., & Ryan, S. G. 2004, ApJ, 600, L47 11. Langanke, K. & Martinez-Pinedo, G. 2000, Nucl. Phys. A, 673, 481 12. Mayle, R. & Wilson, J. R. 1988, ApJ, 334, 909 13. Nomoto, K. 1984, ApJ, 277, 791 14. Otsuki, K., Tagoshi, H., Kajino, T., & Wanajo, S. 2000, ApJ, 533, 424 15. Qian, Y. -Z. & Woosley, S. E. 1996, ApJ, 471, 331 16. Shen, H., Toki, H., Oyamatsu, K., & Sumiyoshi, K. 1998, Nucl. Phys. A, 637, 435 17. Sneden, C., et al. 2003, ApJ, 591, 936 18. Sumiyoshi, K., Terasawa, M., Mathews, G. J., Kajino, T., Yamada, S., & Suzuki, H. 2001, ApJ, 562, 880 19. Thompson, T. A., Burrows, A., & Meyer, B. S. 2001, ApJ, 562, 887 20. Umeda, H. & Nomoto, K. 2003, Nature, 422, 871 21. Wanajo, S., Kajino, T., Mathews, G. J., & Otsuki, K. 2001, ApJ, 554, 578 22. Wanajo, S., Itoh, N., Ishimaru, Y., Nozawa, S., & Beers, T. C. 2002, ApJ, 577, 853 23. Wanajo, S., Tamamura, M., Itoh, N., Nomoto, K., Ishimaru, Y., Beers, T. C., & Nozawa, S. 2003, ApJ, 593, 968 24. Wanajo, S., Goriely, S., Samyn, M., & Itoh, N. 2004, ApJ, 606, in press (ApJ preprint doi:10.1086/383140) 25. Wheeler, J. C., Cowan, J. J., & Hillebrandt, W. 1998, ApJ, 493, L101 26. Woosley, S. E., Wilson, J. R., Mathews, G. J., Hoffman, R. D., & Meyer, B. S. 1994, ApJ, 433, 229 27. Yamada, S. & Sato, K. 1994, ApJ, 434, 268

A R E COLLAPSARS R E S P O N S I B L E FOR SOME R-PROCESS ELEMENTS? H O W COULD W E TELL?

J. PRUET N-Division Lawrence Livermore National Lab 7000 E. Ave, Livermore, GA 94550, USA E-mail: [email protected] We consider the possibility that supernovae which form hyper-accreting black holes might be responsible for synthesis of r-process elements with mass A< 130. Calculations are presented which show that these elements are naturally synthesized in neutron-rich magnetically-dominated bubbles born in the inner regions of a black hole accretion disk. Simple considerations suggest that the total mass ejected in the form of these bubbles is about that needed to account for the entire galactic inventory of the 2nd-peak r-process elements. We also argue that if collapsars are responsible for, e.g., Ag synthesis, then Ag abundances should be correlated with Sc and/or Zn abundances in metal-poor stars.

1. Introduction There is growing evidence that the engines powering long-duration Gamma Ray Bursts (GRBs) are associated with interesting nucleosynthesis. Observations of a characteristic 'red bump' in late-time GRB light curves indicate that many, maybe all, long GRBs copiously produce radioactive nickel moving outwards at fractions of the speed of light 1 ' 2 ' 3 ' 4 . This 56 Ni is familiar as the product of explosive burning occurring as a strong shock sweeps through the stellar mantle in ordinary SNe. In the still mysterious GRB environment, however, the Ni is likely telling us about a unique and different process. Consideration of this will lead to interesting insights about a possible origin for the r-process elements. Though there are other possibilities, we will assume that GRBs are produced by a viscous black hole accretion disk formed after the collapse of a rotating massive star 5 ' 6 . Within the context of this collapsar model there are two ways observed nickel could be synthesized. As in 'successful' SNe, Ni may be synthesized explosively as a strong shock traverses the stellar mantle. One difficulty with this idea is that there is no clear analog of the 214

215 neutron star core bounce that initiates strong shocks in typical SNe. Also, even if some mechanism does initiate a strong shock, the parameters of this mechanism need to be very finely chosen in order to explain observations 7 . Observed nickel might also be synthesized in a vigorous wind blown off the accretion disk surface 6 ' 8 . Here we focus on this possibility. In the next two sections we discuss the composition of the accretion disk and the nucleosynthesis occurring in winds blown from the disk. It turns out that though the disk itself is likely quite neutron rich, it is hard to see how this neutron richness can survive in the wind. So, r-process elements cannot be synthesized in a wind. Section 3 describes a different way of synthesizing heavy, neutron-rich elements - localized bubbles. Section 4 outlines an observational test of whether or not GRBs are responsible for synthesizing some r-process elements. 2. Composition of the accretion disk Before we can understand nucleosynthesis in collapsars, we need to know conditions in the disk material feeding outflows. At large radii the disk is fed by relatively cool bound nuclei found in the stellar mantle. This material has an electron fraction very close to 1/2. Here the electron fraction Ye = p/(n + p), with p and n the number densities of protons and neutrons. As material spirals inwards, viscous heating converts a fraction of the liberated gravitational energy into thermal energy. At a radius of about 108cm the disk becomes hot enough that a-particles and all heavier elements dissociate into free nucleons. Once this happens the charged lepton capture reactions e~p ->• nue +

e n ->• ppe

(1) (2)

begin in earnest. The neutron to proton ratio is then set by a competition between the above processes. The composition of the inner disk is a sensitive function of the rate M at which the disk is accreting onto the black hole and the strength of the viscosity, described here by the usual parameter a. Figure 1 shows the composition of a disk characterized by M = 0.03M Q /sec and a = 0.1 accreting onto a hole of mass 3 M 0 . At small radii neutrino losses become important and sap entropy from the flow. This inner region is characterized by a large electron degeneracy and low electron fraction (Ye w 0.15). Figure 1 was taken from Pruet, Woosley & Hoffman 2003. That work used published disk structures 10 to calculate the disk composition. A somewhat different treatment of the disk composition appeared at about the

216

Log(r)

Figure 1. Composition of an accretion disk characterized by M = O.lMo/sec and a = 0.03. Here Xn is the mass fraction of free nucleons and A e - p ( r / V ) is a rough instantaneous estimate of the number of e^ captures suffered by a nucleon before the nucleon crosses the event horizon. Units for r here are cm.

same time by Beloborodov 11 . Beloborodov develops a useful, semi-analytic, and in some sense self-consistent description of the disk structure and composition. There is basic agreement among different authors that the inner regions of the disk become markedly neutron rich for modest accretion rates (M > 0.1M Q /sec). However, there remain a number of shortcomings in the understanding of accretion disk composition. In the first place, previous efforts are based on 1-d height-integrated approximations for the disk structure. The dependence of Ye on height within the disk, or an adequate understanding of how Ye tends towards the disk surface, has yet to be worked out (though preliminary studies have been made 12 ' 8 ). Secondly, if disk winds really are responsible for observed nickel, then about half of the accreting material must be blown away before it has a chance to get to the black hole. The influence of this mass loss on the disk structure has been studied for a few cases 6 . Feedback on the disk composition remains more or less unstudied. 3. Winds from the Disk MacFadyen & Woosley first calculated that viscous heating above the surface of a disk could deposit entropy and drive a wind. Their observation that nickel might be synthesized in this wind presaged observations of SN-like light curves associated with ordinary GRBs. Calculations and observations of GRBs imply that the wind is very energetic. For SN2003dh, for example,

217 a total outflow kinetic energy of a few times 1052erg was inferred 1 ' 13 . This is an order of magnitude larger than the kinetic energy associated with typical SNe and dwarves the energy in the GRB proper. The large energy carried by the wind implies that the overlying stellar mantle is quickly swept away and can be neglected at the small radii where nuclei are synthesized. This is an important observation because it allows simple treatments of the wind near the central regions of the star. To motivate a discussion of the wind properties we give here a very schematic prescription for calculating the wind: Tds = dQ = (v heating + viscous heating — neutrino losses)

(3)

dYe = ( effect of e±/v capture)

(4)

dv = ( pressure gradient + "centrifugal" forces + gravity )

(5)

Here s is the entropy per baryon and v is the velocity projected along fluid streamlines. Let's compare these terms with their counterparts describing spherically symmetric winds from neutron stars. i) The entropy equation: One interesting result from Qian and Woosley's14 study of outflows from neutron stars (NSs) was that the wind properties important for nucleosynthesis are quite insensitive to the heating rate (i.e neutrino energy deposition rate). For example, those authors found that the asymptotic entropy should scale as L~J , with Lv the ve or De luminosity. In the case of winds from NSs, this insensitivity arises in part because there is an important interplay between the neutrino luminosity and conditions at the base of the wind. At the base of the wind the temperature adjusts itself so that the neutrino heating and neutrino cooling rates balance each other. Things are more complicated for outflows from accretion disks. If a simple a-prescription for the viscosity is used it is found that viscous heating may or may not dominate over neutrino heating, depending on fine details such as the angular momentum of the black hole. Also, there is in general not a tight balance between heating and cooling in the disk. Nonetheless, it has been found that the asymptotic wind entropy is not sensitive to factors of ~ 3 changes in the heating rates 8 . This is comforting because it is generally agreed that "viscous heating" - represented by a shear-stress tensor - is only a very rough representation of the magnetic processes providing viscosity. Because wind properties are not so sensitive to the heating rates, it may be that one can entirely neglect either the neutrino heating or the viscous heating (though not both at the same time) in a description of the wind and get close to the right answer for the asymptotic wind properties.

218 ii) The Ye equation: In winds from neutron stars the electron fraction is set by a competition between ve and ve capture. Apart from effects having to do with nucleosynthesis, the asymptotic Ye just mirrors the neutrino spectrum coming from the NS. Because the neutron star through which the neutrinos diffuse is neutron-rich, the ve spectrum is cooler than the ve spectrum. Consequently, i7ep —>• n wins out over i/en —> p, and the outflow is driven neutron-rich. In winds from accretion disks all factors conspire to drive the outflow proton rich. In part this is because e± capture generally dominates over neutrino capture. Once the entropy of the outflow is raised by viscous heating, the electron degeneracy is removed and positron capture wins out over electron capture because of the neutron-proton mass difference. When neutrinos are important they also tend to drive the outflow proton rich because collapsar-like disks are generally not optically thick to neutrinos and the most energetic neutrinos come from e~p -» nue. iii) Evolution of velocity along fluid streamlines. This is straightforward in the case of spherically symmetric winds from NSs. For winds from disks, this equation seems to kill the possibility of a simple 1-d treatment of the wind. To see why, note that within the disk the azimuthal velocity is essentially Keplerian, so the material already has half the kinetic energy needed to escape the gravitational pull of the black hole. Now, what is the evolution of azimuthal velocity with height above the disk? The answer to this question depends sensitively on the 6 — cj> component of the shear stress tensor, which in turn depends on details of the magnetic processes responsible for viscosity. There are two limiting assumptions. One is that fluid streamlines are frozen into and co-rotate with the disk. In this case no heating is needed to drive material from the disk and the asymptotic entropy can be very low. The other limiting assumption is that the azimuthal velocity reaches the asymptotic value of zero within a few disk-scale heights of the disk mid-plane. In this case the asymptotic entropies are found to be ~ 30 — 50. It is clear from a consideration of the magnetic field strengths needed to anchor streamlines to the disk that the second limiting approximation is closer to the truth. To summarize results of previous studies of disk-winds in broad stroke, asymptotic entropies are modest (< 3 0 - 5 0 ) and the asymptotic Ye is never lower than about 0.45. There is actually a strong anti-correlation between Ye in the disk and Ye at infinity. Heavy neutron rich elements can't be synthesized in winds.

219 4. Bubbles If accretion disks really were characterized by some sort of friction-like microscopic viscosity, then only proton-rich modest entropy outflows would occur. However, it is generally agreed that a magnetic instability, the so called magneto-rotational instability 15 , is responsible for mediating angular momentum transfer in the disk. Because of this, one expects there to be small, localized regions of the disk which have larger than average magnetic field densities. Pressure equilibrium with the ambient fluid implies that these bubbles will be underdense and will rise in the approximately exponential atmosphere of the disk. The time it takes to rise one disk scaleheight is roughly a Kepler period, or about a few ms. This is much faster than the rise time of the wind. The electron capture timescale in the disk is r ec «0.1sec(3MeV/T) 5 ,

(6)

which implies that magnetically dominated bubbles retain their neutronrichness. As a bubble rises magnetic reconnection can convert energy in magnetic fields to thermal energy and in this way increases the entropy of the bubble. In the dynamic collapsar environment there will likely be a wide variety of these bubbles. Without detailed simulations only a few things are known. The electron fraction is somewhere between that characterizing the disk and that characterizing the wind. The asymptotic entropy of the bubbles must be at least as large as that characterizing the wind, otherwise bubbles wouldn't rise, but would instead break early on and mix with the wind. Lastly, the dynamic time scale characterizing the evolution of the wind is likely not much different from the dynamic time scale characterizing the evolution of the bubbles, because both the wind and the bubbles are radiation dominated. For a radiation dominated fluid the pressure is approximately independent of the density. To incorporate these general considerations, we can describe bubbles by s = 50 + 50r; Ye = 0.15 + 0.25r; r = 0.03(1 + 4r) sec; r 9 , m i x = 1 + 2r. (7) Here r is a random number chosen separately for each of the above expressions and T9)mix is the temperature at which the bubble is assumed to break and mix with the wind material. Average overproduction factors for one hundred bubbles generated as described above are shown in Fig. 2. Overall there is quite good agreement with the solar abundance pattern of 90 < A < 130 r-process elements.

220 j

4 ^ / f 10

^f/M /1*%

fRh

i /

T

™X"

*

\ f / v

Y II

X

*

I >5#

-

\

Kr

•

X,

Figure 2. Average overproduction factors for 100 bubbles generated according to eqn. (7). Solid lines connect isotopes of a given element. The most abundant isotope in the Sun for a given element is plotted as an asterisk. A diamond around a data point indicates the production of that isotope as a radioactive progenitor. Agreement with the solar abundance pattern of r-process elements with A < 130 is quite good, though 1 2 7 I is under-produced by a factor of about 4. Production of species heavier than A = 130 is negligible.

If collapsars are responsible for the 2nd peak r-process elements then they must eject Mb « 1 0 _ 5 M Q / / C in the form of bubbles in order to account for the present day inventory of these elements in the galaxy. Here fc is the fraction of core collapse SNe that become collapsars. The collapsar rate is unknown, but is likely ~ 0.1 - 0.01 as large as the SNII rate 1 6 . The total mass needed in the form of bubbles is less than about 0.1% the total wind mass. If typical bubbles are formed with initial radius rj,, temperature T;,, and entropy s& per baryon, the amount of mass needed in the form of bubbles implies that the number of bubbles needed per event is nb

PS

500

sb /^106cm rb J 50

f2MeY\3 \

Tb

J

Mb 1O- 4 M 0 "

(8)

Now, if the disk lasts for a time t comparable to observed durations of GRBs, the number of disk revolutions, or magnetic field windings, per bubble is nwind = wm

J«L „ 8 _*

^_12!,

(9)

2-nnb 50 sec 10 3 sec _1 nb ' which is a reasonable number if magnetic instabilities take a few rotations

221 to develop.

5. How could we tell? There don't seem to be any strong arguments against collapsars as the site of A < 130 r-process elements. In fact, Qian and his collaborators have argued for some time that the 2nd-peak elements are produced in events that occur considerably less frequently than do Type II SNe17 (SNII). This sounds a little like collapsars. Nonetheless, any arguments in favor of collapsars as the source of 2nd peak elements are speculative at best. A clear and convincing observational test is needed. One possible test is a correlation between abundances of second peak relements and nucleosynthetically unrelated elements ejected in the collapsar explosion. To illustrate this idea, suppose that we somehow knew that collapsars make a lot of, say, 45 Sc. A convincing correlation between [Sc/Fe] and [Ag/Fe] in metal-poor stars would be evidence that collapsars make silver. Of course, this idea can only work if other astrophysical events (like SNII) can't explain the correlation. To address this, we need a detailed understanding of what it is that collapsars synthesize. It turns out that even though there are uncertainties concerning the detailed inner-workings of collapsars, a lot can be said about nucleosynthesis in these events by making two plausible assumptions 18 . These are i) that observed nickel is synthesized in a wind from the accretion disk and ii) that the wind provides most of the energy for exploding the star. With these assumptions the only really important unknown is whether Ye in the wind is very close to 1/2, or if instead Ye > 0.51. The assumption that observed 56 Ni comes from the wind means that Ye > 0.485, since more neutron-rich outflows synthesize very little 56 Ni. Figure 3 shows results of nucleosynthesis calculations for collapsar winds characterized by Ye = 0.51 and different dynamic time scales and entropies. In each panel s is the entropy per baryon and -X"(Ni) is the mass fraction of 56 Ni in the wind. A range of s ~ 20 — 50 is thought to approximately bracket the plausible range of entropies found in these winds. The two different calculations shown for each entropy are for the estimated range of plausible dynamic time scales possible in these winds. Though there are some differences between the panels, it is clear that some isotopes - including the only stable Sc isotope - are abundantly synthesized in every case. 46,49 Ti are also abundant, but they make only modest contributions to the total Ti inventory, and it is hard to get isotopic ratios observationally. Cal-

222

culations for winds with Ye very close to 1/2 show that the most abundant elements are 63 Cu and 64 Zn. We'll concentrate on the case Ye > 0.505. For Ye very close to 1/2 one can just substitute 64 Zn for 45 Sc in what follows.

X3

X(Ni)=0.64 s=20

*9

x

\

1 IN

0* # 4?

I

A

I

J_

X(Ni)=0.15 5=50

\ I

X

c» -,

1

1

p—i

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If a wind is responsible for the ~ 1/2M 0 of Ni observed in association with GRBs, then the total wind mass is M win d « 1M Q if X(Ni) ~ 0.5. The production factor of Sc is 0( 4& Sc) =

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223

10 — 20. This means that collapsars make 10 — 50 times more Sc or Zn than typical SNe can. If collapsars are responsible for Ag synthesis, then O(Ag) must also be ~ 300 — 1000, depending on the collapsar rate. In this case, there should be observable correlations between Ag and Sc (or Zn) in metal-poor stars. There are only 4 stars I'm aware of for which both Ag and Sc (or Zn) abundances are known (HD2665, HD6755, HD103095, CS22892-052). For the HD stars there is a modest correlation between [Ag/Fe] and [Sc/Fe] (or [Zn/Fe]). For CS22892-052 [Ag/Fe] ~ 1, while [Sc/Fe] and [Zn/Fe] are close to zero. It will be interesting to see if future observations can confirm or rule out the idea of collapsars as the source of 2nd peak r-process elements. Acknowledgements This research has been supported through a grant from the US DOE Program for Scientific Discovery through Advanced Computing (SciDAC; DEFC-01ER41176). This work was performed under the auspices of the US DOE by the University of California, Lawrence Livermore National Laboratory under contract W-7405-ENG-48. References 1. Woosley, S.E. &; Heger, A. 2003, ApJ, submitted (astro-ph/0309165) 2. Maeda, et al. 2003, ApJ, 593, 931 3. Price, P. A. et al. 2003, ApJ, 589, 838 4. Zeh, A., Klose, S. k. Hartmann, D.H. 2004, ApJ, accepted 5. Woosley, S.E. 1993, ApJ, 405, 273 6. MacFadyen, A.I. & Woosley, S.E. 1999, ApJ, 524, 262 7. Maeda, K. & Nomoto, K. 2003, ApJ, 598, 1163 8. Pruet, J., Thompson, T.A. &: Hoffman, R.D. 2004, ApJ, in press 9. Pruet, J., Woosley, S.E. & Hoffman, R.D. 2003, ApJ, 586, 1254 10. Popham, R., Woosley, S.E. & Fryer, C.L. 1999, ApJ, 518, 356 11. Beloborodov, A.M. 2003, ApJ, 588, 931 12. Surman, R. & McLaughlin, G.C. 2004, ApJ, 603, 611 13. Mazzali, P., et. al. 2003, ApJL, 599, 95 14. Qian, Y.-Z. & Woosley, S.E. 1996, ApJ, 471, 331 15. Balbus, S. A. & Hawley, J. F. 1998, Rev. Mod. Phys., 70, No. 1 16. Heger, A., Fryer, C.L., Woosley, S.E., Langer, N. & Hartmann, D.H. 2003, ApJ, 591, 288 17. Qian, Y.-Z. & Wasserburg, G. J. 2000, Phys. Reps., 333, 77 18. Pruet, J., Surman, R. & McLaughlin, G.C. 2004, ApJL, 602, 101

N E U T R I N O TRANSPORT IN CORE COLLAPSE SUPERNOVAE

MATTHIAS LIEBENDORFER CITA,

University of Toronto, 60 St. George Str., Toronto, ON M5S SH8, Canada E-mail: [email protected] A long lasting pursuit for accurate neutrino transport in core collapse supernovae appears to converge in spherically symmetric simulations. Under the restriction of spherical symmetry, the Boltzmann transport equation can be solved in extenso for neutrinos with individual energies and propagation directions. Comparisons between different numerical methods that solve or approximate the neutrino transport equation are summarized. Neutrino emission is the main channel for the release of the kinetic and thermal energy accrued during gravitational collapse. Recent supernova models with Boltzmann neutrino transport deliver detailed information about the corresponding neutrino luminosities and spectra as a function of time. The impact of the emitted neutrinos on accreted or ejected matter is estimated by the analysis of the equilibrium entropy and electron fraction at fixed neutrino background abundances. Final answers, however, will crucially depend on multidimensional effects, such as the convective turnover in the heating region or debated instabilities in the protoneutron star. What are the main technical difficulties to be encountered in multidimensional simulations and how are they currently approached?

References 1. S. W . B r u e n n , K. R. DeNisco a n d A. M e z z a c a p p a , ApJ 5 6 0 , 326 (2001). 2. R. Buras, M. R a m p p , H.-Th. J a n k a a n d K. Kifonidis, Phys. Rev. Lett. 9 0 , 241101 (2003). 3. C. F . Fryer a n d M. S. W a r r e n , ApJ 5 7 4 , L65 (2002). 4. K. L a n g a n k e et al. a n d Hix et al., Phys. Rev. Lett. 9 0 / 9 1 24/20-1102 (2003). 5. M. Liebendorfer, O. E. B . Messer, A. M e z z a c a p p a , S. W . Bruenn, C. Y. Cardall a n d F.-K. T h i e l e m a n n , ApJS 1 5 0 , 263, (2004). 6. M. Liebendorfer, R a m p p , J a n k a a n d M e z z a c a p p a , astro-ph/0310662. 7. E. Livne, B u r r o w s , Walder, L i c h t e n s t a d t a n d T h o m p s o n , astro-ph/0312633. 8. M. R a m p p a n d H . - T h . J a n k a , A&A 3 9 6 , 361 (2002). 9. T. A. T h o m p s o n , A. Burrows a n d P. A. P i n t o , A p J 5 9 2 , 434 (2003).

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Figure 1. AGILE-BOLTZTRAN solves the neutrino transport equation (7) by the method of discrete ordinates in general relativists space-time. The change of the neutrino distribution function in Eq. (8) is given by spatial advection (9), angular advection (10), gravitational redshift (11), Doppler shift (12), angular aberration (13), and the collision integral (14-16). In the standard setting, the latter includes neutrino scattering on nuclei, nucleons, and electrons. Neutrinos are produced by electron and positron capture on nucleons and nuclei (electron flavor only), or pair production. Neutrinos are annihilated by the inverse reactions. The figure insets demonstrate convergence of the results under the twofold resolution of each neutrino phase space dimension.

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F igure 3. T he electron ca pt ure during collapse determines t he elect ron fraction profile in t he core, which in t urn , de te rm ines where t he shock is form ed at boun ce. If electron ca pt ure on free pr oton s were t he on ly channel, all pr ogeni tor mo de ls would converge on a very sim ilar elect ro n fraction p rofile du ring collapse bec a use of t he h igh sensitivity of t he free proton fracti on on the elect ro n fract ion . T he free pr ot on a bundance acts like an elect ro n-capt ure-am p lifier wit h st ro ng negat ive feedback . However, recent im provem ents of the electron capt ure rates on nu clei ind icate t ha t elect ron captur es on free protons are not t he dom inant channel. It might not com e to t he descr ibed se lf-regulation.

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Figure 9. A c k n o w l e d g e m e n t s : I would like to thank Bronson Messer and Anthony Mezzacappa for their contributions to Agile-Boltztran; Markus Rampp, Thomas Janka, and Steve Bruenn for their prolific exchange of ideas and data for the comparison of methods; Gabriel Martinez-Pinedo, F.-K. Thielemann, and Raph Hix for the collaboration on the analysis of the high electron fraction in the ejecta; and the organizers of this meeting to letting me participate.

C H A N G I N G T H E R-PROCESS P A R A D I G M : MULTI-DIMENSIONAL A N D FALLBACK EFFECTS

C. L. F R Y E R A N D A I M E E H U N G E R F O R D T-6/CCS-4 Los Alamos National Laboratory Los Alamos, NM 87545 E-mail: [email protected]

Supernovae are now known to be far from symmetric. At the very least, rotation and convective instabilities alter the spherically symmetric picture producing asymmetric explosions and leaving behind aspherical neutron stars. These asymmetries may be critical to the mechanism behind supernova explosions. Similarly, asphericities in the core just after the launch of the supernova explosion may well change the yield of r-process nucleosynthesis. Rotation and fallback are two of the major aspherical effects altering the r-process yield. They produce asymmetric winds and can increase the entropy and propagation time of the r-process material. These two processes are reviewed here.

1. Asymmetries in Supernovae Calculations of the r-process yields from core-collapse supernovae have concentrated on the simple picture of a hot, spherically symmetric, neutron star blowing a gentle wind off its surface. This wind produces the r-process yields in supernovae (see Hoffman, Woosley, & Qian 1997; Thompson, Burrows, & Meyer 2001 and references therein). The problem with these spherically-symmetric wind calculations is that spherical winds can not produce the observed r-process yields: either the entropy of the material in these winds is too low, or the time the wind's material spends at nuclear burning temperatures is too short. Theorists have reviewed the nuclear burning cross-sections (e.g. Borzov 2003 and articles in this proceedings), played with neutrino oscillations (e.g. McLaughlin et al. 1999) and even argued for large magnetic fields (Qian & Woosley 1996). But, to date, no one has used any of the information we have learned from studying the core-collapse supernova mechanism itself. One aspect of supernovae ignored in these calculations is that supernovae are generally not symmetric. For example, rotating stars will pro234

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duce asymmetric supernovae with rapidly spinning neutron stars (Fig. 1 Eryer & Heger 2000). Prom figure 1, we see that the velocity of the shock is nearly two times faster along the rotation axis than in the equator and that the neutron star has an accretion disk of sorts in the equator where the angular momentum is highest. Another aspect of supernovae that is ignored is fallback. Even though the shocked material initially moves out from the proto-neutron star, within

236 the first 10 s after the launch of the explosion, 0.1 - 0.5M© falls back onto the proto-neutron star. Although Qian & Woosley mentioned that fallback may have an effect on r-process back in 1996, at that time, very little was known about fallback in supernovae. To date, the only numerical studies of supernova fallback (e.g. Fryer, Benz, k, Herant 1996; Fryer, Colgate, & Pinto 1999) have not investigated the effects fallback would have on the r-process and no r-process calculations have included these effects. Let's address both these effects in more detail. 2. Stellar Rotation and Neutrino Emission Rotation produces asymmetries in the remnant as well as in the explosion ejecta. The weaker explosion along the plane of rotation leads to more mass along this plane. Due to rotation, this material does not accrete onto a spherically symmetric neutron star. Instead, it piles up in a disk around the neutron star. The resulting density profile is far from symmetric (Fig. 2). Fig. 2 shows density contours of the central ~ 100 km of the exploding star 1.5 s after explosion. The density remains above 10 1 2 gcm - 3 beyond 50 km in the equator. Along the poles, the density falls below this value at ~20km. Most of the neutrinos leaving the protoneutron star arise from material lying above this disk (Fig. 3). In the disk and the neutron star core, material densities are high, and neutrinos must diffuse out before they can escape. The bulk of the neutrino heating from absorption occurs just at the point that the disk becomes optically thin to neutrinos (where there is still a lot of material to absorb the neutrinos). This is where the wind will be strongest. But this heating region is far from symmetric (Fig. 4), and the wind from such asymmetric heating will also not be spherically symmetric. Note that we have neglected neutrino/anti-neutrino annihilation in this calculation and this will change the location of neutrino heating. Asymmetric neutrino heating may not be a large effect, but we won't know until we run more detailed simulations. 3. Fallback The launch of an explosion shock off of the proto-neutron star does not signal the end of mass accretion onto that compact remnant. This exploding material decelerates as it pushes against the stellar layers above it and some of this material will fall back onto the proto-neutron star. For strong (normal) supernova explosions, the amount of fallback, occuring primarily

237

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in the irst 10s, ranges from 0.1 - 0.5 M 0 (Hungerford, Fryer & Timmes 2004). This fallback material will rain down on the bubble of r-process material blowing off from the proto-neutron star. Detection of r-process

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material signatures in subsequent generations of stars or meteorites requires that this material somehow percolate up through the fallback and become part of the explosion ejecta.

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Such a process can be very different from the typical models used in today's wind calculations and suggests that we may need a paradigm shift in our basic model for r-process yields. Let's look at the effects of fallback in more detail. In the 1-dimensional case, fallback will halt the expansion

240

of the r-process wind. Assuming neutrinos continue to heat this r-process wind-turned-bubble until it can drive off the infalling material, this delay may both slow down the bubble expansion as well as raise the bubble's entropy (both of which push toward r-process yields that better match observations).

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Can we estimate this delay? Let's assume heating is rapid, and the pressure of the infalling material can be estimated by its ram pressure P = 0.5/9Ufree_fall (if matter builds up at this shock, it can be much higher). Then for the bubble to throw off this material, its pressure must equal this ram pressure. Assuming an equilibrium atmosphere, the entropy is given

241 by (see Fryer, Benz, Herant 1996 for details): 5 r a d = 1.4 x 1 0 - n P 3 / 4 / p ,

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where 5 ra a is the entropy in k& per nucleon, P is the pressure in ergs/cm 3 , and p is the density - which, in turn, is a function of the radius of the accretion shock. Figure 5 shows the entropies of an exploding bubble for 3 different accretion rates as a function of shock radius. Typically fallback accretion rates lie between 104 — 10 5 M Q /y and we see that, for accretion shocks between 100-150km, we can easily achieve entropies in excess of 500 &B per nucleon. This simple 1-dimensional analysis does not present a full picture of what actually happens. The r-process wind material will bubble through the fallback. The fallback will tunnel through the bubble and shock against the proto-neutron star. Some of this shock-heated material will also bubble up, increasing the r-process yield. At the very least, 2-dimensional simulations are required to understand this process. Figure 6 shows the hot rising bubble of shocked fallback material 0.5 s after the fallback has commenced. Although some material is building up on the neutron star, the hottest material is actually rising, and will likely escape. This material becomes neutron rich due to electron capture. It reaches temperatures well above nuclear statistical equilibrium temperatures and its entropy (primarily through shock heating) can exceed a few hundred &B per nucleon (Fig. 7)Depending upon how much of this material ultimately is ejected, it is a prime candidate for r-process. Without further simulations, it is difficult to tell what effect fallback will have on the r-process yields. This meeting jump-started projects on both the fallback and neutrino asymmetry effects and we should have much better analyses of both these aspects of supernovae and their effects on r-process nucleosynthesis soon. Acknowledgments It is a pleasure to thank the Institute for Nuclear Theory where discussions on the r-process prompted this project. This work was performed under the auspices of the University of Arizona and the U.S. Dept. of Energy, and supported by its contract W-7405-ENG-36 to Los Alamos National Laboratory as well as DOE SciDAC grant number DE-FC02-01ER41176. References 1. A. L. Hungerford, C. L. Fryer, and Timmes, in preparation

242

10 x(I000 km) Figure 6. Entropy (shading) and velocity (vectors denote direction and magnitude in the x-y plane) from a 2-dImensional simulation of supernova fallback onto the protoneutron star. An accretion shock moves outward as material builds'up on the protoneutron star. The Innermost material is shocked the hardest and has the highest entropy. It then converts upward, driving plumes out of the star. Because the exploding star was rotating, the fallback material has angular momentum and moves furthest where the angular momentum Is highest.'The shock is at 15000km in this region whereas It is only at 2000 km along the rotation axis. This convection produces a much different entropy profile than one would expect In 1-dimension. This simulation uses the 2»dimensional accretion code of Rryer et al. (1996).

2. Borzov, I. N. Nuc. Phys. A 718, 635 (2003). '3. C. L. Fryer, W. Benz and M. Herant Astrophysical Journal 460, 801 (2000). 4. C. L. Rryer, S. A. Colgate, and P. A. Pinto Astrophysical Journal 5 1 1 , 885 (2000). 5. C. L. Rryer and A. Heger Astrophysical Journal 5 4 1 , 1033 (2000). 6. A. L. Hungerford, C. L. Pryer and M. S. Warren Astrophysical Journal 594, 390 (2003).

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Figure 7. Entropy versus radius for the 2-dimensional simulation (dots) and a 1dimensional analytic calculation (thick line). The hot rising bubble takes the highest entropy material and causes it to rise out into the star. This material becomes neutron rich due to electron capture near the neutron star surface. As it shocks, its entropy can exceed a few hundred fee per nucleon and temperatures are well above the nuclear statistical equilibrium limit. 7. R. D. Hoffman, S. E. Woosley a n d Y.-Z. Qian Astrophysical Journal 4 8 3 , 951 (1997). 8. G. C. McLaughlin, J. M. Fetter, A. B . Balantekin, a n d G. M. Fuller, Phys. Rev. C 5 9 , 2873 (1999). 9. T. A. T h o m p s o n , A. Burrows a n d B . S. Meyer Astrophysical Journal 5 6 2 , 887 (2001). 10. Y.-Z. Qian and S. E. Woosley Astrophysical Journal 4 7 1 , 331 (1996).

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PARTICIPANTS OF THE FIRST ARGONNE/MSU/JINA/INT RIA WORKSHOP NATIONAL INSTITUTE FOR NUCLEAR THEORY UNIVERSITY OF WASHINGTON, SEATTLE JANUARY 8-10, 2004

Dominik Argast University of Basel [email protected]

Oliver Arndt Institut fur Kernchemie [email protected]

Sam Austin Michigan State University [email protected]

Baha Balantekin University of Wisconsin-Madison bahaQnuct h. physics. wise. edu

Wolfgang Bauer Michigan State University [email protected]

Timothy C. Beers Michigan State University [email protected]

Jose Benlliure Universidad de Santiago de Compostela j [email protected]

Jeff Blackmon Oak Ridge National Laboratory [email protected]

Christian Cardall Oak Ridge National Laboratory [email protected]

Jason Clark Argonne National Laboratory [email protected]

Andrew Davis University of Chicago [email protected]

David Dean Oak Ridge National Laboratory [email protected]

Iris Dillmann University of Basel [email protected]

Jacek Dobaczewski Warsaw University [email protected]

Jonathan H. Engel University of North Carolina [email protected]

Chris Fryer Los Alamos National Laboratory [email protected] 245

246 Hans Geissel GSI [email protected]

Wick Haxton University of Washington [email protected]

Paul Hosmer Michigan State University [email protected]

Yuhri Ishimaru Ochanomizu University [email protected]

Jennifer Johnson Hertzberg Institute of Astrophysics Jennifer [email protected]

Filip Kondev Argonne National Laboratory [email protected]

Karl-Ludwig Kratz Universitaet Mainz [email protected].

Matthias Liebendoerfer University of Toronto liebend@cita. utoronto .ca

Grant Mathews University of Notre Dame [email protected]

Bradley Meyer Clemson University [email protected]

Fernando Montes Michigan State University [email protected]

Peter Parker Yale University [email protected]

John Michael Pearson University of Montreal [email protected]

Jason Pruet Lawrence Livermore National Lab [email protected]

Yong-Zhong Qian University of Minnesota [email protected]

Thomas Rauscher University of Basel [email protected]

Sanjay Reddy Los Alamos National Laboratory [email protected]

K. Ernst Rehm Argonne National Laboratory [email protected]

Krzysztof Rykaczewski Oak Ridge National Laboratory [email protected]

Hendrik Schatz Michigan State University [email protected]

Ivo Seitenzahl University of Chicago [email protected]

Andrew Steiner University of Minnesota [email protected]

Mariko Terasawa University of Tokyo [email protected]

Todd Thompson University of California, Berkeley [email protected]

Mark Wallace Michigan State University [email protected]

William Walters University of Maryland [email protected]

Shinya Wanajo Sophia University [email protected]

Andrew Westphal University of California, Berkeley [email protected]