On the Distance of the Sun from the Galactic Plane

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Apeculiar meteorological phenomenon has been noticed bothintheMount Wilson and Tucson measurements. When the sky is perfectly clear, so that no whiteness can be seen up to the limb of the sun from sunrise to sunset, the morning and afternoon observations agree in giving nearly the same results, i.e., the intensity of the ultra-violet light is the same for a given hour-angle east and west of the meridian. Ordinary clouds and haze do not seem to affect the ratio ultra-violet to green remarkably, but haze of another kind does. Estimates of the radius of the corona about the sun due to sky whiteness are made at intervals during each day's run and are recorded on a scale of 0 to 10. Generally, this whiteness is nearly zero until 11 A.M., then it begins to rise rapidly, attaining a value of 6 or 7 by 1 P.M., after which it gradually increases to 8 or 9 by sunset. This haze has the appearance of smoke, and in the afternoon may be seen from Mount Wilson, filling the valley below and rising in clouds considerably above the mountain. Figure 2 illustrates, at the right, a nearly perfect day, and, at the left, a typical day affected by haze in the afternoon. On account of this effect, only morning observations have been used to study the solar variation. It is possible that this phenomenon is connected with atmospheric ionization, and the afternoon runs may furnish material for its study. 1 Ann. Astroph. Obs., Smithsonian Institution, 4, 206, 1922. 2 Proc. Roy. Soc., 104, 252, 1923. J. Physique Radium, 7, 257, 1926.

ON THE DISTANCE OF THE SUN FROM THE GALACTIC PLANE By B. P. GaRAsIMovI6 AND W. J. LUYTZN HARVAw COLLUGS OBSERVATORY Communicated April 27, 1927

It is a well-known fact that when a plane of symmetry is determined from the positions on the sphere of various classes of galactic objects the intersection of this plane with the celestial sphere is not a great circle, showing that the sun is not situated in this plane of symmetry but is displaced to the north of it. From the observed angular "dip" of the circle of symmetry of stars of given apparent magnitude, the elevation of the sun above the galactic plane may be calculated when the absolute brightness of the stars under consideration is known, and conversely, once the linear distance of the sun to the galactic plane is known, the angular "dip" of a group of stars may be used to estimate their absolute brightness. The existing determinations of the elevation of the sun above the galactic

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plane (E) are very discordant, ranging from 0 (Seares') to 250 parsecs (Kreiken2). These discordances may be easily explained by the method used; using the faint stars of the galactic regions we are dealing with very large distances and a small uncertainty of the curves of equal density leads to very large variation in E which measures the eccentric position of the sun inside these curves. On the other hand, using the different objects which show galactic concentration we get concordant values of E. It seems, therefore, that at present the most reliable values of E are those calculated by means of objects showing strong galactic concentration stars of Classes 0 and B, the c and ac stars, and the Cepheid variables. Of these stars we have recent determinations of E for all, except the Cepheids. Cepheids.-Hertzsprung3 in 1913 derived a value of +37 parsecs for E using 68 Cepheids; in 1918 with a different selection and weighting of the material Shapley4 derived E = +60. Considering the large number of Cepheids discovered in recent years a new determination of E which also makes use of a more accurately determined period luminosity curve may be of value. For this purpose we have taken all stars in Abteilung II of the Astronomische Gesellschaft Catalogue of Variable Stars5 for 1927 with periods between one and forty days, which are known to be Cepheids. Using the recently determined photographic period luminosity curve6 and adopting the A. G. data on the spectra to establish the color indices of variables observed visually, the following preliminary four values of E (arithmetic means in parsecs) were calculated. E = +42 using only stars which at minimum are brighter than 8.5 (vis.) or 9.0 (pg.) (45 stars) E = +38 using stars brighter than 9.0 (vis.) 9.5 (pg.) ( 54 stars) E = +39 using stars brighter than 9.5 (vyis.) 10.0 (pg.) ( 78 stars) E = +34 using stars brighter than 10.0 (vis.) 10.5 (pg.) (100 stars) The good agreement between these values indicates that the mean value of E may be considered as statistically stable and not dependent upon selection in apparent magnitude, at least for magnitudes brighter than 10.5. The Cepheids fainter than this limit are mostly confined to restricted regions in the sky, especially near v Carinae, in Cygnus, Aquila and Cassiopeia. Inclusion of these stars would make the whole material statistically inhomogeneous on the one hand and would tend on the other hand to make the resulting value of E dependent upon the average galactic latitude of one or two particular regions. It seems therefore that restriction to stars brighter than apparent magnitude 10.5 in minimum (photographic) is justifiable inasmuch as it will give us a material of optimum homogeneity. The distribution of the Z coordinates of 100 Cepheids is shown in figure 1

VoL. 13, 1927

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ASTRONOMY:

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389

plotted on probability paper. The ordinates represent the number of stars whose Z coordinates are algebraically larger than the values indicated by the corresponding abcissae. We read from the curve Probable error = 70 Mean Z = -32, (strictly speaking these are the median and the quartile deviation). The computed arithmetic mean is -35, closely agreeing with the value found here from the integrated curve. We may, therefore, adopt as a final value s

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for the elevation of the sun above the plane defined by the Cepheid var-

iables: 11 (mean error) c and ac Stars.-Using only the three clusters of c stars in Carina, Scutum, and Perseus and adopting -3.2 as mean absolute magnitude of these stars, Schilt7 has derived a value of +53 parsecs for the distance of the sun from the galactic plane. It seems to us that a more generally representative value of E may be derived by using the angular dip of - 1O0 found by Schilt from all the c and ac stars (400 in number). Retaining his value of -3.2 for the mean absolute magnitude we then find:

E = + 34

E = +33

O and B Stars.-Gerasimovic has derived a value of +31 6 parsecs using 144 non-Magellanic 0 stars.8 Using all BO and B5 stars of the H. D. C. between 6.7 and 8.75 apparent magnitude the same investigator9 found E = +34 parsecs with an estimated mean error of not more than 4 parsecs. This value was derixved not from the apparent elevation but by calculating the coordinates of the center of gravity. =

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We thus have:

Cepheids c and ac stars 0 stars B stars

E = +34 parsecs E = + 33 parsecs E = +31 parsecs E = +34 parsecs.

The four different determinations lead to such closely accordant results that it seems unnecessary to consider the matter of giving different weights to the individual values and we adopt E = +33 parsecs as the best value for the elevation of the sun above the galactic plane defined by the Cepheid variables, the 0, B and c and ac stars. The mean error of this result is estimated at not more than 3 parsecs. Novae.-It may be of interest to apply the results derived above to the problem of novae. For two reasons, however, it does not seem advisable to do so at present; firstly, because the observational data are largely subject to selection on the basis of apparent magnitude, and secondly, since some novae are known to have originated from dwarf stars, it is not a priori evident that novae must have a strong galactic concentration. The combined effect of these causes is visible in the lack of correlation between apparent magnitude and galactic latitude. If novae have a galactic concentration then the existing material is statistically incomplete and the results would be too dependent upon single cases (e.g., Nova T Coronae and Nova Aquarii). M-Supergiants.-In their recent paper on the parallaxes of M stars Adams, Joy and Humason10 make the statement that the M giants with absolute magnitude brighter than -1.0 show a pronounced galactic concentration. It is rather unfortunate that the number of stars available is too small to afford an independent accurate determination of E. Rejecting the stars in the ht and x Persei cluster there remain only 20 stars, for which the Mount Wilson parallaxes give a mean Z coordinate of + 1S 9, or E = -18, thus placing the sun on the south side of the plane of these M1 stars. 1 Seares, Amer. Astr. Soc., Dec., 1926. Kreiken, M. N. R. A. S., 86, 1926 (665). 3 Hertzsprung, A. N., 196, 1913 (207). 4Shapley, Mt. TVilson Contr., 157, 1918 (23). 5 Kleinere Veroff. Babelsberg, 1, 1927. 6 Shapley, Yamamoto, and Wilson, Harz. Circ., 280, 1925. 7Schilt, B. A. N., 48, 1924 (47). 8 Gerasimovic, A. N., 226, 1926 (327). 9 Gerasimovic, V. J. S., A. G., 61, 1926 (227). '° Adams, Joy and Humason, Ap. J., 64, 1926 (225). 2