.719L THE SPECTRA OF WHITE DWARFS .125. J. Beverly T. Lynds Ap Berkeley Astronomical Department, University of California Received December 10, 1956; revised January 7, 1957 1957 ABSTRACT The spectra of twenty-three white dwarfs were obtained with the Crossley nebular spectrograph of the Lick Observatory. Seventeen of these stars show strong hydrogen absorption lines which, by a com- parison with S. Verweij’s theoretical profiles, indicate log g values of the order of 7.0. A correlation is found between the strength of the hydrogen lines and the colors of the white dwarfs such that those stars hav- ing B — V colors of about +0.1 have the strongest hydrogen lines, in keeping with the same correlation found for main-sequence stars. Three of the white dwarfs observed have no strong absorption features and are classified as í<continuous-spectrum,, stars. Of the three remaining stars observed, two have spectra similar to van Maanen 2, and one is the helium star, L 930-80. SPECTROGRAPHIC DATA Twenty-three white dwarfs were observed with the Lick Observatory Crossley nebu- lar spectrograph, which has a dispersion of 430 A/mm at H7. Eastman IIa-0 plates, baked for 2 days at 50° C, were used. The calibration was put on a separate plate from the same packet. The calibration plate and the spectral plates were developed simulta- neously. At least two spectra of each white dwarf were obtained, with the exception of L 930-80. For all stars but 40 Eri (B), Luyten’s finding charts (1949) were used. Colors of seventeen white dwarfs observed were kindly supplied by D. L. Harris. C. R. Lynds furnished the colors of VR 7 and L 1244-26. All the colors are unpublished preliminary values. THE HYDROGEN LINES IN WHITE DWARES The hydrogen lines in white dwarfs are so broad that it has been possible to determine the profiles of some of them, in spite of the low dispersion of the spectra. Line profiles and equivalent widths were measured for H7, H<5, and He for all the hydrogen-line stars observed, while Hf was also measured when possible. No correction was applied for instrumental broadening because of the width of the lines. Luyten (1952) suggested a possible correlation between color and line strength, but his data gave no evidence of this. There seems to be such a correlation, as illustrated in Figure t, in which the equivalent widths of H7 are plotted as a function of the B — V color of the white dwarfs. The variation in hydrogen strength with color for main-sequence stars is given in Figure 2. The equivalent widths of H7 were taken from Günther (1933), and the colors are those of Johnson (1953). A maximum is reached at about the B — V color of +0.1. In this respect the main-sequence stars and the white dwarfs are similar. DETERMINATION OF LOG g Kuiper (1939) found that the hydrogen lines in white dwarfs are primarily broadened by the interatomic electric fields in the dense atmospheres of white dwarfs, and thus they may be represented by Stark-broadened profiles. Since the physical parameters determining the Stark profiles of an absorption lines are the surface gravity and the temperature, the profiles of the hydrogen lines offer a method of determining the surface gravity, g, or the effective temperature. The procedure adopted here is that of determin- ing the effective temperatures of a star from its color and then using the profiles of the 719 © American Astronomical Society • Provided by the NASA Astrophysics Data System .719L 720 BEVERLY T. LYNDS .125. J. hydrogen lines to determine log g. The temperatures adopted are the effective tempera- Ap tures of the main-sequence stars having the same B — V color as the white dwarf. Once the temperatures are determined for the stars, log g’s may be estimated if a suitable 1957 theory is available. For very strong fields the Holtsmark distribution may be used; con- sequently, it is possible to use Verweij’s theoretical profiles (1936) with some confidence. For lower temperatures, however, his results are not valid, because of the neglect of H“ as a source of opacity. Actually, in white dwarfs, H- becomes important at temperatures less than or equal to 10000°. In Figure 3 the half-width of H7 at a residual intensity of 0.9 is plotted against the adopted teperatures. The curves in the figure represent the variation of the half-width of the theoretical profiles of Hy, as computed by Verweij, with the temperature for vari- E A. 40 20 Fig. 1.—Correlations between equivalent widths of H7 and the B — V colors of white dwarfs E.A. 1 1 1 \ ^ ^—i 1 r 20 10 i i i 0.2 0.0 +0.2 +0.4 B-V Fig. 2.—Correlation between equivalent widths of H7 and the B — V colors of main-sequence stars © American Astronomical Society • Provided by the NASA Astrophysics Data System WHITE DWARFS 721 ous log g values. Thus, if Verweij’s theory is applicable to the atmospheres of white dwarfs, one should be able to read off the appropriate value of log g for each point, once the temperature is known. The stars observed have similar log g values, most of them lying between 6.8 and 7.5 c.g.s. units. According to Verweij’s results, the sharp increase in width of Hy as the temperature increases and the temperature of maximum width are essentially independ- ent of log g, although the magnitude of the variation is sensitive to the surface gravity. This is probably the reason why the general variation of hydrogen strength with color or spectral type is the same as that of main-sequence stars with respect to the sharp rise before maximum as well as the location of the maximum intensity. The difference be- tween main-sequence stars, with a maximum equivalent width of Hy of about 17 A, and white dwarfs, with a maximum equivalent width of Hy of about 50 A, is the result of the much higher surface gravities of the white dwarfs. The fact that there is a corre- Fig. 3 —^Variation in the half-width of H7 at a residual intensity of 0.9 with the temperature The curves represent the variation in half-width of the theoretical profiles of Hy as computed by Verweij. The solid curve is the variation for log g = 7.0; the dashed curve, for log g = 60; the dashed portion of the curve above the log g = 7 0 curve is the interpolated variation for log g = 7.5. latíon bétween equivalent width and color of white dwarfs indicates that the values of the surface gravity for these stars are similar. One check on the determination of the temperature and surface gravity by this method is available in the case of 40 Eri (B). If the value of 13000° is adopted for the temperature (Berger, Chalonge, Divan, and Fringant 1952) and a mass of 0.43 solar mass (Popper 1954), then, since the parallax is known, the radius and consequently the surface gravity may be calculated. These values give a log g = 7.7 According to Verweij^ theory, such a combination should give a half-width for Hy of 60 A, while the observed half-width is 63 A. COMPARISON OP THEORETICAL AND OBSERVED PROPILES Using this method of determining log g, we are assured that the theoretical and ob- served profiles will fit at one point. Figure 4 contains a comparison of the entire profiles for three of the white dwarfs whose log g values are close to 7.0. Because of the approxi- mations in the theory, the central parts of the theoretical lines are not valid ; therefore, © American Astronomical Society • Provided by the NASA Astrophysics Data System 722 BEVERLY T. LYNDS we require a fit only in the wings. We are limited in the direct comparison by the number of theoretical profiles computed by Verweij. In some cases it was necessary to plot the two theoretical profiles which bracket the observed temperatures. The agreement be- tween the observed and the theoretical profiles is very good, except for the case of HZ 43, possibly caused by the extreme shallowness of the line or possibly due to a very high surface temperature, as suggested by Greenstein (1954). The two sharp-line stars have temperatures well into the region where H~ plays an important role, so that this analysis should not be used. Although it has not been possible to compare directly the profiles of 40 Eri (B) (log g = 7.7) and L 1244-26 (log g = 8.4), the wings of the theoretical profiles may be cal- culated to a first approximation by the relation given by Verweij : AX ^ gO-«)/5. This has been done, and the comparison is given in Figure 5. The agreement is surprisingly good. 100 a Fig. 4 —Profiles of the H7 line for L 1512-34 (B) (top) ; VR 7 (left), and He 3 (right). The dashed lines are Verweij’s theoretical profiles of H7 for the same temperatures and surface gravities of the white dwarfs. too a Fig. 5.—^Profiles of the H7 line for o2 Eri (B) (left) and L 1244-26 (right). The dashed curves are Ver- weifs theoretical profiles of H7 for the same temperatures and surface gravities of the two stars. © American Astronomical Society • Provided by the NASA Astrophysics Data System WHITE DWARFS 723 Since Verweij has calculated the profiles of the first four Balmer lines, it is possible to repeat this analysis for Hô.