Computer Science
Scientific paper
Feb 1969
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1969saosr.293.....p&link_type=abstract
SAO Special Report #293 (1969)
Computer Science
76
Scientific paper
We consider the calculation of the emergent contours of the Balmer lines in the early type stars and possible sources of errors in these calculations. In particular, we consider 1) the uncertainties in the broadening theory, 2) the uncertainties in the temperature distributions from the model atmospheres, and 3) the possibility of significant departures from LTE. The broadening thoeries of Kolb and Griem and of Edmonds, Schluter, and Wells (ESW) are discussed and compared. It is found that the ratio of the equivalent widths of Ha and Hy for temperatures and gravities corresponding to late B main-sequence stars is sensitive to the differences in the broadening theories. And, we find that this ratio is insensitive to uncertainties in the model atmospheres. We also discuss the approximation of detailed balancing in the lines as applied to the calculations of the departures from LTE in the lower states of hydrogen. We extend previous arguments and show that detailed balancing in the bound-bound transitions is a valid approximation through at least the fifth level of hydrogen for calculating the departures in the photospheric layers of a model atmosphere. We further show that the approximation is valid for calculating the wings of the Balmer lines to within 1 AÅ of line center. The effects of departures on the emergent wings of the Balmer lines are discussed and it is shown that the equivalent width of Ha may be significantly reduced at sufficiently low surface gravities. Again, the ratio of the equivalent width of Hα and Hγ is found to be a sensitive test of the effects of departures, but among the late B stars, important effects are limited to high luminosity objects. We also consider the problem of calculating correctly the centers (Δλ 1 Å) of the Balmer lines. To this end we discuss an integral equaltion method, the "simultaneous method," for dealing with line transfer problems. We apply this method to the calculation of Hα and find that that we reproduce at least qualitatively the structure in the core of Ha found in the early type stars. Finally, we consider from two points of view the problem of uncertainties in the temperature distributions in the models. First we derive a temperature correction method based on the integral equation for the integrated flux. This procedure is tested on a few standard cases and is found to be rapidly convergent and practical for the modern computer. Second, we consider the use of Hα as a probe of the relative temperature distribution over four decades in optical depth. This is possible only if we have an accurate method of calculating the line centers of Ha, and the line transfer methods described above meet that requirement. To test the accuracy of our Balmer line calculations we have obtained photoelectric and photographic observations of the first three Balmer lines in a number of late B stars over a wide range of luminosities. The following results are obtained. 1) Temperature distributions: We find that the line center observations of Hα in Sirius and Vega suggest that the temperatures of these stars at τ5000 ~ 10-4 as compared to the temperatures at optical depth unity are significantly lower than predicted by the models. In the case of Sirius the differences are as much as 800°K. We attribute this to the blanketing effects of the strong lines. 2) The broadening theories: We find that the observations of Sirius and Vega, as graphed in a plot of the equivalent widths of Hγ versus Hα, indicate a serious disagreement with the Kolb-Griem broadening theory for the lowest Balmer lines. We consider this as further support for the ESW broadening theory and conclude that gravity determinations from Hγ profiles may now be made with systematic errors smaller than +/- 0.1 in log g. 3) Departures from LTE: The observations of high luminosity B stars, again plotted in the W(Hγ) - W(Hα) graph find good quantitative agreement with the non-LTE calculations. We find that important effects from departures from LTE in the Balmer lines in late B stars are limited to luminosity classes I and II. Finally, perhaps the most interesting result of the thesis is the prediction of emission in the wings of Hα at the lowest surface gravities allowed by radiation pressure. this emission is in good qualitative agreement with the observations of Hα in the less luminous Iα supergiant B stars.
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