The abundances of the elements in the atmospheres, i.e. the directly observable layers, of the stars are related to the energy production by nuclear processes in the interior of the stars and to their evolutionary states. For purposes of quantitative analysis of a given stellar spectrum, several “model atmospheres” are first calculated, assuming tentative numerical values for the effective temperature Te, for the gravitational acceleration g at the surface of the star, and for the relative abundances of the more important elements. The appropriate temperature distribution is obtained from the theory of radiative equilibrium in conjunction with the quantum theory of the continuous absorption coefficient; the pressure stratification is obtained from the hydrostatic equation. Evaluation of the Fraunhofer lines requires a theory of line absorption coefficients and line widths. In conclusion, the final numerical values for Te, g, and the abundances of the elements in the stellar atmosphere are determined by comparison of the calculated spectra with the measured spectrum of the star. The main sequence stars and the hot supergiants, i.e. the star population I of the spiral arms and the disk population of the Milky Way, all have the same chemical composition, which coincides with that of the interstellar medium. In the old population II stars of the galactic halo (high velocity stars, subdwarfs), on the other hand, the abundance of all the heavy elements relative to that of hydrogen is reduced by a factor of as high as 200, possibly even 500; hydrogen seems to be the original material of our Milky way. In helium stars, almost all the hydrogen has been transformed into helium even in the atmosphere; it is likely that these are well mixed stars.
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