Introduction

Stellar spectra differ widely. Lines of atomic hydrogen are strong in the spectrum of the bright star Sirius, relatively weak in the solar spectrum, while lines of iron and other metals are strong in the solar spectrum, weak or absent in the spectrum of Sirius. Do such differences in the relative strengths of spectral lines reflect differences in relative abundances? Can we conclude that the atmosphere of Sirius is made up largely of hydrogen while the solar atmosphere consists largely of metal atoms?

Since the early 1920s astronomers have understood that the most conspicuous differences between stellar spectra arise from differences in the temperature of the atmospheric layers where the spectral lines are formed, rather than from differences in the relative abundances of the chemical elements. To absorb light at the frequency of one of the Balmer lines, a hydrogen atom must be in its first excited state. The fraction of hydrogen atoms in this state depends on the temperature (and, much more weakly, on the pressure). At the temperature of the solar photosphere (the visible layer of the Sun's atmosphere), nearly all of the hydrogen atoms are in the ground state, where they can absorb lines of the ultraviolet Lyman series. The spectrum of Sirius is formed at a temperature of around 10000 K. A much larger (though still numerically small) fraction of the hydrogen atoms is in the first excited state at this temperature. At still higher temperatures hydrogen is almost fully ionized, so the relative population of the first excited state is again very low.