As a result of studying many binary systems, astronomers have a good idea of the masses of main sequence stars. These results are summarized in Table 5.1. Just as the Sun's temperature places it in the middle of the main sequence, its mass is in the middle of the range of stellar masses. The lowest mass main sequence stars have about 0.07 of a solar mass, and the most massive stars commonly encountered have about 60 solar masses. When we think of how large or small stars might have turned out to be, the observed range of stellar masses is not very large. This range is an important constraint on theories of stellar structure.
Table 5.1.1 Mass and spectral type (MS).
Spectral type M/M
An even more stringent constraint is the relationship between mass and temperature on the main sequence. The cooler stars are less massive and the hotter stars are more massive. We have already said that the existence of the main sequence implies a certain relationship between size and temperature. This means that if a star is on the main sequence, once its mass is specified, its radius and temperature are determined. Another way of looking at this to say that a star's mass determines where on the main sequence it will fall.
Since the mass determines the radius and temperature of a main sequence star, it should not be surprising that it also determines the luminosity. The exact dependence of the luminosity on mass is called the mass-luminosity relationship. This relationship is also explainable from theories of stellar structure. This relationship is shown in Fig. 5.12. We can summarize it by saying that the luminosity varies approximately as some power, a, of the mass. If we express luminosities in terms of solar luminosities, and masses in terms of solar masses, this means that
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