Stellar Masses

Dependence of other stellar parameters on mass The Russell–Vogt theorem states that, if we know a star’s mass and its CHEMICAL COMPOSITION, we can use the laws of physics to determine all of its other properties: its luminosity, its radius, its temperature and density profiles, and how these properties change with time. (We know that this is a slight simplification; for instance, the amount of net ANGULAR MOMENTUM will also affect a star’s structure and evolution.) Compared with the possible range of masses a star may have ((0.08– 150)M⊙), there is only modest variation possible in the initial composition, and thus it is primarily a star’s mass at birth which determines the basic essentials of its structure and future life. Some of the properties of stars are given in table 1 as a function of stellar mass for stars on the main sequence, the core H-burning phase that accounts for 90% of a star’s life. These values have been taken from stellar models computed with a composition that is initially solar. We list the stellar parameters at the beginning and end of the main-sequence lifetimes, except for the lowest-mass stars, for which we adopt the parameters corresponding to an age of 1 Gyr, by which time these stars are stably burning hydrogen. Generally the behavior of the stellar parameters with stellar mass is quite different for the higher-mass stars ((25–120) M⊙) than for solar-type stars ((0.8–1.2) M⊙). The dependence of luminosity on stellar mass is shown in figure 1. This mass–luminosity relationship is considered one of the most fundamental descriptions of stellar properties; the ability to reproduce this by stellar models was one of the great vindications of theory (see also HERTZSPRUNG–RUSSELL DIAGRAM). EDDINGTON first demonstrated that radiative diffusion in stars requires that the stellar luminosity will depend on mass roughly as the fourth power, i.e. L ~ M. However, it is clear from figure 1 that no single exponent describes the dependence of luminosity on mass over the entire range of stellar masses. If we consider different mass ranges we would find that the following are good approximations: and