I will endeavor to motivate the seemingly paradoxical fact that while main sequence
stars exhibit a strong dependence of luminosity on mass, the maximum brightness
of almost all stars is quite independent of mass.
- Main Sequence Luminosity--- For a forming star to collapse under gravity, a tremendous amount of gravitational potential energy must be liberated. This is accomplished mainly by frictional heating of gas as it falls in, so that it can radiate away its gravitaional energy. However, as the protostar gets denser, heat becomes trapped, and by the time gas has condensed into a star, the center has become extremely hot, of order 10 million degrees. This is so hot, that spontaneous nuclear fusion ensues (see my previous article Why the Sun Shines). The outward pressure from the heat of fusion balances the inward pressure of gravity. More massive stars have more gravitational energy, and must burn hydrogen much more quickly to stave of further gravitational collapse. This faster burning translates into greater luminosity. In fact, for these main sequence stars, the luminosity (rate of burning) goes as roughly the 4th power of the mass, so that a star with twice the mass of the sun is about 16 times brighter. Since the available hydrogen to burn goes as the mass, the lifetimes of stars on the main sequence goes roughly as 1 over the cube of the mass. Thus a star twice as massive as the sun lives only 1/8 as long.
- Red Giant Luminosity--- Given the above description of how more massive main sequence stars are much, much brighter than lesser main sequence entrants, it seems very strange that in the next stage of evolution, the red giant branch, stars of nearly all masses exhibit the same luminosity. The reason for this is a difference in the physics of red giant stars compared with main sequence stars. As stars in the latter stages of the main sequence burn, helium (heavier than hydrogen) begins to settle to the center of the core. This helium is just as hot (10 million degrees) as the surrounding hydrogen, but does not fuse, because even higher temeratures are required for helium to fuse. Slowly more and more helium builds up in the core and contracts into an inner core which resists gravity only by stacking atoms upon atoms, like bricks. This contraction liberates more gravitational energy and hence produces still more heat. The helium becomes so hot that it acts as a stove and causes the surrounding hydrogen to blaze away at incredible speed, which produces still more helium. The core has now become so hot that energy cannot
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