The Size, Structure, and Variability of Late-Type Stars Measured ...

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giant stars nearing the final stages of their lives. The bottom-left contains a few hot white
dwarf stars which mark the final stage of a star’s active life.
The stages of stellar evolution in the H-R diagram for a star of mass 1, 5, and
25 M ⊙ are outlined in Figure 1.6 (from Iben (1985) [49]). When stars first form from a
collapsing cloud of gas, they take their place on the main sequence. Here, hydrogen at
the core is under enough pressure and hot enough to fuse. The released radiation pressure
supports the star from further gravitational collapse, and a steady-state is reached. More
massive stars reach equilibrium at hotter temperatures and are more luminous. Most of the
life of the star is spent on the main-sequence as hydrogen gradually is converted to helium.
More massive stars have much higher rates of fusion at their core and consequently run out
of hydrogen sooner than less massive stars. As the core becomes deficient in hydrogen, the
star enters the next stage in its evolution.
The lack of hydrogen in the stellar core means much less energy generation at the
star’s center. With no radiation pressure to support it, the core collapses under gravity,
and becomes very hot. This causes the hydrogen in the shell surrounding the core to heat
up as well and because of its extreme temperature dependence, the rate of fusion soars.
This radiation increases the luminosity of the star several magnitudes, and the radiation
pressure causes the outer stellar layers to expand to many times their original size and
become cooler. As this occurs, the star will move up and to the right in the H-R diagram
as shown in Figure 1.6. At this point the star could be classified as a sub-giant. Eventually,
the helium core will become so dense that the degeneracy pressure of the free electrons
provide the dominant support against gravitational collapse. When this occurs, the star is
a red giant.
That the star expands when its core contracts is reproducible using hydrodynamic
theory. However, there is a more fundamental reason that this is so. The Virial Theorem,
applied to a gravitationally bound body composed of an ideal gas in hydrostatic equilibrium,
states that the total gravitational potential energy stored in the star is twice the thermal
energy stored in the kinetic motion of the gas particles. The evolution from main sequence
to giant occurs as the hydrogen in the core is used up. This process occurs slowly enough
that hydrostatic equilibrium can be assumed. Thermal equilibrium can also be assumed
if the change in energy of the star is small compared to its total energy. In this case, the
Virial theorem will hold. Since the total energy of the star is conserved and a fixed relation
exists between the thermal and gravitational energy, each can be supposed to be conserved