Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 31
As hydrogen burning continues it dumps more and more helium on
the core which at first supports itself by thermal pressure. Soon it
becomes so dense, however, that the electrons become degenerate, inverting
the mass-radius relationship to R ∝ M −1/3 (Sect. 1.2.2). Thus,
as the helium core mass M c grows, the core radius R c shrinks. The
gravitational potential Φ c at the edge of the core is determined entirely
by the core because the envelope contributes little due to its large extension
so that Φ c ≈ −G N M c /R c ∝ M 4/3
c . Because the hydrogen-burning
shell above the core still supports itself by thermal pressure, the temperature
near the core edge is determined by Φ c ∝ M 4/3
c . The growing
core mass causes the hydrogen burning shell to become ever hotter!
Because of the steep T dependence of the hydrogen burning rates, the
growing core causes the star to become ever brighter (Fig. 2.6). In this
Fig. 2.6. Evolutionary track of a 0.8 M ⊙ star (Z = 0.004) from zero age
to the asymptotic giant branch. The evolutionary phases are as in Fig. 2.3.
(Calculated with Dearborn’s evolution code.)