Stars as Laboratories for Fundamental Physics - MPP Theory Group

The Energy-Loss Argument 13
ing M; stars with M < ∼ 0.25 M ⊙ are fully convective. For M > ∼ M ⊙
the outer regions are radiative while the core is convective out to an ever
increasing mass fraction of the star with increasing M. A star with M
near 1 M ⊙ is very special in that it is radiative almost throughout; the
Sun is thought to have only a relatively minor convective surface layer.
Besides transporting energy, convection also moves matter and thus
affects the composition profile of a star. This is seen, for example, in
the upper panels of Fig. 2.4 where the hydrogen depletion of a solar
model (which is radiative) is a function of the local nuclear burning
rates while for the convective helium core of a horizontal-branch (HB)
star the helium depletion reaches to much larger radii than nuclear
burning. The long lifetimes of HB stars cannot be understood without
the convective supply of fuel to the nuclear furnace at the center. The
Sun, on the other hand, will complete its main-sequence evolution when
hydrogen is depleted at the center, corresponding to about a 10% global
depletion only.
The extent of convective regions can change during the course of
stellar evolution. They can leave behind composition discontinuities
which are a memory of a previous configuration. For example, on the
lower red-giant branch (RGB) the convective envelope reaches so deep
that it penetrates into the region of variable hydrogen content caused
by nuclear burning. Later, the convective envelope retreats from the advancing
hydrogen-burning shell which encounters a discontinuity in the
hydrogen profile. This causes a brief “hesitation” on the RGB ascent
and thus a “bump” in the distribution of stars in the color-magnitude
diagram of globular clusters on the lower RGB. This bump has been
identified in several clusters (Figs. 2.18 and 2.19); its location is in good
agreement with theoretical expectations (Fusi Pecci et al. 1990).
1.2.5 Gravitational Settling
The composition profile of a star can also change by diffusion, and notably
by gravitational settling of the heavier elements. This effect was
ignored in most evolution calculations because the time scales are very
large. Still, the settling of helium will displace hydrogen from the center
of a hydrogen-burning star and thus accelerate the depletion and
main-sequence turnoff. The gravitational settling of metals will lead
to an opacity increase in the central regions. Helium settling reduces
the inferred globular cluster ages by 1 Gyr or more which is about a
10% effect (Proffitt and Michaud 1991; Chaboyer et al. 1992). Because
the inferred globular cluster ages are larger than the expansion