Stars as Laboratories for Fundamental Physics - MPP Theory Group

34 Chapter 2
stellar-evolution codes use hydrostatic stellar structure equations which
ignore kinetic energies which are small in stationary phases or phases
of slow expansion or contraction (Sect. 1.2.1). However, in a phase of
fast expansion kinetic energies can be large. It is not known whether
the helium flash is a hydrostatic or a hydrodynamic event. Secondly,
convection undoubtedly plays a large role at transferring energy from
the ignition point. Note that helium ignites off-center because neutrino
losses cause a temperature dip at the center. A fundamental theory
of convection does not exist; it is likely that one would have to perform
a three-dimensional hydrodynamic calculation to develop a full
understanding of the helium flash.
2.1.4 The Horizontal Branch
After helium ignition the overall luminosity has dropped as explained
above, and the surface has shrunk considerably, leading to a substantially
hotter (bluer) configuration. Precisely how blue an HB star becomes
depends on the size of its envelope and thus on its total mass.
A substantial amount of mass loss occurs on the RGB where the photosphere
of the star is so inflated that it is only weakly gravitationally
bound; a red giant may typically lose about 0.2 M ⊙ of its envelope
before helium ignites. Presumably, the amount of mass loss is not exactly
the same from star to star; a small spread of order 0.03 M ⊙ is
enough to explain the wide range of surface radii and thus colors found
for these objects which form a horizontal branch in the color-magnitude
diagram. 6 The downward turn of the HB in Fig. 2.3 is an artifact of the
filter which determines the visual brightness—the bolometric brightness
is the same. It is fixed by the core properties.
In practice, the HB morphology found in different clusters is complicated.
Some clusters have widely spread HBs such as that shown in
Fig. 2.3 while others have stars only near the red or blue end, and gaps
and blue tails occur. One important parameter is the metallicity of the
envelope which determines the opacity to which the envelope structure
is very sensitive. However, one finds clusters with the same chemical
composition but different HB morphologies, a phenomenon which has
prompted a search for the “second parameter.” Many suggestions have
been made by some and refuted by others. One candidate second parameter
which appears to remain viable is the cluster age, or rather,
the MS mass of the stars observed today on the HB. The envelope mass
6 For recent synthetic HBs see Lee, Demarque, and Zinn (1990, 1994).