Stars as Laboratories for Fundamental Physics - MPP Theory Group

78 Chapter 2
Y env > 0.22 is probably a conservative estimate. This takes us back
to the conclusion that δM c ≈ 0 within at least 0.025 M ⊙ . Again, the
core mass at helium ignition is found to agree with the standard result
to better than 5%.
2.4.6 Systematic Uncertainties
The globular-cluster argument yields some of the most restrictive limits
on novel modes of energy loss. Therefore, it is important to understand
some of the systematic uncertainties that enter the nominal limit
δM < c ∼ 0.025 M ⊙ .
Core rotation has often been quoted as an effect to change M c .
However, as it would actually delay helium ignition it cannot be invoked
to compensate for anomalous cooling effects. In addition, if fast core
rotation were an important effect one would expect it to vary from star
to star, causing a random broadening of the distribution of ∆M tip
HB,
HB is
an effect not indicated by the observations. The scatter of ∆M tip
completely within observational errors and within the scatter caused
by the effect that the brightest red giant is not exactly at the tip of the
RGB in a given cluster. Further discussions of the rotational impact
on M c are found in Catelan, de Freitas Pacheco, and Horvath (1995).
The uncertainty of the conductive opacities are relatively large as
stressed by Catelan, de Freitas Pacheco, and Horvath (1995). However,
conceivable modifications of M c do not seem to exceed the 0.010 M ⊙
level even with extreme assumptions.
One of the main theoretical weaknesses of the helium-ignition argument
is that the helium flash has never been properly calculated.
Because helium ignites off-center one expects that convection plays a
major role in the process of heating the entire core and its expansion.
One may worry that in the process of the flash, parts of the core are
ejected into the stellar envelope, reducing its post-flash size. However,
if significant amounts of helium were ejected, the inferred Y env would be
changed dramatically. Even the ejection of 0.010 M ⊙ of helium would
increase Y env by 0.03 if one assumes an envelope mass of 0.3 M ⊙ and
thus would brighten RR Lyrae stars by 0.12 mag. Within the stated
limit of δM c < 0.025 M ⊙ , mass ejection from the core is a dramatic
effect that would be hard to hide in the data.
One significant systematic uncertainty arises from the relative abundance
of metals among each other which is usually fixed by the solar
mixture (Ross and Aller 1976). The assumption of a Ross-Aller mixture
for metal-poor systems like globular-cluster stars has been called