Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 67
log Z ⊙ = −1.7 one finds
log Z = [Fe/H] + log Z ⊙ = [Fe/H] − 1.7. (2.15)
Because globular-cluster metallicities cover a range of Z = 10 −4 to 10 −2
a typical average value is log Z = −3 or [Fe/H] = −1.3. The primordial
helium abundance is thought to be about 23%. Therefore, it is useful
to employ the “reduced” composition parameters
Y 23 ≡ Y env − 0.23,
Z 13 ≡ log Z + 3 = [Fe/H] + 1.3, (2.16)
which are zero for a typical globular cluster.
b) Core Mass at Helium Ignition
One of the most important quantities to be affected by a novel energyloss
mechanism is the core mass at the helium flash because helium
ignition is an extremely sensitive function of the temperature. Based
on the Sweigart and Gross (1978) models Raffelt (1990b) has derived
the analytic approximation
M c = 0.500 − 0.22 Y 23 − 0.011 Z 13 − 0.021 M 7 + δM c , (2.17)
where all stellar masses are understood in units of the solar mass M ⊙ .
Here, M c is the core mass at helium ignition and M 7 ≡ M − 0.7 is
the “reduced total mass.” I have increased M c by 0.004 relative to
the original calculation to account for the corrected plasma neutrino
emission rate (Haft, Raffelt, and Weiss 1994). Within about 0.003 M ⊙
Raffelt and Weiss (1992) found the same expression (when corrected for
the plasma rates) except for a slightly shallower metallicity dependence.
Recently, Sweigart (1994) has reviewed the core-mass calculations
at the helium flash. All workers seem to agree within a few 10 −3 M ⊙
except for Mazzitelli (1989) who found core masses larger by some
0.020 M ⊙ . Sweigart (1994) claims that this disagreement cannot be
attributed to the algorithm adopted to accomplish the “shell shifting”
of the numerical grid which represents the star on a computer.
Because of substantial mass loss on the RGB the meaning of the
total mass M in this equation is not entirely obvious. If there were
enough time to relax to equilibrium one would think that it is the instantaneous
mass at the helium flash. Indeed, Raffelt and Weiss (1992)
found in an evolutionary sequence with mass loss that the end mass determined
M c . However, in this calculation the mass loss was stopped