Stars as Laboratories for Fundamental Physics - MPP Theory Group

68 Chapter 2
sometime before helium ignition and so this finding is not surprising.
Castellani and Castellani (1993) studied RG sequences with mass loss
in more detail and found the surprising result that the core mass at
helium ignition was determined by the initial stellar mass while the envelope
structure followed the instantaneous envelope mass. Apparently,
in these calculations the core retained memory of a previous configuration.
The total amount of mass loss on the RGB may be of order
0.2 M ⊙ , causing a maximum discrepancy between the two scenarios of
about 0.005 M ⊙ in the expected M c .
In Eq. (2.17) a deviation δM c was explicitly included which represents
nonstandard changes of M c . The core-mass increase δM c is
the main quantitity to be constrained by observations. It should be
thought of as a function of the parameters which govern the physics
which causes the delay of helium ignition such as coupling constants of
particles which contribute to the energy loss, or a more benign parameter
such as the angular frequency of core rotation.
c) Brightness at Helium Ignition
Next, the brightness at helium ignition is needed, identical with the
brightness at the tip of the RGB. In the Sweigart and Gross (1978)
calculations, both the luminosity and the core mass at the helium flash
are functions of Z, Y env , and M. For the present purposes, however, the
core mass at helium ignition must be viewed as another free parameter
which is controlled, for example, by the amount of energy loss by novel
particle emission. In order to determine how the luminosity at helium
ignition varies with M c if all other parameters are held fixed Raffelt
(1990b) considered ∂ log L/∂M c for a grid of Sweigart and Gross tracks
near the flash. An interpolation yields
log L tip = 3.328 + 0.68 Y 23 + 0.129 Z 13 + 0.007 M 7 + 4.7 M c ,
(2.18)
with L tip the luminosity at the RGB tip in units of L ⊙ . Ignoring the
dependence on the total mass here and in Eq. (2.17) one finds for the
absolute bolometric brightness of the RGB tip 11
M tip = −3.58 + 0.89 Y 23 − 0.19 Z 13 − 11.8 δM c , (2.19)
slightly different from the results of Raffelt (1990b) who used the mass
of RR Lyrae stars for the total mass in Eq. (2.18).
11 Recall that the absolute bolometric brightness is given by M = 4.74 − 2.5 log L
for L in units of L ⊙ , M in magnitudes.