The Helium-Core Mass at the Helium Flash in Low-Mass Red Giant Stars: Observations and Theory

The method developed by Raffelt (1990a,b,c) to estimate a possible increase in the standard values of the helium-core mass at the tip of the red giant branch, $\Mc$, from properties of the color-magnitude diagrams of Galactic globular clusters is employed. In the present study, we revise and update Raffelt's database, including also constraints from RR Lyrae pulsation, and find that a small increase, by $\Delta\Mc \approx 0.01\pm 0.015 \Msun$, cannot be ruled out with the present data and evolutionary models. Our new upper limits on $\Delta\Mc$ are less restrictive than those previously obtained by Raffelt, as are the corresponding constraints on novel astroparticle phenomena which may affect the evolution of low-mass red giants. Within the estimated uncertainties, however, the standard values of $\Mc$ may also be acceptable. Raffelt's method does not rule out a low envelope helium abundance in globular cluster giants, though again the standard values are compatible with the available constraints. The influence of a non-solar ratio for the $\alpha$-capture elements upon these results is also investigated. In addition, we review several aspects of the input physics employed in red giant stellar evolutionary calculations, with the purpose of evaluating possible sources of uncertainty in the value of the helium-core mass at the helium flash that is obtained from evolutionary computations, such as: heat conduction by electrons in the degenerate core; Coulomb effects upon the Equation of State; triple-$\alpha$ reaction rates and screening factors; neutrino emission rates, both standard and enhanced by a possible non-zero magnetic moment; stellar rotation; microscopic element diffusion; and energy losses by axions and Weakly Interacting Massive Particles.