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

Abstract

The method developed by Ra elt (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, M c , from properties of the color-magnitude diagrams of Galactic globular clusters is employed. In the present study, we revise and update Ra elt's database, including also constraints from RR Lyrae pulsation, and nd that a small increase, by M c 0:01 0:015 M , cannot be ruled out with the present data and evolutionary models. Our new upper limits on M c are less restrictive than those previously obtained by Ra elt, as are the corresponding constraints on novel astroparticle phenomena which may a ect the evolution of low-mass red giants. Within the estimated uncertainties, however, the standard values of M c may also be acceptable. Ra elt'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 in uence of a non-solar ratio for the -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 ash that is obtained from evolutionary computations, such as: heat conduction by electrons in the degenerate core; Coulomb e ects upon the Equation of State; triple-reaction rates and screening factors; neutrino emission rates, both standard and enhanced by a possible non-zero magnetic moment; stellar rotation; microscopic element di usion; and energy losses by axions and Weakly Interacting Massive Particles.

Astrophysical Axion Bounds

“…One consequence is that the RGB will extend to brighter stars, i.e., the brightness of the brightest red giant in a given globular cluster signifies the core mass at helium ignition. Detailed studies reveal that the core mass at helium ignition agrees with theoretical expectations within 5-10% [10,[52][53][54][55]. In turn, this implies that a novel energy-loss rate at T = 10 8 K and an average density ̺ = 2 × 10 5 g cm −3 should not exceed about 10 erg g −1 s −1 .…”

Red Giant Branch Stars: The Theoretical Framework

“…As pointed out by Catelan, de Freitas Pacheco, & Horvath (1996), the most recent results by I83 are an improvement over the older HL69 ones, but their range of validity does not cover the He cores of RGB stars. The I83 opacities are generally smaller than those obtained from the HL69 tables, thus implying larger values of at the He He M core flash.…”

“…The appropriate regime for the He ignition in low-mass stars is the intermediate one (e.g., Graboske et al 1973 (Caloi, D'Antona, & Mazzitelli 1997). More recent developments do not modify appreciably the He core masses obtained with this formalism (e.g., Catelan et al 1996;Cassisi et al 1998). …”

“…Their formula improves the previous results by Munakata, Kohyama, & Itoh (1985), which were widely used in stellar evolution calculations. Switching from the Munakata et al (1985) results to the Haft et al (1994) Catelan et al 1996;Cassisi et al 1998). The quoted uncertainty on the Haft et al (1994) result is ‫,%5ע‬ corresponding to a negligible uncertainty on the core mass at the flash (Castellani & Degl'Innocenti 1999).…”

Variable Stars in the Unusual, Metal-rich, Globular Cluster NGC 6441

“…The mean mass of 0.47 is M _ about 0.02 smaller than the canonical helium core mass M _ at the helium Ñash (see Table 1 in Sweigart 1987 ; see also Sweigart 1994 andCatelan, de Freitas Pachaco, &Horvath 1996 for extensive discussions of possible sources of uncertainty in the helium core mass at the helium Ñash). It is unlikely that a star with this mass would become an RRL.…”