The treatment of mixing in core helium burning models -- II. Constraints from cluster star counts

TL;DR

This study uses star counts in globular clusters to constrain models of core helium burning, revealing that certain mixing schemes align with observations if specific conditions are met, challenging previous assumptions about core breathing pulses.

Contribution

It provides the most statistically robust measurement of the star ratio R_2 in globular clusters and links asteroseismic constraints to stellar evolution models.

Findings

Measured R_2 = 0.117 ± 0.005, more consistent than previous estimates.

Luminosity difference between HB and AGB is ΔlogL = 0.455 ± 0.012.

Standard models underestimate R_2 compared to observations.

Abstract

The treatment of convective boundaries during core helium burning is a fundamental problem in stellar evolution calculations. In Paper~I we showed that new asteroseismic observations of these stars imply they have either very large convective cores or semiconvection/partially mixed zones that trap g-modes. We probe this mixing by inferring the relative lifetimes of asymptotic giant branch (AGB) and horizontal branch (HB) from $R_2$, the observed ratio of these stars in recent HST photometry of 48 Galactic globular clusters. Our new determinations of $R_2$ are more self-consistent than those of previous studies and our overall calculation of $R_2 = 0.117 \pm 0.005$ is the most statistically robust now available. We also establish that the luminosity difference between the HB and the AGB clump is $\Delta \log{L}_\text{HB}^\text{AGB} = 0.455 \pm 0.012$. Our results accord with earlier findings that standard models predict a lower $R_2$ than is observed. We demonstrate that the dominant sources of uncertainty in models are the prescription for mixing and the stochastic effects that can result from its numerical treatment. The luminosity probability density functions that we derive from observations feature a sharp peak near the AGB clump. This constitutes a strong new argument against core breathing pulses, which broaden the predicted width of the peak. We conclude that the two mixing schemes that can match the asteroseismology are capable of matching globular cluster observations, but only if (i) core breathing pulses are avoided in models with a semiconvection/partially mixed zone, or (ii) that models with large convective cores have a particular depth of mixing beneath the Schwarzschild boundary during subsequent early-AGB `gravonuclear' convection.