Stellar Envelope Convection Calibrated by Radiation Hydrodynamics Simulations: Influence on Globular Cluster Isochrones

Abstract

One of the largest sources of uncertainty in the computation of globular cluster isochrones and hence in the age determination of globular clusters is the lack of a rigorous description of convection. Therefore, we calibrated the superadiabatic temperature gradient in the envelope of metal-poor low-mass stars according to the results from a new grid of two-dimensional hydrodynamical models, which cover the main sequence and the lower red giant branch of globular cluster stars. In practice, we still use for computing the evolutionary stellar models the traditional mixing-length formalism, but we fix the mixing-length parameter α in order to reproduce the run of the entropy of the deeper adiabatic region of the stellar envelopes with effective temperature and gravity as obtained from the hydrodynamical models. The detailed behavior of the calibrated α depends in a nontrivial way on the effective temperature, gravity, and metallicity of the star. Nevertheless, the resulting isochrones for the relevant age range of Galactic globular clusters have only small differences with respect to isochrones computed adopting a constant solar calibrated value of the mixing length. Accordingly, the age of globular clusters is reduced by 0.2 Gyr at most.