A non-local mixing-length theory able to compute core overshooting

TL;DR

This paper introduces a novel non-local mixing-length theory based on plume and mean-field equations that accurately models core overshooting in stellar convection zones, improving upon existing approximative methods.

Contribution

It presents a new non-mixing length theory for stellar convection that computes temperature gradients and overshooting zones without relying on free parameters or Taylor's hypothesis.

Findings

The theory models temperature gradients in shrinking convective cores.

It provides a set of differential equations for core overshooting.

Numerical simulations are advancing towards integrated convection models.

Abstract

Turbulent convection is certainly one of the most important and thorny issues in stellar physics. Our deficient knowledge of this crucial physical process introduces a fairly large uncertainty concerning the internal structure and evolution of stars. A striking example is overshoot at the edge of convective cores. Indeed, nearly all stellar evolutionary codes treat the overshooting zones in a very approximative way that considers both its extent and the profile of the temperature gradient as free parameters. There are only a few sophisticated theories of stellar convection such as Reynolds stress approaches, but they also require the adjustment of a non-negligible number of free parameters. We present here a theory, based on the plume theory as well as on the mean-field equations, but without relying on the usual Taylor's closure hypothesis. It leads us to a set of eight differential equations plus a few algebraic ones. Our theory is essentially a non-mixing length theory. It enables us to compute the temperature gradient in a shrinking convective core and its overshooting zone. The case of an expanding convective core is also discussed, though more briefly. Numerical simulations have quickly improved during recent years and enabling us to foresee that they will probably soon provide a model of convection adapted to the computation of 1D stellar models.