Convective Boundary Mixing in Main-Sequence Stars: Theory and Empirical Constraints

Abstract

The convective envelopes of solar-type stars and the convective cores of intermediate- and high-mass stars share boundaries with stable radiative zones. Through a host of processes we collectively refer to as “convective boundary mixing” (CBM), convection can drive efficient mixing in these nominally stable regions. In this review, we discuss the current state of CBM research in the context of main-sequence stars through three lenses. (1) We examine the most frequently implemented 1D prescriptions of CBM—exponential overshoot, step overshoot, and convective penetration—and we include a discussion of implementation degeneracies and how to convert between various prescriptions. (2) Next, we examine the literature of CBM from a fluid dynamical perspective, with a focus on three distinct processes: convective overshoot, entrainment, and convective penetration. (3) Finally, we discuss observational inferences regarding how much mixing should occur in the cores of intermediate- and high-mass stars as well as the implied constraints that these observations place on 1D CBM implementations. We conclude with a discussion of pathways forward for future studies to place better constraints on this difficult challenge in stellar evolution modeling.

Multidimensional Simulations of Core Convection

“…This estimate of the overshoot length is smaller than the convection zone radius by a factor of 10 3 ; see Anders and Pedersen [34] for other ways of estimating the overshoot length. Simulations thus require a very fine resolution near the radiative-convective boundary to accurately simulate overshooting dynamics.…”

“…They find that the entrainment of Herwig et al [81] slows down with time, and builds up an adiabatically stratified region outside of the convection zone. These are hallmarks of convective penetration [34]. They find that the entropy profiles evolve in the same way in simulations with a range of luminosity boosting factors, but that the evolution is faster in simulations with higher luminosities.…”

“…Within the convection zone, the chemical composition is nearly homogeneous and the star is nearly adiabatic, so a radially dependent opacity is sufficient. However, the temperature, pressure, and chemical dependence of the opacity are important for setting the structure of the radiative-convective boundary in thermal equilibrium [34]. Thus, studies of convective boundary mixing should include realistic opacities.…”

“…This mixing encompasses several different physical mechanisms including (i) growth of the convection zone ("entrainment"); (ii) transport of fluid across the radiative-convective boundary ("overshoot"); and (iii) developing an adiabatic region outside the Schwarzschild boundary ("penetration"). These mechanisms are discussed in depth in Anders and Pedersen [34], along with observational, theoretical, and numerical evidence for each mechanism. Here, we briefly summarize the numerical studies of convective boundary mixing in simulations of core convection.…”

The Structure and Evolution of Stars: Introductory Remarks

“…[24,30,34]). In Chapter 5, Anders & Pedersen (2023) [113] discuss the recent advances in combining knowledge from state-of-the-art hydrodynamical simulations and observations of CBM, with a particular focus for main-sequence stars as these are the most common in the Universe.…”