The shape of convection in 2D and 3D global simulations of stellar interiors

¹ Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30303, USA
² Lawrence Livermore National Laboratory, 7000 East Ave, Livermore, CA 94550, USA
³ Astrophysics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, EX4 4QL Exeter, United Kingdom
⁴ École Normale Supérieure de Lyon, CRAL (UMR CNRS 5574), Université de Lyon 1, 69007 Lyon, France
⁵ Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
⁶ Laboratoire de Météorologie Dynamique (IPSL), Sorbonne University, CNRS, Ecole Polytechnique, Ecole Normale Superieure, Paris, France

^⋆ Corresponding author; pratt34@llnl.gov

Received: 6 August 2024
Accepted: 14 September 2024

Abstract

Context. Theoretical descriptions of convective overshooting in stellar interiors often rely on a basic one-dimensional parameterization of the flow called the filling factor for convection. Several different definitions of the filling factor have been developed for this purpose, based on: (1) the percentage of the volume, (2) the mass flux, and (3) the convective flux that moves through the boundary.

Aims. We examine these definitions of the filling factor with the goal of establishing their ability to explain differences between 2D and 3D global simulations of stellar interiors that include fully compressible hydrodynamics and realistic microphysics for stars.

Methods. We study convection and overshooting in pairs of identical two-dimensional (2D) and three-dimensional (3D) global simulations of stars produced with MUSIC, a fully compressible, time-implicit hydrodynamics code. We examine pairs of simulations for (1) a 3 M_⊙ red giant star near the first dredge-up point, (2) a 1 M_⊙ pre-main-sequence star with a large convection zone, (3) the current sun, and (4) a 20 M_⊙ main-sequence star with a large convective core.

Results. Our calculations of the filling factor based on the volume percentage and the mass flux indicate asymmetrical convection near the surface for each star with an outer convection zone. However, near the convective boundary, convective flows achieve inward-outward symmetry for each star that we study; for 2D and 3D simulations, these filling factors are indistinguishable. A filling factor based on the convective flux is contaminated by boundary-layer-like flows, making a theoretical interpretation difficult. We present two possible new alternatives to these frequently used definitions of a filling factor, which instead compare flows at two different radial points. The first alternative is the penetration parameter of Anders et al. (2022, ApJ, 926, 169). The second alternative is a new statistic that we call the plume interaction parameter. We demonstrate that both of these parameters captures systematic differences between 2D and 3D simulations around the convective boundary.