Idealised hydrodynamic simulations of turbulent oxygen-burning shell convection in 4{\pi} geometry

TL;DR

This study uses high-resolution 3D hydrodynamic simulations to analyze turbulent convection and entrainment in the oxygen-burning shell of massive stars, providing new insights into boundary mixing processes.

Contribution

It presents the first 4π geometry simulations of turbulent O-shell convection at high resolution, establishing scaling laws for entrainment and validating a 1D diffusion model for boundary mixing.

Findings

Entrainment rate scales linearly with luminosity and with the cube of shear velocity.

Radial RMS velocity scales with the cube root of luminosity.

The exponential diffusion model with f=0.03 reproduces 3D abundance profiles.

Abstract

This work investigates the properties of convection in stars with particular emphasis on entrainment across the upper convective boundary (CB). Idealised simulations of turbulent convection in the O-burning shell of a massive star are performed in $4\pi$ geometry on $768^3$ and $1536^3$ grids, driven by a representative heating rate. A heating series is also performed on the $768^3$ grid. The $1536^3$ simulation exhibits an entrainment rate at the upper CB of $1.33\times10^{-6}~M_\odot~\mathrm{s}^{-1}$. The $768^3$ simulation with the same heating rate agrees within 17 per cent. The entrainment rate at the upper convective boundary is found to scale linearly with the driving luminosity and with the cube of the shear velocity at the upper boundary, while the radial RMS fluid velocity scales with the cube root of the driving luminosity, as expected. The mixing is analysed in a 1D diffusion framework, resulting in a simple model for CB mixing. The analysis confirms previous findings that limiting the MLT mixing length to the distance to the CB in 1D simulations better represents the spherically-averaged radial velocity profiles from the 3D simulations and provides an improved determination of the reference diffusion coefficient $D_0$ for the exponential diffusion CB mixing model in 1D. From the 3D simulation data we adopt as the convective boundary the location of the maximum gradient in the horizontal velocity component which has $2\sigma$ spatial fluctuations of $\approx0.17 H_P$ . The exponentially decaying diffusion CB mixing model with $f = 0.03$ reproduces the spherically-averaged 3D abundance profiles.