On the penetration of large-scale flows into stellar radiative zones

TL;DR

This study uses 3D simulations to analyze how large-scale meridional flows penetrate stellar radiative zones, revealing their dependence on the Eddington-Sweet to viscous timescale ratio and their role in angular momentum transport.

Contribution

It provides the first systematic analysis of meridional flow penetration depths in stellar radiative zones based on 3D global simulations, highlighting the influence of the parameter sigma.

Findings

Meridional flows penetrate up to ~0.21r_o below the convection zone.

Penetration depth scales as sigma^{-0.22} when sigma<1.

Angular momentum transport is dominated by Coriolis force in the solar-like regime.

Abstract

The propagation of meridional circulation below the base of the convection zone of low-mass stars may play a crucial role in the transport of angular momentum and also significantly contribute to the transport of chemical species and magnetic fields within their stable radiative zone. We systematically study these large-scale mean flows by performing three-dimensional (3D) global numerical simulations in a spherical shell that consists of a convection zone (CZ) overlying a stably stratified region. We find that the meridional flows can penetrate distances as large as $\sim 0.21r_o$ (where $r_o$ is the outer radius) below the base of the convection zone, provided that the Eddington-Sweet timescale $t_{ES}$ is much shorter than the viscous timescale $t_{\nu}$ as measured by the parameter $\sigma=(t_{ES}/t_{\nu})^{1/2}$. In the solar-like regime where $\sigma\lesssim 1$ in the upper radiative zone (RZ), we find that the angular momentum transport in the deep RZ is determined primarily by the action of the Coriolis force on meridional flows. In contrast, in models run in the $\sigma> 1$ regime, the meridional flows become weaker and the viscous effects dominate. We find that the penetration lengthscale $\delta_{MC}$ of these mean flows when $\sigma\lesssim 1$ is proportional to $\sigma^{-0.22}$. Our findings may provide a better understanding of the role of the meridional flows in the dynamics of the solar interior and inform future numerical studies that are focused on capturing solar-like dynamics self-consistently.