On the Penetration of Meridional Circulation below the Solar Convection Zone II: Models with Convection Zone, the Taylor-Proudman constraint and Applications to Other Stars

TL;DR

This paper models the meridional circulation in the solar convection zone and radiative interior, revealing how stratification and internal stresses influence circulation penetration and mixing, with implications for stellar evolution.

Contribution

It introduces a self-consistent model of meridional flows considering the convection zone pump and analyzes the effects of stratification and stresses on circulation penetration.

Findings

Circulation timescale depends on stratification and internal stresses.

Weakly stratified systems are sensitive to the presence of stresses breaking the Taylor-Proudman constraint.

Neglected mixing mechanisms in stellar models may be significant.

Abstract

The solar convection zone exhibits a strong level of differential rotation, whereby the rotation period of the polar regions is about 25-30% longer than the equatorial regions. The Coriolis force associated with these zonal flows perpetually "pumps" the convection zone fluid, and maintains a quasi-steady circulation, poleward near the surface. What is the influence of this meridional circulation on the underlying radiative zone, and in particular, does it provide a significant source of mixing between the two regions? In Paper I, we began to study this question by assuming a fixed meridional flow pattern in the convection zone and calculating its penetration depth into the radiative zone. We found that the amount of mixing caused depends very sensitively on the assumed flow structure near the radiative--convective interface. We continue this study here by including a simple model for the convection zone "pump", and calculating in a self-consistent manner the meridional flows generated in the whole Sun. We find that the global circulation timescale depends in a crucial way on two factors: the overall stratification of the radiative zone as measured by the Rossby number times the square root of the Prandtl number, and, for weakly stratified systems, the presence or absence of stresses within the radiative zone capable of breaking the Taylor-Proudman constraint. We conclude by discussing the consequences of our findings for the solar interior and argue that a potentially important mechanism for mixing in Main Sequence stars has so far been neglected.