Inversion for Inferring Solar Meridional Circulation: The Case with Constraints on Angular Momentum Transport inside the Sun

TL;DR

This study uses inverse modeling of solar travel times to infer the internal meridional circulation profile, suggesting a double-cell structure consistent with angular momentum transport constraints, but with resolution limitations.

Contribution

It introduces a regularized least-squares inversion with an angular momentum transport constraint, revealing potential double-cell meridional circulation inside the Sun.

Findings

Double-cell MC structure consistent with angular momentum transport

Both single-cell and double-cell profiles fit the data similarly

Adding constraints reduces resolution of the inferred profiles

Abstract

We have carried out inversions of travel times as measured by Gizon et al. (2020) to infer the internal profile of the solar meridional circulation (MC). A linear inverse problem has been solved by the regularized least-squares method with a constraint that the angular momentum (AM) transport by MC should be equatorward (HK21-type constraint). Our motivation for using this constraint is based on the result by Hotta and Kusano (2021) where the solar equator-fast rotation was reproduced successfully without any manipulation. The inversion result indicates that the MC profile is a double-cell structure if the so-called HK21 regime, in which AM transported by MC sustains the equator-fast rotation, correctly describes the physics inside the solar convective zone. The sum of the squared residuals computed with the inferred double-cell MC profile is comparable to that computed with the single-cell MC profile obtained when we exclude the HK21-type constraint, showing that both profiles can explain the data more or less at the same level. However, we also find that adding the HK21-type constraint degrades the resolution of the averaging kernels. Although it is difficult for us to determine the large-scale morphology of the solar MC at the moment, our attempt highlights the relevance of investigating the solar MC profile from both theoretical and observational perspectives.