Inversions for Deep Solar Meridional Flow Using Spherical Born Kernels

TL;DR

This study improves the inversion of solar meridional flow beneath the Sun's surface by using the Born approximation and full covariance matrices, revealing complex flow structures and confirming a shallow return flow around 0.9 solar radii.

Contribution

It introduces the use of spherical Born kernels and refined covariance-based inversions to better estimate deep solar meridional flows, addressing previous methodological limitations.

Findings

Confirmed a shallow return flow at about 0.9 R_sun.

Discovered multiple stacked flow cells in the southern hemisphere with lower SVD thresholds.

Showed that earlier assumptions underestimated inversion errors by a factor of 2-4.

Abstract

The solar meridional flow is a crucial ingredient in modern dynamo theory. Seismic estimates of this flow have, however, been contradictory in deeper layers below about $0.9\,R_\odot$. Results from time-distance helioseismology have so far been obtained using the ray approximation. Here, we perform inversions using the Born approximation. The initial result is similar to the result previously obtained by Jackiewicz et al. (2015) using ray kernels while using the same set of GONG data and the SOLA inversion technique. However, we show that the assumption of uncorrelated measurements used in earlier studies may lead to inversion errors being underestimated by a factor of about two to four. In a second step, refined inversions are performed using the full covariance matrix and a regularization for cross-talk. As the results are found to depend on the threshold used in the singular value decomposition, they were obtained for a medium threshold ($10^{-7}-10^{-5}$, about 50% of the values used) and a threshold lower by a factor of 10 (about 70% of the values used). The result obtained with the medium threshold is again similar to the original, with less latitudinal variation. However, using the lower threshold, the inverted flow in the southern hemisphere shows two or three cells stacked radially depending on the associated radial flows. Both the single-cell and the multi-cell profiles are consistent with the measured travel times. All our results confirm a shallow return flow at about $0.9\,R_\odot$.