Helioseismic inversion to infer depth profile of solar meridional flow using spherical Born kernels

TL;DR

This paper develops a spherical Born kernel-based inversion method to map the solar meridional flow profile, revealing a single-cell structure with return flow below 0.78 solar radii, using 6 years of observational data.

Contribution

It introduces a new inversion approach using spherical Born kernels and B-spline basis functions to infer the solar meridional flow profile from helioseismic travel-time data.

Findings

Inversion indicates a single-cell meridional flow with return flow below 0.78 R_sun.

Method validated with synthetic data before applying to real observations.

Flow profile consistent with previous helioseismic studies.

Abstract

Accurate inference of solar meridional flow is of crucial importance for the understanding of solar dynamo process. Wave travel times, as measured on the surface, will change if the waves encounter perturbations e.g. in the sound speed or flows, as they propagate through the solar interior. Using functions called sensitivity kernels, we may image the underlying anomalies that cause measured shifts in travel times. The inference of large-scale structures e.g meridional circulation requires computing sensitivity kernels in spherical geometry. Mandal et al. (2017) have computed such spherical kernels in the limit of the first-Born approximation. In this work, we perform an inversion for meridional circulation using travel-time measurements obtained from 6 years of SDO/HMI data and those sensitivity kernels. We enforce mass conservation by inverting for a stream function. The number of free parameters is reduced by projecting the solution on to cubic B-splines in radius and derivatives of the Legendre-polynomial basis in latitude, thereby improving the condition number of the inverse problem. We validate our approach for synthetic observations before performing the actual inversion. The inversion suggests a single-cell profile with the return-flow occurring at depths below 0.78 $R_\odot$.