Inferring solar differential rotation through normal-mode coupling using Bayesian statistics

TL;DR

This paper applies Bayesian statistics to analyze mode coupling in helioseismic data, providing a more accurate inference of solar differential rotation, especially at high angular degrees, and demonstrating the importance of mode coupling techniques.

Contribution

It introduces a Bayesian approach to infer $a$-coefficients from cross spectra, improving the accuracy of differential rotation measurements in helioseismology.

Findings

Bayesian method works well for modes with angular degrees 50-291.

Inferred $a_3$-coefficients are within 1 nHz of frequency splitting results for $ ext{l} > 200$.

Technique is ineffective for $ ext{l} < 50$ due to insensitivity.

Abstract

Normal-mode helioseismic data analysis uses observed solar oscillation spectra to infer perturbations in the solar interior due to global and local-scale flows and structural asphericity. Differential rotation, the dominant global-scale axisymmetric perturbation, has been tightly constrained primarily using measurements of frequency splittings via "$a$-coefficients". However, the frequency-splitting formalism invokes the approximation that multiplets are isolated. This assumption is inaccurate for modes at high angular degrees. Analysing eigenfunction corrections, which respect cross coupling of modes across multiplets, is a more accurate approach. However, applying standard inversion techniques using these cross-spectral measurements yields $a$-coefficients with a significantly wider spread than the well-constrained results from frequency splittings. In this study, we apply Bayesian statistics to infer $a$-coefficients due to differential rotation from cross spectra for both $f$-modes and $p$-modes. We demonstrate that this technique works reasonably well for modes with angular degrees $\ell=50-291$. The inferred $a_3-$coefficients are found to be within $1$ nHz of the frequency splitting values for $\ell > 200$. We also show that the technique fails at $\ell < 50$ owing to the insensitivity of the measurement to the perturbation. These results serve to further establish mode coupling as an important helioseismic technique with which to infer internal structure and dynamics, both axisymmetric (e.g., meridional circulation) and non-axisymmetric perturbations.