Inferring Solar Differential Rotation through Normal-mode Coupling Using Bayesian Statistics

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