Minuscule Corrections to Near-surface Solar Internal Rotation Using Mode Coupling

The observed solar oscillation spectrum is influenced by internal perturbations such as flows and structural asphericities. These features induce splitting of characteristic frequencies distort the resonant-mode eigenfunctions. Global axisymmertric flow -- differential rotation a very prominent perturbation. Tightly constrained profiles function latitude radius are products established helioseismic pipelines that use Dopplergrams to generate frequency-splitting measurements at high precision. However, inference using frequency-splittings do not consider effect mode-coupling. This approximation worsens for high-angular-degree modes, they become increasingly proximal in frequency. Since modes with angular degrees probe near-surface layers Sun, inversions considering coupled could potentially lead more accurate estimates close surface. In order investigate if this indeed case, we perform rotation, coupling $160 \leq \ell 300$ surface gravity $f$-branch first-overtone $p$ modes. keeping character mode coupling, carry out non-linear inversion an eigenvalue solver. Differences inverted frequency from MDI HMI compared discussed. We find corrections profile, when accounting mode-coupling effects, smaller than 0.003 nHz hence insignificant. minuscule found be correlated cycle. also present even-order coefficients, which consequently impact structure magnetic fields.