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

Author(s): Kashyap, Samarth G; Das, Srijan B; Hanasoge, Shravan M; Woodard, Martin F; Tromp, Jeroen

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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. Analyzing 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 ℓ = 50–291. The inferred a3-coefficients are found to be within 1 nHz of the frequency-splitting values for ℓ > 200. We also show that the technique fails at ℓ < 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.
Publication Date: 29-Mar-2021
Citation: Kashyap, Samarth G., Srijan Bharati Das, Shravan M. Hanasoge, Martin F. Woodard, and Jeroen Tromp. "Inferring Solar Differential Rotation through Normal-mode Coupling Using Bayesian Statistics." The Astrophysical Journal Supplement Series 253, no. 2 (2021). doi:10.3847/1538-4365/abdf5e.
DOI: doi:10.3847/1538-4365/abdf5e
ISSN: 0067-0049
Type of Material: Journal Article
Journal/Proceeding Title: Astrophysical Journal Supplement Series
Version: Author's manuscript

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