TY - JOUR
T1 - Inferring Solar Differential Rotation through Normal-mode Coupling Using Bayesian Statistics
AU - Kashyap, Samarth G.
AU - Das, Srijan Bharati
AU - Hanasoge, Shravan M.
AU - Woodard, Martin F.
AU - Tromp, Jeroen
N1 - Publisher Copyright:
© 2021. The American Astronomical Society. All rights reserved.
PY - 2021/4
Y1 - 2021/4
N2 - 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 a 3-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.
AB - 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 a 3-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.
UR - http://www.scopus.com/inward/record.url?scp=85103824369&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85103824369&partnerID=8YFLogxK
U2 - 10.3847/1538-4365/abdf5e
DO - 10.3847/1538-4365/abdf5e
M3 - Article
AN - SCOPUS:85103824369
SN - 0067-0049
VL - 253
JO - Astrophysical Journal, Supplement Series
JF - Astrophysical Journal, Supplement Series
IS - 2
M1 - 47
ER -