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

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 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.

Detection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling

“…Interested readers are referred to Zaqarashvili et al (2021) and references therein for a detailed review on Rossby waves in the Sun and other astrophysical problems. Although very powerful in its scope and inferential quality, the method of mode coupling is only slowly gaining traction in helioseismology (see Schad & Roth 2020;Hanson et al 2021;Kashyap et al 2021, for some other recent developments with this method); for instance, there is limited work on characterizing its limitations and developing mitigation strategies. The detection of Rossby modes by Hanasoge & Mandal (2019) using this method added an important milestone to this methodology.…”

Imaging the Sun's near-surface flows using mode-coupling analysis

“…While the derivation of the mode-coupling technique is mathematically challenging, the data analysis is simple and utilizes all the information registered by the mode. Thus far, global mode-coupling has been validated through observations of the meridional flow (Vorontsov 2011;Woodard et al 2013), differential rotation (Schad & Roth 2020;Kashyap et al 2021), global-scale convection (Woodard 2014(Woodard , 2016Hanasoge et al 2020;Mani & Hanasoge 2021) and Rossby modes (Hanasoge & Mandal 2019;Mandal & Hanasoge 2020;Mandal et al 2021). Local mode-coupling analysis in the Cartesian approximation, formulated by Woodard (2006), was validated by Hanson et al (2021) (hereafter H21) by examining the power-spectrum of supergranular waves and comparing with previous time-distance studies (Langfellner et al 2018).…”

Bayesian Rotation Inversion of KIC 11145123

“…For more thorough introductions and discussions on Bayesian statistics in astronomical contexts, readers should refer to, e.g., Gregory (2005). Applications in global and local helioseismology can also be found in Kashyap et al (2021) and Jackiewicz (2020), respectively.…”