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

  • Authors: Samarth G. Kashyap, Srijan Bharati Das, Shravan M. Hanasoge, Martin F. Woodard, and Jeroen Tromp

2021 The Astrophysical Journal Supplement Series 253 47.

  • Provider: AAS Journals

Caption: Figure 7.

Sensitivity of spectral fitting to a-coefficients as a function of angular degree ℓ. The top panel shows the variation of misfit between synthetic data calculated using frequency-splitting a-coefficients ﹩{a}_{s,\mathrm{FS}}^{n{\ell }}﹩ and synthetic spectra computed from a scaled set of a-coefficients ﹩{a}_{s}^{n{\ell }}﹩. A well-defined minimum along ﹩{a}_{s}^{n{\ell }}/{a}_{s,\mathrm{FS}}^{n{\ell }}=1.0﹩, which broadens toward smaller , shows a drop in sensitivity of the spectra to variations in a-coefficients, as predicted by theory. The middle panel shows the sensitivity of a-coefficients, but now computed using the misfit between HMI and synthetic spectra computed from a scaled set of a-coefficients ﹩{a}_{s}^{n{\ell }}﹩. While it has the same qualitative drop in a-coefficient sensitivity for decreasing , the ridge of the minimum (darkest patch) is seen to deviate from ﹩{a}_{s,\mathrm{FS}}^{n{\ell }}﹩. The bottom panel shows in black the effective variance of misfit for each . The narrowing confinement of the data misfit toward higher is seen as a decreasing effective variance with increasing . The red line shows the increase in the factor /(∂ωn/∂) that enhances sensitivity at higher , as predicted by Equation (18). The areas corresponding to radial orders n = 0, 1 are indicated on top of each plot.

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