A Method for the Estimation of f- and p-mode Parameters and Rotational Splitting Coefficients from Un-averaged Solar Oscillation Power Spectra

We present a new methodology for the fitting of the peaks in solar oscillation power spectra that is equally well-suited for the estimation of low-, medium, and high-degree f- and p-mode parameters and frequency-splitting coefficients. The method can provide accurate input data over a wide portion of the dispersion plane for both structural and rotational inversions. This method, which we call the Multiple-Peak, Tesseral-Spectrum (MPTS) method, operates directly upon of all of the modes in a multiplet (n, l) of radial order n and degree l, and employs a fitting profile that consists of the sum of numerous individual overlapping profiles whose relative amplitudes are determined by the leakage matrix appropriate to the targeted mode. Hence, 2l + 1 sets of modal parameters are obtained simultaneously for each multiplet (n, l). By fitting an appropriate polynomial to the run of the fitted frequencies versus the azimuthal order, frequency-splitting coefficients are also obtained for the same multiplet. Using power spectra obtained from the 66 day long 2010 MDI Dynamics Run, we present sample structural and rotational inversions that employed frequencies and frequency-splitting coefficients from modes in the degree range of 0–1000 and the frequency range of 965–4600 μHz. The structural inversion confirms evidence for a pronounced departure of the sound speed in the outer solar convection zone from the radial sound-speed profile contained in Model S of Christensen-Dalsgaard and his collaborators that we obtained previously using a different fitting method.