Analysis of MDI High-Degree Mode Frequencies and their Rotational Splittings

TL;DR

This paper provides a detailed analysis of high-degree solar acoustic mode frequencies and their rotational splittings, improving mode characterization by accounting for instrumental effects and studying solar cycle variations.

Contribution

It introduces a physically motivated model including a complete leakage matrix for analyzing high-degree modes, enabling better structure inversion of the near-surface solar layers.

Findings

Frequency shifts follow a power law with frequency, scaled by mode inertia.

The power law exponent is twice as large for p modes compared to f modes.

Frequency shifts correlate with solar activity indices.

Abstract

Here we present a detailed analysis of solar acoustic mode frequencies and their rotational splittings for modes with degree up to 900. They were obtained by applying spherical harmonic decomposition to full-disk solar images observed by the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory spacecraft. Global helioseismology analysis of high-degree modes is complicated by the fact that the individual modes cannot be isolated, which has limited so far the use of high-degree data for structure inversion of the near-surface layers (r > 0.97 R). In this work, we took great care to recover the actual mode characteristics using a physically motivated model which included a complete leakage matrix. We included in our analysis the following instrumental characteristics: the correct instantaneous image scale, the radial and non-radial image distortions, the effective position angle of the solar rotation axis and a correction to the Carrington elements. We also present variations of the mode frequencies caused by the solar activity cycle. We have analyzed seven observational periods from 1999 to 2005 and correlated their frequency shift with four different solar indices. The frequency shift scaled by the relative mode inertia is a function of frequency alone and follows a simple power law, where the exponent obtained for the p modes is twice the value obtained for the f modes. The different solar indices present the same result.