Solar rotation inversions and the relationship between a-coefficients and mode splittings

TL;DR

This paper clarifies the relationship between a-coefficients, mode splittings, and solar rotation rate in helioseismology, aiding the comparison of different data types from various solar observation networks.

Contribution

It provides a detailed analysis of how a-coefficients relate to mode splittings and the solar rotation rate, improving data interpretation in helioseismology.

Findings

Clarified the relationship between a-coefficients and mode splittings.

Demonstrated how these relate to the solar rotation rate.

Facilitated comparison between different helioseismic data types.

Abstract

From the observing campaigns of a number of helioseismic telescope networks such as the Global Oscillation Network Group (GONG) and also from the Solar Heliospheric Observatory satellite (SoHO), helioseismologists now have data on in excess of 20000 oscillation frequencies of the modes known collectively as the 5 minute oscillations. Depending on the order and degree of the modes these data are available either as individual frequencies of modes with known radial order n, spherical harmonic degree l, and order m, or as so-called `a-coefficients' which are obtained by fitting polynomials to ridges of power in the (l,\nu) diagram. Although there is a one-to-one relationship between these two types of data, the conversion between them is not straightforward which complicates comparison of helioseismic inference between the two types of data. Their relationship with each other and with the solar rotation rate is clarified in this paper.