Parametrizing the time-variation of the "surface term" of stellar p-mode frequencies: application to helioseismic data

TL;DR

This paper introduces a parametrization method for the surface term in stellar p-mode frequencies, accounting for solar cycle variations and magnetic activity, with potential applications to solar-like stars.

Contribution

It proposes a simple model combining cubic and inverse frequency terms scaled by mode inertia to describe surface term variations.

Findings

Cubic term dominates the average surface term and its variation.

Inverse term improves fit for medium-degree frequency variations.

The model captures activity-related frequency changes across the solar cycle.

Abstract

The solar-cyle variation of acoustic mode frequencies has a frequency dependence related to the inverse mode inertia. The discrepancy between model predictions and measured oscillation frequencies for solar and solar-type stellar acoustic modes includes a significant frequency-dependent term known as the surface term that is also related to the inverse mode inertia. We parametrize both the surface term and the frequency variations for low-degree solar data from Birmingham Solar-Oscillations Network (BiSON) and medium-degree data from the Global Oscillations Network Group (GONG) using the mode inertia together with cubic and inverse frequency terms. We find that for the central frequency of rotationally split multiplets the cubic term dominates both the average surface term and the temporal variation, but for the medium-degree case the inverse term improves the fit to the temporal variation. We also examine the variation of the even-order splitting coefficients for the medium-degree data and find that, as for the central frequency, the latitude-dependent frequency variation, which reflects the changing latitudinal distribution of magnetic activity over the solar cycle, can be described by the combination of a cubic and an inverse function of frequency scaled by inverse mode inertia. The results suggest that this simple parametrization could be used to assess the activity-related frequency variation in solar-like asteroseismic targets.