Surface correction of main sequence solar-like oscillators with the $Kepler$ LEGACY sample

TL;DR

This study evaluates different empirical surface correction methods for modeling solar-like oscillators, using Kepler LEGACY data, and finds that frequency scaling and inverse terms improve model fits, with physics assumptions having a significant impact.

Contribution

It introduces a frequency scaling approach and compares three surface correction methods across a broad stellar sample, highlighting the importance of model physics.

Findings

Frequency scaling improves model-observation fit.

Inverse frequency terms enhance fits for lower gravity stars.

Model physics choice impacts stellar parameter estimates more than correction method.

Abstract

Poor modelling of the surface regions of solar-like stars causes a systematic discrepancy between the observed and model pulsation frequencies. We aim to characterise this frequency discrepancy for main sequence solar-like oscillators for a wide range of initial masses and metallicities. We fit stellar models to the observed mode frequencies of the 67 stars, including the Sun, in the $Kepler$ LEGACY sample, using three different empirical surface corrections. The three surface corrections we analyse are a frequency power-law, a cubic frequency term divided by the mode inertia, and a linear combination of an inverse and cubic frequency term divided by the mode inertia. We construct a grid of stellar evolution models using the stellar evolution code MESA and calculate mode frequencies using GYRE. We scale the frequencies of each stellar model by an empirical calculated homology coefficient, which greatly improves the robustness of our grid. We calculate stellar parameters and surface corrections for each star using the average of the best-fitting models from each evolutionary track, weighted by the likelihood of each model. The resulting model stellar parameters agree well with an independent reference, the $\texttt{BASTA}$ pipeline. However, we find that the adopted physics of the stellar models has a greater impact on the fitted stellar parameters than the choice of correction method. We find that scaling the frequencies by the mode inertia improves the fit between the models and observations. The inclusion of the inverse frequency term produces substantially better model fits to lower surface gravity stars.