Determining the Best Method of Calculating the Large Frequency Separation For Stellar Models

Abstract

Asteroseismology of solar-like oscillators often relies on the comparisons between stellar models and stellar observations in order to determine the properties of stars. The values of the global seismic parameters, $\nu_\mathrm{max}$ (the frequency where the smoothed amplitude of the oscillations peak) and $\Delta \nu$ (the large frequency separation), are frequently used in grid-based modeling searches. However, the methods by which $\Delta \nu$ is calculated from observed data and how $\Delta \nu$ is calculated from stellar models are not the same. Typically for observed stars, especially for those with low signal-to-noise data, $\Delta \nu$ is calculated by taking the power spectrum of a power spectrum, or with autocorrelation techniques. However, for stellar models, the actual individual mode frequencies are calculated and the average spacing between them directly determined. In this work we try to determine the best way to combine model frequencies in order to obtain $\Delta \nu$ that can be compared with observations. For this we use stars with high signal-to-noise observations from Kepler as well as simulated TESS data of Ball et al. (2018). We find that when determining $\Delta \nu$ from individual mode frequencies the best method is to use the $\ell=0$ modes with either no weighting or with a Gaussian weighting around $\nu_\mathrm{max}$.