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

## TL;DR

This paper investigates the most effective method to calculate the large frequency separation ($
u$) from stellar models for better comparison with observational data in asteroseismology.

## Contribution

It identifies the optimal approach to derive $
u$ from stellar model frequencies, aligning model calculations with observational techniques.

## Key findings

- Using $
u$ from $$ modes with no or Gaussian weighting yields the best results.
- The study compares methods using Kepler and simulated TESS data.
- Optimal method improves consistency between models and observations.

## 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 $\nu_\mathrm{max}$.