The relation between $\Delta\nu$ and $\nu_{max}$ for solar-like oscillations

TL;DR

This paper establishes an empirical relation between the large frequency separation and the frequency of maximum power in solar-like oscillations, enabling better interpretation of stellar observations.

Contribution

It presents a new observed relation between $ abla u$ and $ u_{max}$, supported by models, for stars with solar-like oscillations.

Findings

$ abla u$ is proportional to $( u_{max})^{0.77}$

Prediction of $ abla u$ within 15% from $ u_{max}$

Applicable to stars with 0.5<M/Msol<4.0

Abstract

Establishing relations between global stellar parameters and asteroseismic quantities can help improve our understanding of stellar astrophysics and facilitate the interpretation of observations. We present an observed relation between the large frequency separation, $\Delta\nu$, and the frequency of maximum power, $\nu_{max}$. We find that $\Delta\nu$ is proportional to $(\nu_{max})^0.77$, allowing prediction of $\Delta\nu$ to about 15 per cent given $\nu_{max}$. Our result is further supported by established scaling relations for $\Delta\nu$ and $\nu_{max}$ and by extended stellar model calculations, which confirm that $\Delta\nu$ can be estimated using this relation for basically any star showing solar-like oscillations in the investigated range (0.5<M/Msol<4.0).