# Mitigating the mass dependence in the $\Delta\nu$ scaling relation of red-giant stars

## TL;DR

This paper introduces a new reference function for the asteroseismic scaling relation involving large frequency separation, which accounts for mass dependence and reduces systematic errors in estimating stellar masses and radii of red-giant stars.

## Contribution

The authors develop a mass-dependent reference function for the large frequency separation scaling relation, improving accuracy for red-giant star mass and radius estimates.

## Key findings

- Significant reduction in systematic errors in mass and radius estimates.
- Mitigation of trends with $
u_{
m max}$ in asteroseismic measurements.
- Enhanced reliability of stellar property determinations for red giants.

## Abstract

The masses and radii of solar-like oscillators can be estimated through the asteroseismic scaling relations. These relations provide a direct link between observables, i.e. effective temperature and characteristics of the oscillation spectra, and stellar properties, i.e. mean density and surface gravity (thus mass and radius). These scaling relations are commonly used to characterize large samples of stars. Usually, the Sun is used as a reference from which the structure is scaled. However, for stars that do not have a similar structure as the Sun, using the Sun as a reference introduces systematic errors as large as 10\% in mass and 5\% in radius. Several alternatives for the reference of the scaling relation involving the large frequency separation (typical frequency difference between modes of the same degree and consecutive radial order) have been suggested in the literature. In a previous paper, we presented a reference function with a dependence on both effective temperature and metallicity. The accuracy of predicted masses and radii improved considerably when using reference values calculated from our reference function. However, the residuals indicated that stars on the red-giant branch possess a mass dependence that was not accounted for. Here, we present a reference function for the scaling relation involving the large frequency separation that includes the mass dependence. This new reference function improves the derived masses and radii significantly by removing the systematic differences and mitigates the trend with $\nu_{\rm max}$ (frequency of maximum oscillation power) that exists when using the solar value as a reference.