New scaling relations from MESA models for mass and radius of subgiant stars: application to Kepler targets

Abstract

The precise determination of the fundamental parameters of stars is crucial for understanding stellar structure and evolution. In this regard, the asteroseismic parameters of solar-like oscillating stars obtained from space telescopes are very useful for determining the mass ($M$) and radius ($R$) of single stars using classical scaling relations. These relations still need to be improved. In this study, we develop alternative scaling relations based on reference frequencies (${\nu }_{\min }$) due to helium ionization zone glitches, specifically for subgiant (SG) stars. We compile main-sequence and SG {\small{MESA}} models from the literature and derive new scaling relations for stellar $R$ and surface gravity ($g$) of evolved stars. The expressions for $R$ and $g$ are obtained simultaneously as functions of the large frequency separation, ${\nu }_{\min }$, and metallicity. These new relations allow $M$ and $R$ to be reliably determined only from observational parameters, without the need for detailed stellar modelling. The resulting ${\nu }_{\min }$-based relations are applied to a sample of 31 SG stars observed by the \emph{Kepler} mission, with masses in the range 0.85-1.74 M${}_{\odot }$ and radii between 1.03 and 2.82 R${}_{\odot }$. Using simultaneous solutions, we estimate new mass and radius ranges of 0.89-1.62 M${}_{\odot }$ and 1.04-2.95 R${}_{\odot }$, respectively. The results demonstrate significant improvements in the determination of $M$ and $R$ for evolved \emph{Kepler} target stars, highlighting the potential of the new scaling relations in asteroseismic analyses.

15 pages, 13 figures

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