Nonlinear seismic scaling relations

TL;DR

This paper revises seismic scaling relations for red giants by introducing nonlinear corrections, improving the accuracy of mass and radius estimates from asteroseismic data across different evolutionary stages.

Contribution

It proposes new nonlinear seismic scaling relations that better match independent measurements for red giants, addressing overestimations in traditional linear relations.

Findings

Nonlinear scaling relations align seismic and dynamical parameters.

Curvature and glitch corrections improve seismic parameter accuracy.

Relations are valid for RGB and RC stars across evolutionary stages.

Abstract

In recent years the global seismic scaling relations for the frequency of maximum power and for the large frequency separation have caught the attention of various fields of astrophysics. With the exquisite photometry of \textit{Kepler}, the uncertainties in the seismic observables are small enough to estimate masses and radii with a precision of only a few per cent. Even though this seems to work quite well for main-sequence stars, there is empirical evidence, mainly from studies of eclipsing binary systems, that the seismic scaling relations overestimate the mass and radius of red giants by about 15 and 5\%, respectively. Model-based corrections of the $\Delta\nu -$scaling reduce the problem but do not solve it. We re-examine the global oscillation parameters of the giants in the binary systems in order to determine their seismic fundamental parameters and find them to agree with the dynamic parameters from the literature if we adopt nonlinear scalings. We note that a curvature and glitch corrected $\Delta\nu_\mathrm{cor}$ should be preferred over a local or average values. We then compare the observed seismic parameters of the cluster giants to those scaled from independent measurements and find the same nonlinear behaviour as for the eclipsing binaries. Our final proposed scaling relations are based on both samples and cover a broad range of evolutionary stages from RGB to RC stars: $g/\sqrt{T_\mathrm{eff}} = (\nu_\mathrm{max}/\nu_\mathrm{max,\odot})^{1.0075\pm0.0021}$ and $\sqrt{\bar\rho} = (\Delta\nu_\mathrm{cor}/\Delta\nu_\mathrm{cor,\odot})[\eta - (0.0085\pm0.0025) \log^2 (\Delta\nu_\mathrm{cor}/\Delta\nu_\mathrm{cor,\odot})]^{-1}$, where $g$, $T_\mathrm{eff}$, and $\bar\rho$ are in solar units, $\nu_\mathrm{max,\odot}=3140\pm5\mu$Hz and $\Delta\nu_\mathrm{cor,\odot}=135.08\pm0.02\mu$Hz , and $\eta$ is equal to one in case of RGB stars and $1.04\pm0.01$ for RC stars.