Fundamental properties of stars from Kepler and Gaia data: parallax offset and revised scaling relations

TL;DR

This study compares parallax and asteroseismic data from multiple space missions to refine stellar scaling relations, accurately determine parallax offsets, and validate stellar mass and radius estimates for red giants.

Contribution

It introduces an empirical relation for asteroseismic density scaling and refines parallax offset and scaling parameters using combined Gaia and Kepler data.

Findings

Derived a new empirical relation for asteroseismic density scaling.

Estimated parallax offset for red giants as -0.0463 mas.

Confirmed stellar mass and radius ranges align with APOKASC-2 results.

Abstract

Data from the space missions {\it Gaia}, {\it Kepler}, {\it CoRoT} and {\it TESS}, make it possible to compare parallax and asteroseismic distances. From the ratio of two densities $\rho_{\rm sca}/\rho_{\pi}$, we obtain an empirical relation $f_{\Delta \nu}$ between the asteroseismic large frequency separation and mean density, which is important for more accurate stellar mass and radius. This expression for main-sequence (MS) and subgiant stars with $K$-band magnitude is very close to the one obtained from interior MS models by Y{\i}ld{\i}z, \c{C}elik \& Kayhan. We also discuss the effects of effective temperature and parallax offset as the source of the difference between asteroseismic and non-asteroseismic stellar parameters. We have obtained our best results for about 3500 red giants (RGs) by using 2MASS data and model values for $f_{\Delta \nu}$ from Sharma et al. Another unknown scaling parameter $f_{\nu_{\rm max}}$ comes from the relationship between the frequency of maximum amplitude and gravity. Using different combinations of $f_{\nu_{\rm max}}$ and the parallax offset, we find that the parallax offset is generally a function of distance. The situation where this slope disappears is accepted as the most reasonable solution. By a very careful comparison of asteroseismic and non-asteroseismic parameters, we obtain very precise values for the parallax offset and $f_{\nu_{\rm max}}$ for RGs of $-0.0463\pm0.0007$ mas and $1.003\pm0.001$, respectively. Our results for mass and radius are in perfect agreement with those of APOKASC-2: the mass and radius of $\sim$3500 RGs are in the range of about 0.8-1.8 M$_{\odot}$ (96 per cent) and 3.8-38 R$_{\odot}$, respectively.