Testing the radius scaling relation with \({\it Gaia}\) DR2 in the \({\it Kepler}\) field

Abstract

We compare radii based on \({\it Gaia}\) parallaxes to asteroseismic scaling relation-based radii of \(\sim 300\) dwarfs \(\&\) subgiants and \(\sim 3600\) first-ascent giants from the \({\it Kepler}\) mission. Systematics due to temperature, bolometric correction, extinction, asteroseismic radius, and the spatially-correlated \({\it Gaia}\) parallax zero-point, contribute to a \(2\%\) systematic uncertainty on the \({\it Gaia}\)-asteroseismic radius agreement. We find that dwarf and giant scaling radii are on a parallactic scale at the \(-2.1 \% \pm 0.5 \% {\rm \ (rand.)} \pm 2.0\% {\rm \ (syst.)}\) level (dwarfs) and \(+1.7\% \pm 0.3\% {\rm \ (rand.)} \pm 2.0\% {\rm (syst.)}\) level (giants), supporting the accuracy and precision of scaling relations in this domain. In total, the \(2\%\) agreement that we find holds for stars spanning radii between \(0.8R_{\odot}\) and \(30 R_{\odot}\). We do, however, see evidence for \(\textit{relative}\) errors in scaling radii between dwarfs and giants at the \(4\% \pm 0.6\%\) level, and find evidence of departures from simple scaling relations for radii above \(30 R_{\odot}\). Asteroseismic masses for very metal-poor stars are still overestimated relative to astrophysical priors, but at a reduced level. We see no trend with metallicity in radius agreement for stars with \(-0.5 <\) [Fe/H] \(< +0.5\). We quantify the spatially-correlated parallax errors in the \({\it Kepler}\) field, which globally agree with the \({\it Gaia}\) team's published covariance model. We provide \({\it Gaia}\) radii, corrected for extinction and the \({\it Gaia}\) parallax zero-point for our full sample of \(\sim 3900\) stars, including dwarfs, subgiants, and first-ascent giants.