Testing the radius scaling relation with $Gaia$ DR2 in the $Kepler$ field

We compare radii based on $Gaia$ parallaxes to asteroseismic scaling relation-based radii of $\sim 300$ dwarfs $\mathrm{\&}$ subgiants and $\sim 3600$ first-ascent giants from the $Kepler$ mission. Systematics due to temperature, bolometric correction, extinction, asteroseismic radius, and the spatially-correlated $Gaia$ parallax zero-point, contribute to a $2\mathrm{\%}$ systematic uncertainty on the $Gaia$-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 $2\mathrm{\%}$ agreement that we find holds for stars spanning radii between $0.8R_{\odot }$ and $30R_{\odot }$. We do, however, see evidence for $\mathit{\text{relative}}$ errors in scaling radii between dwarfs and giants at the $4\mathrm{\%}\pm 0.6\mathrm{\%}$ level, and find evidence of departures from simple scaling relations for radii above $30R_{\odot }$. 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 $Kepler$ field, which globally agree with the $Gaia$ team’s published covariance model. We provide $Gaia$ radii, corrected for extinction and the $Gaia$ parallax zero-point for our full sample of $\sim 3900$ stars, including dwarfs, subgiants, and first-ascent giants.