Testing the asteroseismic estimates of stellar radii with surface brightness-colour relations and {\it Gaia} DR3 parallaxes. II. Red giants and red clump stars from the {\it Kepler} catalogue

Abstract

A recent investigation highlighted peculiar trends between the radii derived from surface brightness-colour relations (SBCRs) combined with Gaia DR3 parallaxes with respect to asteroseismic scaling relation radii from K2 data. [...] We investigated on the robustness of the results based on Kepler data. We cross-matched asteroseismic and astrometric data for over 12,000 red giant branch and red clump stars from the end-of-mission Kepler catalogue with the Gaia DR3 and TIC v8.2 to obtain precise parallaxes, V- and K-band magnitudes, and E(B - V) colour excesses. Two well-tested SBCRs from the literature were adopted to estimate stellar radii. The analysis confirmed that SBCR and asteroseismic radii agree very well. The overall differences are only 1-2% depending on the adopted SBCR. The dispersion of 7% was about two-thirds of what was found for K2-based data. As a difference from the K2-based investigation, the ratio of SBCRs-to-asteroseismic radii did not depend on the metallicity [Fe/H]. Moreover, the intriguing decreasing trend with [$\alpha$/Fe] of the radius ratio for massive stars that was observed in K2 data was absent in Kepler data. The SBCR radii are systematically higher than asteroseismic estimates by 5% for stars with masses below 1.0 $M_{\odot}$. The SBCRs have proven to be a highly effective tool for estimating radii with a precision comparable to that obtained from asteroseismology, but at a significantly lower observational cost. Moreover, the superior concordance of Kepler-derived radii with SBCR measurements and the absence of the discrepancies observed in the K2-derived radii suggest the existence of underlying systematic errors that impact specific mass and metallicity regimes within the K2 dataset.