Testing the asteroseismic estimates of stellar radii with surface brightness-colour relations and Gaia DR3 parallaxes

Context. 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.Aims.Kepler data differ from K2 data in many aspects. We investigated on the robustness of the results based on Kepler data.Methods. 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 TESS Input Catalogue 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.Results. 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 [α/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_{⊙.Conclusions. 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.}