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

Aims. We compared stellar radii derived from asteroseismic scaling relations with those estimated using two independent surface brightness-colour relations (SBCRs) combined with Gaia DR3 parallaxes. Methods. We cross-matched asteroseismic and astrometric data for over 6400 red giant branch (RGB) and red clump (RC) stars from the APO-K2 catalogue with the TESS Input Catalogue v8.2 to obtain precise V band magnitudes and E ( B − V ) colour excesses. We then adopted two different SBCRs from the literature to derive stellar radius estimates, denoted as R a and R b , respectively. We analysed the ratio of these SBCR-derived radii to the asteroseismic radius estimates, R , provided in the APO-K2 catalogue. Results. Both SBCRs exhibited good agreement with asteroseismic radius estimates. On average, R a was overestimated by 1.2% with respect to R , while R b was underestimated by 2.5%. For stars larger than 20 R ⊙ , SBCR radii are systematically lower than asteroseismic ones. The dispersion in the radius ratio was similar for the two methods (around 10%). The agreement with asteroseismic radii shows a strong dependence on the parallax. The dispersion is halved for stars with a parallax greater than 2.5 mas. In this subsample, R b showed perfect agreement with R , while R a remained slightly overestimated, by 3%. A trend with [Fe/H] was found at a level of 4% to 6% per dex. Additionally, a clear trend with asteroseismic mass is found. For stars less massive than about 0.95 M ⊙ , SBCR radii were significantly higher than asteroseismic ones, by about 6%. This overestimation correlated with the presence of extended helium cores in these stars’ structures relative to their envelopes. Furthermore, radius ratios showed a dichotomous behaviour at higher masses, mainly due to the presence of several RC stars with SBCR radii significantly lower with respect to asteroseismology. This behaviour originates from a different response of asteroseismic scaling relations and SBCR to [ α /Fe] abundance ratios for massive stars, both in RGB and RC phases, which is reported here for the first time.