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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. We cross-matched asteroseismic and astrometric data for over 6, 400 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 Rᵃ and Rᵇ, respectively. We analysed the ratio of these SBCR-derived radii to the asteroseismic radius estimates, R, provided in the APO-K2 catalogue. Both SBCRs exhibited good agreement with asteroseismic radius estimates. On average, Rᵃ was overestimated by 1. 2 with respect to R, while Rᵇ was underestimated by 2. 5. For stars larger than 20 R_ sun, 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, Rᵇ showed perfect agreement with R, while Rᵃ 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_ sun, 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 alpha /Fe abundance ratios for massive stars, both in RGB and RC phases, which is reported here for the first time.
Valle et al. (Sat,) studied this question.