RGB surface brightness-color relation

We explored three fitting strategies: metallicity-free, metallicity-binned, and global metallicity-dependent relations. Over the range V-Ks, the SBCR shows only a weak metallicity dependence. A change of 1dex in [Fe/H] modifies the predicted angular diameter by less than 1%, well below the intrinsic scatter of the calibration (~0.05mag).

This result is consistent with theoretical expectations. Comparison with the interferometric sample reveals a systematic offset of ~1.5% toward smaller angular diameters in our SBCR predictions, with a mild color dependence. The metallicity effect on the SBCR is small in the color range explored here, but it becomes relevant for sub-percent distance measurements.

Our results show that large RGB samples with asteroseismic radii and Gaia distances provide a powerful observational route for SBCR calibration, with clear potential for extension to cooler and redder giants as the precision and parameter coverage of the input data improve.