Surface brightness-color relations for red giant branch stars using asteroseismic radii and Gaia distances (the ARD method)

Context. Surface brightness-color relations (SBCRs) are essential for estimating distances and stellar properties. Previously, SBCRs were based on a limited number of red clump giant (RCG) stars, and red giant branch (RGB) stars with infrared interferometric measurements or eclipsing binaries with high-precision radii measurements, resulting in discrepancies in precision and accuracy. Recently, the large number of RGB stars with asteroseismic parameters and precise Gaia distance measurements has enabled the development of more accurate and robust SBCRs. Aims. The asteroseismic radius and Gaia distance (ARD) method has been proposed to establish the SBCRs for late-type stars. Methods. We selected Kepler RGB stars with high-precision asteroseismic radii (uncertainties < 1%) and crossmatched them with 2MASS, APASS, and Gaia to obtain Johnson-B, Johnson-V, G, J, H, and Ks-band photometric data. After applying selection criteria, we obtained 626 RGB stars to build the SBCR. Among these, 100 RGBs were used as independent validation for the distance, and the remaining samples were used to fit the SBCR. Results. First, using 526 targets with asteroseismic radii and Gaia distances, nine SBCRs were proposed based on 2MASS (J, H, Ks), APASS (Johnson-B, Johnson-V), and Gaia (G) photometry. The average rms scatter in these relations is 0.075 mag, which corresponds to an uncertainty of approximately 3.5% in distance. These relations were further validated using 100 independent samples with Gaia distances, showing no bias, with a dispersion of approximately 3%. Compared to interferometric measurements, a systematic underestimation of 2.3% was observed, and the discrepancy decreases as the angular diameter increases. Additionally, the distances of eclipsing binaries in the Large Magellanic Cloud and Small Magellanic Cloud obtained using our SBCRs are generally consistent with the ones measured in the literature, with a dispersion of 1% and a slight overestimation of 1% to 2.5%. Conclusions. The ARD method capitalizes on two key advantages for precise stellar distance determination: a statistically robust sample of homogeneous RGB stars with low observational costs, and independent distance verification through Gaia data. Such SBCRs can be further calibrated and expanded more efficiently and effectively.