Distance to the Globular Cluster M 3 from the Infrared Surface Brightness Technique applied to RR Lyrae stars

The Infrared Surface Brightness (IRSB) technique is a specific application of the Baade-Wesselink method. Given a proper calibration, well covered optical and near-infrared photometry, as well as radial velocity curves, it allows for estimation of distances to individual pulsating stars and determination of their mean radii. The technique is fully empirical and does not depend on stellar atmosphere models. The goal of the work is to test the precision of distance determinations to individual RR Lyrae stars and to their host system as a whole using the IRSB technique for a relatively distant globular cluster M 3 (NGC 5272). We also aim to determine mean radii and period-radius relations for these stars in order to compare them with the existing theoretical prediction and empirical estimations for the field stars from the solar neighborhood. We use data available in the literature and the calibration of the IRSB technique based on the RR Lyrae stars from the solar neighborhood we published previously in order to determine distances to 14 RR Lyrae stars in the globular cluster M 3. We study the impact of the selection of the fitting procedure (bisector v.s. the LS fit) on the results. We apply five different empirical surface brightness-color relations from the literature in the analysis. We obtained a mean distance to M 3 of $r_{M3} = (10.07 \pm 0.19 \pm 0.29) \,kpc$ that corresponds to a distance modulus $μ_{M3} = (15.015 \pm 0.041 \pm 0.063) \,mag$ and a $7\%$ scatter of individual stellar distances for 14 RR Lyrae stars in M 3. We received a very good agreement between the two fitting techniques. We also determined mean stellar radii for pulsators from the sample with a precision of $0.5\%$ and obtained excellent agreement with a theoretical prediction of the period-radius relation for RRab stars available in the literature.