Distance to the globular cluster M 3 from the infrared surface brightness technique applied to RR Lyrae stars

Context. The infrared surface brightness (IRSB) technique is a specific application of the Baade-Wesselink method. Given proper calibration, well-covered optical and near-infrared photometry, as well as radial velocity curves, it allows the estimation of distances to individual pulsating stars and the determination of their mean radii. Even though it is observationally demanding, it offers a way of distance determination to systems of pulsating stars that is independent of period-luminosity relations. The technique is fully empirical and does not depend on stellar atmosphere models. Aims. 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 determined the mean radii and period-radius relations for these stars in order to compare them with the existing theoretical predictions and empirical estimations for the field stars from the solar neighborhood. Methods. We used the 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 applied the IRSB technique, as previously presented in our work for RR Lyraes, from the solar vicinity with an extra determination and implementation of phase shifts between observables due to the phase incoherence of data gathered at different epochs. We studied the impact of the selection of the fitting procedure (bisector vs. the least-squares fit) on the results. We applied five different empirical surface brightness-color relations from the literature in the analysis. Results. We obtained a mean distance to M 3 of rM3 = (10.07 ± 0.19 ± 0.29) kpc, which corresponds to a distance modulus μM3 = (15.015 ± 0.041 ± 0.063) mag and a 7% scatter of individual stellar distances for 14 RR Lyrae stars in M 3. We obtained a very good agreement between the two fitting techniques; the bisector proved to be a biased estimator, while the least-squares fit yielded slightly larger uncertainties. We also determined mean stellar radii for pulsators in 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.