On the distance of the globular cluster M4 (NGC 6121) using RR Lyrae stars. I. Optical and near-infrared period-Luminosity and period-Wesenheit relations

We present new distance determinations to the nearby globular M4 (NGC 6121) based on accurate optical and near-infrared (NIR) mean magnitudes for fundamental (FU) and first overtone (FO) RR Lyrae variables (RRLs), and new empirical optical and NIR period-luminosity (PL) and period-Wesenheit (PW) relations. We have found that optical-NIR and NIR PL and PW relations are affected by smaller standard deviations than optical relations. The difference is the consequence of a steady decrease in the intrinsic spread of cluster RRL apparent magnitudes at fixed period as longer wavelengths are considered. The weighted mean visual apparent magnitude of 44 cluster RRLs is =13.329 ± 0.001 (standard error of the mean) ±0.177 (weighted standard deviation) mag. Distances were estimated using RR Lyr itself to fix the zero-point of the empirical PL and PW relations. Using the entire sample (FU+FO) we found weighted mean true distance moduli of 11.35 ± 0.03 ± 0.05 mag and 11.32 ± 0.02 ± 0.07 mag. Distances were also evaluated using predicted metallicity dependent PLZ and PWZ relations. We found weighted mean true distance moduli of 11.283 ± 0.010 ± 0.018 mag (NIR PLZ) and 11.272 ± 0.005 ± 0.019 mag (optical-NIR and NIR PWZ). The above weighted mean true distance moduli agree within 1σ. The same result is found from distances based on PWZ relations in which the color index is independent of the adopted magnitude (11.272 ± 0.004 ± 0.013 mag). These distances agree quite well with the geometric distance provided by Kaluzny et al. based on three eclipsing binaries. The available evidence indicates that this approach can provide distances to globulars hosting RRLs with a precision better than 2%-3%.