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 \left < V \right > = 13.329 \pm 0.001 ( standard error of the mean ) \pm 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 \pm 0.03 \pm 0.05 mag and 11.32 \pm 0.02 \pm 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 \pm 0.010 \pm 0.018 mag ( NIR PLZ ) and 11.272 \pm 0.005 \pm 0.019 mag ( optical–NIR and NIR PWZ ) .
The above weighted mean true distance moduli agree within 1 \sigma .
The same result is found from distances based on PWZ relations in which the color index is independent of the adopted magnitude ( 11.272 \pm 0.004 \pm 0.013 mag ) .
These distances agree quite well with the geometric distance provided by ( 62 ) 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 % .