We developed a new approach to provide accurate estimates of metal content , reddening and true distance modulus of RR Lyrae stars ( RRLs ) .
The method is based on homogeneous optical ( BVI ) and near-infrared ( JHK ) mean magnitudes and on predicted period–luminosity–metallicity relations ( IJHK ) and absolute mean magnitude–metallicity relations ( BV ) .
We obtained solutions for three different RRL samples in \omega Cen : first overtone ( RRc , 90 ) , fundamental ( RRab , 80 ) and global ( RRc+RRab ) in which the period of first overtones were fundamentalized .
The metallicity distribution shows a well defined peak at [ Fe/H ] \sim –1.98 and a standard deviation of \sigma =0.54 dex .
The spread is , as expected , metal-poor ( [ Fe/H ] \leq –2.3 ) objects .
The current metallicity distribution is \sim 0.3 dex more metal-poor than similar estimates for RRLs available in the literature .
The difference vanishes if the true distance modulus we estimated is offset by –0.06/–0.07 mag in true distance modulus .
We also found a cluster true distance modulus of \mu =13.720 \pm 0.002 \pm 0.030 mag , where the former error is the error on the mean and the latter is the standard deviation .
Moreover , we found a cluster reddening of E ( B - V ) =0.132 \pm 0.002 \pm 0.028 mag and spatial variations of the order of a few arcmin across the body of the cluster .
Both the true distance modulus and the reddening are slightly larger than similar estimates available in the literature , but the difference is within 1 \sigma .
The metallicity dependence of distance diagnostics agree with theory and observations , but firm constraints require accurate and homogeneous spectroscopic measurements .