We present new Near-Infrared ( J , K ) magnitudes for 114 RR Lyrae stars in the globular cluster \omega Cen ( NGC 5139 ) which we combine with data from the literature to construct a sample of 180 RR Lyrae stars with J and K mean magnitudes on a common photometric system .
This is presently the largest such sample in any stellar system .
We also present updated predictions for J , K -band Period-Luminosity relations for both fundamental and first-overtone RR Lyrae stars , based on synthetic horizontal branch models with metal abundance ranging from Z =0.0001 to Z =0.004 .
By adopting for the \omega Cen variables with measured metal abundances an \alpha -element enhancement of a factor of 3 ( \approx 0.5 dex ) with respect to iron we find a true distance modulus \mu _ { 0 } = 13.70 \pm 0.06 \pm 0.06 ( random and systematic errors respectively ) , corresponding to a distance d = 5.5 \pm 0.03 \pm 0.03 Kpc .
Our estimate is in excellent agreement with the distance inferred for the eclipsing binary OGLEGC-17 , but differ significantly from the recent distance estimates based on cluster dynamics and on high amplitude \delta Scuti stars .