Mid-infrared PL relations for Globular Cluster RR Lyrae

The period - metallicity - WISE W1- and W2-band luminosity relations are derived for RR Lyrae stars based on WISE epoch photometry for 360 and 275 stars in 15 and 9 Galactic globular clusters, respectively. Our final relations have the form <MW1> = gamma(W1) - (2.381 +/- 0.097) log PF + (0.096 +/- 0.021)[Fe/H] and <MW2> = gamma(W2)-(2.269 +/- 0.127)log PF + (0.108 +/- 0.021)[Fe/H], where [Fe/H] values are on the scale of Carretta et al. (2009). We obtained two appreciably discrepant estimates for the zero points gamma(W1) and gamma(W2) of both relations: one based on a statistical-parallax analysis -- gamma(W1) = -0.829 +/- 0.093 and gamma(W2)=-0.776 +/- 0.093 and another, significantly brighter one, based on HST FGS trigonometric parallaxes -- gamma(W1, HST) =-1.150 +/- 0.077 and gamma(W2, HST) =-1.105 +/- 0.077. The period-metallicity-luminosity relations in the two bands yield highly consistent distance moduli for the calibrator clusters and the distance moduli computed using the W1- and W2-band relations with the HST zero points agree well with those computed by \citet{sollima} based on their derived period-metallicity-K-band luminosity relation whose zero point is tied to the HST trigonometric parallax of RR Lyrae itself (Delta DM0 = +0.04 and +0.06, respectively, with a scatter of only 0.06).