Mid-infrared period-luminosity 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 <M_W1> = γ_W1- (2.381 ± 0.097) log P_F + (0.096 ± 0.021)[Fe/H] and <M_W2> = γ_W2 -(2.269 ± 0.127)log P_F + (0.108 ± 0.021)[Fe/H], where [Fe/H] values are on the scale of Carretta et al. We obtained two appreciably discrepant estimates for the zero-points γ_W1 and γ_W2 of both relations: one based on a statistical-parallax analysis - γ_W1 = -0.829 ± 0.093 and γ_W2 = -0.776 ± 0.093 and another, significantly brighter one, based on Hubble Space Telescope (HST) Fine Guidance Sensor (FGS) trigonometric parallaxes - γ_W1,HST = -1.150 ± 0.077 and γ_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 Sollima, Cacciari & Valenti based on their derived period-metallicity-K-band luminosity relation whose zero-point is tied to the HST trigonometric parallax of RR Lyrae itself (ΔDM₀ = 0.04 and 0.06, respectively, with a scatter of only 0.06).