Mid-infrared Period-luminosity Relations of RR Lyrae Variables via Color-transformed Data

We derive RR Lyrae period metallicity mid-infrared luminosity relations in the WISE W1 and W2 bands based on intensity-mean W1 and W2 magnitudes computed from intensity-mean Gaia G_(BP) and G_(RP) magnitudes and known metallicity [Fe/H] for ~5000 field RR~Lyrae variables and ~700 variables in 24 globular clusters: = -0.486(+/-0.004)-2.418(+/-0.021)log P_F + 0.25) + 0.166(+/0.007) ([Fe/H] + 1.6) and = -0.464(+/-0.004) -2.449(+/-0.021) (log P_F + 0.25) + 0.170(+/-0.007) ([Fe/H] + 1.6). The period slopes are based on period magnitude relations for RR Lyraes in globular clusters and the zero points and metallicity slopes, on bias-corrected Gaia DR3 triginometric parallaxes of field variables. The scatter of the derived relations depends on magnitude and varies from ~0.02 mag for bright stars to ~0.17 mag for LMC RR Lyraes. We find the period magnitude relations for Gaia color-transformed intensity-mean W1 and W2-band magnitudes for ~12000 LMC RR Lyraes to have practically the same slopes: = 18.039(+/-0.002)2.414(+/-0.020)(log P_F + 0.25) +/0.166 and = 18.061(+/-0.002) 2.448(+/-0.020) (log P_F + 0.25) +/0.168. The distances to globular clusters implied by the derived period metallicity mid-infrared luminosity relations are, on the average, longer by a factor of 1.016+/-0.010 than those inferred by Baumgardt & Vasiliev from trigonometric parallaxes of individual cluster members or totally consistent with them (a factor of 0.994+/-0.016$ or 0.992+/-0.016) if the comparison allows for eventual parallax bias, which in that case is found to be (5.4 5.6)+/-2.8 microas in the sense that Baumgardt & Vasiliev parallaxes appear to be slightly overestimated. Our photometric distances are shorter by a factor of ~1.028+/-0.010 and ~1.024+/-0.016 than kinematical distances computed using Gaia EDR3 or Hubble Space Telescope-based proper-motion dispersion profiles, respectively.