Abstract
We derive color transformation relations for determining mid-infrared WISE W1- and W2-band intensity-mean magnitudes of moderately reddened RR Lyrae variables from their intensity-mean ZTF \(g\) - and \(r\) -band magnitudes combined with photometric metallicity estimates inferred from ZTF light-curve parameters. We combine the the W1- and W2-band magnitudes so determined with Gaia DR3 parallaxes bias corrected as per Lindegren et al. to estimate the metallicity slopes and zero points of the RR Lyrae W1- and W2-band period-metallicity-luminosity relations and the remaining parallax bias. The resulting period-metallicity-luminosity relations are \(M_{W1}={-}0.492({\pm}0.009)-2.418\times(\log P_{F}+0.25)+0.163({\pm}0.008)(\textrm{[Fe/H]}+1.6)\) and \(M_{W2}={-}0.463({\pm}0.010)-2.449(\log P_{F}+0.25)+0.165({\pm}0.009)(\textrm{[Fe/H]}+1.6)\) . The Lindegren et al. Gaia DR3 parallax bias corrections appear to be overestimated on the average by \(2.9{-}3.0\pm 0.7\) \(\mu\) as.
