Estimate of the Lindegren et al. Gaia DR3 Trigonometric-Parallax Bias Correction Based on the IR Period-Metallicity-Luminosity for RR Lyrae Type Variables

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 Mₖ₁=-0. 492 (0. 009) -2. 418 (P₅+0. 25) +0. 163 (0. 008) (Fe/H+1. 6) and Mₖ₂=-0. 463 (0. 010) -2. 449 (P₅+0. 25) +0. 165 (0. 009) (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 0. 7 as.