The Calibration of the WISE W1 and W2 Tully-Fisher Relation

In order to explore local large-scale structures and velocity fields, accurate galaxy distance measures are needed. We now extend the well-tested recipe for calibrating the correlation between galaxy rotation rates and luminosities – capable of providing such distance measures – to the all-sky, space-based imaging data from the Wide-field Infrared Survey Explorer (WISE) W1 ($3.4\mu$m) and W2 ($4.6\mu$m) filters. We find a linewidth to absolute magnitude correlation (known as the Tully-Fisher Relation, TFR) of ${\mathcal{M}}_{W1}^{b,i,k,a}=-20.35-9.56(\log W_{mx}^i-2.5)$ (0.54 magnitudes rms) and $$\mathcal{M}$^{b,i,k,a}{W2} = -19.76 - 9.74 (\log W^i{mx}

• 2.5)$ (0.56 magnitudes rms) from 310 galaxies in 13 clusters. We update the I-band TFR using a sample 9% larger than in Tully & Courtois (2012). We derive ${\mathcal{M}}_I^{b,i,k}=-21.34-8.95(\log W_{mx}^i-2.5)$ (0.46 magnitudes rms). The WISE TFRs show evidence of curvature. Quadratic fits give $$\mathcal{M}$^{b,i,k,a}{W1} = -20.48 - 8.36 (\log W^i{mx} - 2.5) + 3.60 (\log W^i_{mx} - 2.5)^2$(0.52magnitudesrms)and$$\mathcal{M}$^{b,i,k,a}{W2} = -19.91 - 8.40 (\log W^i{mx} - 2.5) + 4.32 (\log W^i_{mx} - 2.5)^2$ (0.55 magnitudes rms). We apply an I-band – WISE color correction to lower the scatter and derive ${\mathcal{M}}_{C_{W1}}=-20.22-9.12(\log W_{mx}^i-2.5)$ and ${\mathcal{M}}_{C_{W2}}=-19.63-9.11(\log W_{mx}^i-2.5)$ (both 0.46 magnitudes rms). Using our three independent TFRs (W1 curved, W2 curved and I-band), we calibrate the UNION2 supernova Type Ia sample distance scale and derive $H_0=74.4\pm 1.4$(stat) $\pm 2.4$(sys) kms${}^{-1}$ Mpc${}^{-1}$ with 4% total error.