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

TL;DR

This paper calibrates the Tully-Fisher Relation using WISE W1 and W2 infrared data, updating previous models, and applies it to determine the Hubble constant with improved accuracy.

Contribution

It introduces new WISE W1 and W2 TFR calibrations, including curvature and color corrections, and uses these to refine the local universe's distance scale and estimate H0.

Findings

W1 and W2 TFRs have rms scatter around 0.55 magnitudes.

Curved quadratic fits improve the TFR accuracy.

Derived Hubble constant is 74.4 km/s/Mpc with 4% total error.

Abstract

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 $\mathcal{M}^{b,i,k,a}_{W1} = -20.35 - 9.56 (\log W^i_{mx} - 2.5)$ (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 $\mathcal{M}^{b,i,k}_I = -21.34 - 8.95 (\log W^i_{mx} - 2.5)$ (0.46 magnitudes rms). The WISE TFRs show evidence of curvature. Quadratic fits give $\mathcal{M}^{b,i,k,a}_{W1} = -20.48 - 8.36 (\log W^i_{mx} - 2.5) + 3.60 (\log W^i_{mx} - 2.5)^2$ (0.52 magnitudes rms) 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 $\mathcal{M}_{C_{W1}} = -20.22 - 9.12 (\log W^i_{mx} - 2.5)$ and $\mathcal{M}_{C_{W2}} = -19.63 - 9.11 (\log W^i_{mx} - 2.5)$ (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.