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

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 μm) and W2 (4.6 μm) filters. We find a correlation of line width to absolute magnitude (known as the Tully-Fisher relation, TFR) of M^(b,i,k,ɑ)_(W1) = -20.35 - 9.56(log W^i_(mx) - 2.5) (0.54 mag rms) and M^(b,i,k,ɑ)_(W2) = -19.76 - 9.74 (log W^i_(mx)-2.5)(0.56 mag rms) from 310 galaxies in 13 clusters. We update the I-band TFR using a sample 9% larger than in Tully & Courtois. We derive M^(b,i,k)_I = -21.34 - 8.95 (log W^i_(mx) - 2.5) (0.46 mag rms). The WISE TFRs show evidence of curvature. Quadratic fits give M^(b,i,k,ɑ)_(W1) = -20.48 - 8.36 (log W^i_(mx) - 2.5) + 3.60(log W^i_(mx) - 2.5)^2(0.52 mag rms) and M^(b,i,k,ɑ)_(W2) = -19.91 - 8.40(log W^i_(mx) - 2.5) + 4.32 (log W^i_(mx) - 2.5)^2 (0.55 mag rms). We apply an I-band –WISE color correction to lower the scatter and derive M_C_(W1)} = -20.22 - 9.12(log W^i_(mx) - 2.5) and M_C_(W2) = -19.63 - 9.11(log W^i_(mx) - 2.5) (both 0.46 mag rms). Using our three independent TFRs (W1 curved, W2 curved, and I band), we calibrate the UNION2 Type Ia supernova sample distance scale and derive H_0 = 74.4 ± 1.4(stat) ± 2.4(sys) km s^(–1) Mpc^(–1) with 4% total error.

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