The Calibration of Thewisew1 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 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 Wⁱ_ (mx) - 2. 5) (0. 54 mag rms) and M^ (b, i, k, ɑ) _ (W2) = -19. 76 - 9. 74 (log Wⁱ_ (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 Wⁱ_ (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 Wⁱ_ (mx) - 2. 5) + 3. 60 (log Wⁱ_ (mx) - 2. 5) ² (0. 52 mag rms) and M^ (b, i, k, ɑ) _ (W2) = -19. 91 - 8. 40 (log Wⁱ_ (mx) - 2. 5) + 4. 32 (log Wⁱ_ (mx) - 2. 5) ² (0. 55 mag rms). We apply an I-band –WISE color correction to lower the scatter and derive MC_ (W1) } = -20. 22 - 9. 12 (log Wⁱ_ (mx) - 2. 5) and MC_ (W2) = -19. 63 - 9. 11 (log Wⁱ_ (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 H₀ = 74. 4 ± 1. 4 (stat) ± 2. 4 (sys) km s^ (–1) Mpc^ (–1) with 4% total error.