Calibration of the Tully-Fisher relation in the WISE W1 (3.4 μm) and W2 (4.6 μm) bands

In this paper, we present our calibrations of the Tully-Fisher relation in the mid-infrared W1 (3.4 μm) and W2 (4.6 μm) bands, using large samples of 877 galaxies and 876 galaxies from 31 clusters in the W1 and W2 bands, respectively. Using a new, iterative bivariate fitting procedure we performed two corrections, one for the cluster population incompleteness bias and a second morphological type correction. We initially performed calibrations using total absolute magnitudes and H i line widths WF50 derived from the H i global profiles as a measure of rotational velocity. We then used (i) isophotal magnitudes and (ii) average rotational velocities measured along the flat sections of the spatially resolved rotation curves of the galaxies, which were obtained from the empirical conversion between rotational velocity definitions. We determined that the calibrations using total magnitudes and H i line widths had smaller total scatter around the TF relations in the W1 and W2 bands than those using either isophotal magnitudes or spatially resolved rotational velocities. These calibrations are MTot,W1 = (1.77 ± 0.40) - (9.99 ± 0.16)log10(WF50) and MTot,W2 = (2.03 ± 0.40) - (10.12 ± 0.16)log10(WF50), with associated total scatters of σW1 = 0.66 and σW2 = 0.67. We compared these with previous calibrations in the near-infrared J, H, and K bands and the long-wavelength optical I band which used the same two corrections. The differences between calibrations can be explained by considering the different regions and components of spiral galaxies that are traced by the different wavelengths. The codes used for the calibrations of the Tully-Fisher relation are available from https://github.com/RiannaBell/WISE-TF-Calibration.