An improved Tully-Fisher estimate of $H_0$

We propose an improved comprehensive method for determining the Hubble constant ($H_0$) using the Tully-Fisher relation. By fitting a peculiar velocity model in conjunction with the Tully-Fisher relation, all available data can be used to derive self-consistent Tully-Fisher parameters. In comparison to previous approaches, our method offers several improvements: it can be readily generalised to different forms of the Tully-Fisher relation and its intrinsic scatter; it uses a peculiar velocity model to predict distances more accurately; it can account for all selection effects; it uses the entire dataset to fit the Tully-Fisher relation; and it is fully self-consistent. The Tully-Fisher relation zero-point is calibrated using the subset of galaxies with distances from absolute distance indicators. We demonstrate this method on the Cosmicflows-4 catalogue $i$-band and $W1$-band Tully-Fisher samples and show that the uncertainties from fitting the Tully-Fisher relation amount to only 0.2 km s$^{-1}$Mpc$^{-1}$. Using all available absolute distance calibrators, we obtain $H_0=73.3$ $\pm$ 2.1 (stat) $\pm$ 3.5 (sys) km s$^{-1}$Mpc$^{-1}$, where the statistical uncertainty is dominated by the small number of galaxies with absolute distance estimates. The substantial systematic uncertainty reflects inconsistencies between various zero-point calibrations of the Cepheid period-luminosity relation, the tip of the red giant branch standard candle, and the Type Ia supernova standard candle. However, given a reliable set of absolute distance calibrators, our method promises enhanced precision in $H_0$ measurements from large new Tully-Fisher samples such as the WALLABY survey.