Calibrating the Tully-Fisher Relation to Measure the Hubble Constant

Abstract

Boubel et al. 2024 (B24) recently used the Tully-Fisher (TF) relation to measure calibrated distances in the Hubble flow and found $H_0= 73.3 \pm 2.1 (stat) \pm 3.5 (sys)$ km/s/Mpc. The large systematic uncertainty was the result of propagating the conflict between two sources of empirical distance calibration: a difference in zeropoint when calibrating the TF relation with Type Ia supernovae (SNe Ia) versus Cepheids and Tip-of-the-Red-Giant-Branch (TRGB) and an apparent difference in zeropoint between two distinct TRGB datasets. We trace the SN Ia-based calibration used in the TF analysis to a study where $H_0$ was fixed to 70 km/s/Mpc rather than measured, (with host distances derived from redshifts and the Hubble law), thus introducing a discrepancy with the other empirically calibrated indicators. In addition, we trace the difference in TRGB zeropoints to a miscalibration of $0.14$ mag that should be $\sim0.01-0.04$ mag. Using the consistent Cepheid and TRGB calibration from B24 while removing the problematic data reduces the systematic error by a factor of two and results in $H_0 = 76.3 \pm 2.1 \textrm{(stat)} \pm 1.5 \textrm{(sys)}$ km/s/Mpc. This measurement is consistent with previous determinations of $H_0$ using the TF relation. We also show that most determinations of $H_0$ measurements that replace Type Ia supernovae measurements with another far-field distance indicator yield $H_0>73$ km/s/Mpc, reinforcing previous findings that the Hubble tension is not tied to any one distance indicator.