Tully-Fisher Rotation Bias

The Tully-Fisher relation connects the rotational velocity of a spiral galaxy to its intrinsic luminosity: faster-rotating galaxies are intrinsically brighter. Calibrated against Cepheids or TRGB in nearby galaxies, it can reach galaxies far beyond where individual stars are resolved, extending the distance ladder into the Hubble flow. Modern baryonic Tully-Fisher relation (BTFR) analyses, using total baryonic mass rather than luminosity, are tighter and more physically motivated. When these analyses are used to derive H₀, they consistently return values in the range 71–76 km/s/Mpc depending on calibration choices — again systematically higher than the Planck CMB value.

A subtle but important bias exists in all Tully-Fisher surveys: galaxies must be spatially resolved enough to measure rotation curves, which preferentially selects against distant, compact, or face-on systems. This Malmquist-like selection bias, if incompletely corrected, can shift the derived H₀. More fundamentally, the BTFR assumes that the relationship between baryonic mass and rotational velocity is universal and does not evolve with redshift or environment — an assumption that ΛCDM's galaxy formation models actually predict should break down at the ~5–10% level due to varying dark matter halo concentrations and merger histories. Correcting for this predicted scatter in the ΛCDM framework does not reduce the inferred H₀; it merely increases the uncertainty, leaving the tension intact.