Tully-Fisher Rotation Bias

The Tully-Fisher relation correlates spiral galaxy rotation velocity with luminosity and has long been used as a secondary distance indicator in the extragalactic distance ladder. More fundamentally, the baryonic Tully-Fisher relation (BTFR) — extending the correlation to total baryonic mass — exhibits a remarkably tight power-law form M_bary ∝ V_flat⁴ with essentially zero intrinsic scatter, a precision that has become one of the most challenging relationships for ΛCDM to explain from first principles since it requires a conspiracy between the dark matter halo profile and the baryonic mass fraction at each galaxy's rotation velocity. Tensions arise from systematic differences between BTFR-inferred distances and those from Cepheids or TRGB, contributing to Hubble constant uncertainties, and from the BTFR's slope and zero-point varying with sample selection in ways that ΛCDM predicts but observations do not always confirm.

Successive Collision Theory provides a natural, first-principles derivation of both the BTFR's tight form and its distance-ladder contribution. In SCT, the flat rotation velocity of any disk galaxy is set by two contributions: the centrifugal barrier velocity from inherited angular momentum, and the additional gravitational acceleration from the superposition of overlapping nested comoving frames. The inherited angular momentum produces a density profile ρ(r) ∝ r⁻² whose circular velocity asymptotes to a constant V_flat ∝ j^(1/2), where j is the specific angular momentum of the formation debris stratum. Since j itself scales with total baryonic mass through the universal angular momentum scaling law J ∝ M^(5/3), the resulting V_flat ∝ M^(5/6) which for the appropriate mass-to-velocity coupling reproduces the observed M ∝ V⁴ scaling. The tight scatter follows because the collision-inherited angular momentum distribution is smooth and deterministic, not a stochastic function of merger history as CDM requires.

The BTFR distance bias in the Hubble tension context follows from the same local void environment argument that applies to all distance ladder anchors: Tully-Fisher calibrators within the KBC supervoid sample the locally enhanced expansion rate and therefore yield H₀ values on the high side of the tension. SCT predicts the BTFR zero-point to be stable across environments except for the systematic offset between void and wall galaxies reflecting the local Λ_eff gradient — a prediction testable by comparing BTFR H₀ values for samples drawn from different large-scale density environments.