The Baryonic Tully–Fisher Relation (BTFR) exhibits an intrinsic scatter of only ~0. 07–0. 10 dex in log velocity, making it one of the tightest empirical scaling relations in galaxy dynamics. The physical origin of this tightness remains unresolved. In this work, we address a complementary and previously underexplored question: what is the minimum velocity scatter that a population of rotationally supported disk galaxies must exhibit, given their observed structural diversity? Using Newtonian disk mechanics and the measured dispersion in disk scale lengths from the SPARC sample (σ (log Rd) ≈ 0. 18 dex), we derive a geometric lower bound—a structural scatter floor—on the BTFR. Propagating size variance through surface density to rotation velocity yields σ (log V) ₛtruct = (1/2) σ (log Rd) ≈ 0. 09 dex. This value coincides, within uncertainties, with the observed intrinsic scatter. We term this agreement the near-coincidence problem: if additional sources of scatter (e. g. , stellar feedback, gas fraction variations, inclination uncertainties, and environmental effects) are non-negligible, the total scatter should exceed the structural floor. The observed near-equality therefore implies that these contributions are either collectively subdominant or partially anti-correlated with the structural component. We formalize this constraint through a variance decomposition framework and show that it provides a direct, falsifiable diagnostic for galaxy formation models and cosmological hydrodynamic simulations. We further derive regime-dependent predictions: the structural floor should be approximately saturated in regular, stellar-dominated disks, while it should be exceeded in gas-rich dwarfs, dynamically disturbed systems, and high-redshift galaxies in proportion to their structural dispersion. These predictions are testable with current and upcoming surveys. The structural scatter floor is independent of specific dark matter or modified gravity frameworks and instead represents a geometric constraint imposed by disk structure itself. It reframes the BTFR scatter not as a residual to be explained, but as a lower bound that galaxy formation physics must respect.
Alim ul haq khan (Tue,) studied this question.