What question did this study set out to answer?

This work aims to provide a structural explanation for the Baryonic Tully–Fisher Relation based on an analysis of disk galaxies.

February 19, 2026Open Access

Structural Fixed-Point Theory of Disk Galaxies: Geometric Cancellation, Scatter Floor, and Acceleration Convergence in the Baryonic Tully–Fisher Relation (Version 2.0)

Key Points

This work aims to provide a structural explanation for the Baryonic Tully–Fisher Relation based on an analysis of disk galaxies.
Analyzed the SPARC sample of 175 disk galaxies.
Investigated Newtonian disk equilibrium and empirical size–mass scaling (R_d ∝ M_b^0.5).
Assessed structural dispersion and its impact on the scatter floor in the BTFR.
Identified a BTFR slope resulting from Newtonian disk equilibrium.
Determined an intrinsic scatter floor of approximately 0.09 dex due to structural dispersion.
Found a mass-independent acceleration scale of around 10^-10 m s^-2, linked to stability under Toomre Q ≈ 1.

Abstract

This work presents a structural interpretation of the Baryonic Tully–Fisher Relation (BTFR) using the SPARC sample of 175 disk galaxies. We show that: • The BTFR slope emerges from Newtonian disk equilibrium combined with empirical size–mass scaling (Rd ∝ Mb⁰. 5). • The intrinsic scatter floor (~0. 09 dex) arises from structural dispersion in disk scale length. • A mass-independent acceleration scale (~10^-10 m s^-2) appears as a stability fixed point under Toomre Q ≈ 1. • Structural regulation is strongest in low-mass galaxies. The results suggest that the BTFR and galactic acceleration scale reflect structural self-organization in rotating stellar disks rather than modified gravity.

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