Galaxy dynamics from Newtonian gravity and a non-baryonic mass set by the baryons
Year: 2026
Type: preprint
Abstract: Can MOND's regularities follow from a mass that responds to the potential and enters the Poisson equation only through its source term? Galaxies obey regularities that MOND predicted from the baryons alone: the baryonic Tully-Fisher relation (BTFR) and the radial acceleration relation (RAR). Weak lensing extends the RAR to accelerations two decades lower (Brouwer et al. 2021) and finds the circular speeds of isolated galaxies flat to 1 Mpc (Mistele et al. 2024b). We ask whether these regularities can follow, with gravity unmodified, from a non-baryonic mass whose density is set by the present baryons. We present a constitutive relation for such a mass, adapted from the cored isothermal sphere. Its velocity scale is fixed by the BTFR and its response saturates at the MOND acceleration, so MOND’s two limits are inputs and the transition between them is an output, with one fitted constant, the central density. Each halo ends at an ambient density set by a posited smooth background. The mass gravitates and lenses as ordinary mass; a full dynamical treatment is deferred. The paper is conditional: if non-baryonic mass is distributed this way, then (i) on the SPARC rotation curves a single central density reproduces the mean RAR, including the transition, to within 0.1 dex in every acceleration bin, inside the RAR’s observed scatter (∼0.13 dex; Lelli et al. 2017); (ii) the fit improves when the central density depends on galaxy properties, and with one free parameter per galaxy it matches the empirical relation; (iii) the lensing signal of isolated galaxies turns down within a few Mpc (closer in for galaxies with neighbours), at a radius growing as the fourth root of their baryonic mass, because the response ends at an ambient density set by a smooth background field; the downturn persists in voids, where MOND’s external-field decline recedes; (iv) there is no phantom density: the extra mass is real and positive everywhere, so where MOND’s phantom density turns negative, in systems embedded in an external field, the two differ: wide binaries of low central density are Newtonian; (v) dwarf galaxies do not depend on their environment. It falls short in four ways, each of which weakens it: with a single central density its scatter about the RAR is larger than observed, by well over the relation’s measured intrinsic scatter; it over-predicts the lowest accelerations, by up to 0.08 dex, and the outer speeds of low-surface-brightness galaxies, by a few per cent; the central density is fitted, not derived; and a first pre-registered test on dwarf dispersions misses its target. We set out the tests that can decide. This version, v2.0.0, obsoletes GPRF Paper I v1.0.14 (10.5281/zenodo.20450130). The source (.tex), the analysis scripts and the pre-registrations of the tests are in a public repository linked from this record.
Author: Marsen, James Richard
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224465346