Letter to the Editor

MUSE-DARK

III. The evolution of the radial acceleration relation at intermediate redshifts

¹ Université Lyon 1, ENS de Lyon, CNRS, CRAL, UMR 5574, Saint-Genis-Laval, France
² Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482, Potsdam, Germany
³ Univ. de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, 11 rue de l’Université, 67000, Strasbourg, France
⁴ Institute of Cosmology & Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth, PO1 3FX, UK

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 30 January 2026
Accepted: 24 April 2026

Abstract

Context. The radial acceleration relation (RAR) is a tight empirical correlation between the observed radial acceleration (a_tot) and the baryonic radial acceleration (a_bar) measured across galaxy radii; these two accelerations start to deviate significantly from each other below a characteristic acceleration scale, a₀. To date, observational studies of the RAR have predominantly focused on galaxies in the local Universe, leaving its evolution with cosmic time largely unexplored.

Aims. Using high signal-to-noise data from the MUSE Hubble Ultra Deep Field survey, we investigated the RAR with a sample of 79 star-forming galaxies (complete above M_★ > 10^8.8 M_⊙) at intermediate redshifts (0.33 < z < 1.44).

Methods. We estimated the observed intrinsic acceleration (a_tot) and the baryonic acceleration (a_bar) from a disk-halo decomposition that incorporates stellar, gas, and dark matter components, with corrections for pressure support, using 3D forward modelling.

Results. We find a RAR in our intermediate-z sample offset from the local relation, with a higher characteristic acceleration scale (a₀|_z∼1 = 2.38^+0.12_−0.10 × 10⁻¹⁰ m/s²) and a larger intrinsic scatter (∼0.17 dex). Dividing the sample into redshift bins and refitting the RAR in each bin, we find a characteristic acceleration scale that systematically increases with z. Parametrising the z-dependence as a₀(z) = a₀(0)+a₁ ⋅ z, we obtain a₁ = 1.59^+0.11_−0.10 × 10⁻¹⁰ m/s², providing evidence for a z-evolution. We find similar results using various dark matter halo profiles as well as the modified Newtonian dynamics framework in our 3D forward modelling.

Conclusions. Our results show that the RAR persists at intermediate redshifts, with statistically significant redshift evolution of the characteristic acceleration, pointing to a possible evolution of the baryon-missing mass connection over cosmic time.