The underlying radial acceleration relation

Harry Desmond*

*Corresponding author for this work

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The radial acceleration relation (RAR) of late-type galaxies relates their dynamical acceleration, gobs, to that sourced by baryons alone, gbar, across their rotation curves. Literature fits to the RAR have fixed the galaxy parameters on which the relation depends – distance, inclination, luminosity, and mass-to-light ratios – to their maximum a priori values with an uncorrelated Gaussian contribution to the uncertainties in gbar and gobs. In reality these are free parameters of the fit, contributing systematic rather than statistical error. Assuming a range of possible functional forms for the relation with or without intrinsic scatter (motivated by modified Newtonian dynamics with or without the external field effect), I use Hamiltonian Monte Carlo to perform the full joint inference of RAR and galaxy parameters for the Spitzer Photometry and Accurate Rotation Curves (SPARC) dataset. This reveals the intrinsic RAR underlying that observed. I find an acceleration scale a0 = (1.19 ± 0.04 (stat) ± 0.09 (sys)) × 10-10 m s-2, an intrinsic scatter σint = (0.034 ± 0.001 (stat) ± 0.001 (sys)) dex (assuming the SPARC error model is reliable), and weak evidence for the external field effect. I make summary statistics of all my analyses publicly available for future SPARC studies or applications of a calibrated RAR, for example direct distance measurement.

Original languageEnglish
Pages (from-to)3342-3351
Number of pages10
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
Early online date11 Oct 2023
Publication statusPublished - 1 Dec 2023


  • dark matter
  • galaxies: formation
  • galaxies: fundamental parameters
  • galaxies: kinematics and dynamics
  • galaxies: statistics

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