The underlying radial acceleration relation

Abstract

The radial acceleration relation (RAR) of late-type galaxies relates their dynamical acceleration, g obs , to that sourced by baryons alone, g bar , 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 on g bar and g obs . 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 SPARC dataset. This reveals the intrinsic RAR underlying that observed. I find an acceleration scale a 0 = (1.19 ± 0.04 (stat) ± 0.09 (sys)) × 10 −10 m s −2 , an intrinsic scatter σ int = (0.034 ± 0.01 (stat) ± 0.01 (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 redshift-independent distance measurement.