Fitting the radial acceleration relation to individual SPARC galaxies

Abstract: Galaxies follow a tight radial acceleration relation (RAR): the acceleration observed at every radius correlates with that expected from the distribution of baryons. We use the Markov Chain Monte Carlo method to fit the mean RAR to 175 individual galaxies in the SPARC database, marginalizing over stellar mass-to-light ratio ($\Upsilon_{\star}$), galaxy distance, and disk inclination. Acceptable fits with astrophysically reasonable parameters are found for the vast majority of galaxies. The residuals around these fits have an rms scatter of only 0.057 dex ($\sim$13$\%$). This is in agreement with the predictions of modified Newtonian dynamics (MOND). We further consider a generalized version of the RAR that, unlike MOND, permits galaxy-to-galaxy variation in the critical acceleration scale. The fits are not improved with this additional freedom: there is no credible indication of variation in the critical acceleration scale. The data are consistent with the action of a single effective force law. The apparent universality of the acceleration scale and the small residual scatter are key to understanding galaxies.