The radial acceleration relation and dark baryons in MOND

Abstract: Recent observations of rotationally supported galaxies show a tight correlation between the observed radial acceleration at every radius and the Newtonian acceleration generated by the baryonic mass distribution, the so-called radial acceleration relation (RAR). The rotation curves (RCs) of the SPARC sample of disk galaxies with different morphologies, masses, sizes and gas fractions are investigated in the context of modified Newtonian dynamics (MOND). We include the effect of cold dark baryons by scaling the measured mass in the atomic form by a factor of $c$ in the mass budget of galaxies. In addition to the standard interpolating function, we also fit the RCs and the RAR with the empirical RAR-inspired interpolating function. Slightly better fits for about $47\%$ of galaxies in our sample are achieved in the presence of dark baryons ($c>1$) with the mean value of $c = 2.4\pm 1.3$. Although the MOND fits are not significantly improved by including dark baryons, it results in a decrease in the characteristic acceleration $g_\dag$ by $40\%$. We find no correlation between the MOND critical acceleration $a_0$ and the central surface brightness of the stellar disk, $\mu_{3.6}$. This supports $a_0$ being a universal constant for all galaxies.