Hooks & Bends in the Radial Acceleration Relation: Discriminatory Tests for Dark Matter and MOND

Abstract

The Radial Acceleration Relation (RAR) connects the total gravitational acceleration of a galaxy at a given radius, $a_{\rm tot}(r)$, with that accounted for by baryons at the same radius, $a_{\rm bar}(r)$. The shape and tightness of the RAR for rotationally-supported galaxies have characteristics in line with MOdified Newtonian Dynamics (MOND) and can also arise within the Cosmological Constant + Cold Dark Matter ($\Lambda$CDM) paradigm. We use zoom simulations of 20 galaxies with stellar masses of $M_{\star} \, \simeq 10^{7-11} \, M_{\odot}$ to study the RAR in the \texttt{FIRE-2} simulations. We highlight the existence of simulated galaxies with non-monotonic RAR tracks that ``hook'' down from the average relation. These hooks are challenging to explain in Modified Inertia theories of MOND, but naturally arise in all of our \lcdm-simulated galaxies that are dark-matter dominated at small radii and have feedback-induced cores in their dark matter haloes. We show, analytically and numerically, that downward hooks are expected in such cored haloes because they have non-monotonic acceleration profiles. We also extend the relation to accelerations below those traced by disc galaxy rotation curves. In this regime, our simulations exhibit ``bends'' off of the MOND-inspired extrapolation of the RAR, which, at large radii, approach $a_{\rm tot} \, \approx \, a_{\rm bar} \, /f_{\rm b}$, where $f_{\rm b}$ is the cosmic baryon fraction. Future efforts to search for these hooks and bends in real galaxies will provide interesting tests for MOND and $\Lambda$CDM.