The radial acceleration relation in a ΛCDM universe

We study the radial acceleration relation (RAR) between the total (a(tot)) and baryonic (a(bary)) centripetal acceleration profiles of central galaxies in the cold dark matter (CDM) paradigm. We analytically show that the RAR is intimately connected with the physics of the quasi-adiabatic relaxation of dark matter in the presence of baryons in deep potential wells. This cleanly demonstrates how the mean RAR and its scatter emerge in the low-acceleration regime (10(-12) ms(-2) less than or similar to a(bary) less than or similar to 10(-10) ms(-2)) from an interplay between baryonic feedback processes and the distribution of CDM in dark haloes. Our framework allows us to go further and study both higher and lower accelerations in detail, using analytical approximations and a realistic mock catalogue of similar to 342 000 low-redshift central galaxies with M-r <= -19. We show that, while the RAR in the baryon-dominated high-acceleration regime (a(bary) greater than or similar to 10(-10) ms(-2)) is very sensitive to details of the relaxation physics, a simple 'baryonification' prescription matching the relaxation results of hydrodynamical CDM simulations is remarkably successful in reproducing the observed RAR without any tuning. And in the (currently unobserved) ultra-low-acceleration regime (a(bary) less than or similar to 10(-12) ms(-2)), the RAR is sensitive to the abundance of diffuse gas in the halo outskirts, with our default model predicting a distinctive break from a simple power-law-like relation for HI-deficient, diffuse gas-rich centrals. Our mocks also show that the RAR provides more robust, testable predictions of the Lambda CDM paradigm at galactic scales, with implications for alternative gravity theories than the baryonic Tully-Fisher relation.