The origin of the mass discrepancy-acceleration relation in Λ CDM

We examine the origin of the mass discrepancy-radial acceleration relation (MDAR) of disc galaxies. This is a tight empirical correlation between the disc centripetal acceleration and that expected from the baryonic component. The MDAR holds for most radii probed by disc kinematic tracers, regardless of galaxy mass or surface brightness. The relation has two characteristic accelerations: a(0), above which all galaxies are baryon dominated, and amin, an effective minimum acceleration probed by kinematic tracers in isolated galaxies. We use a simple model to show that these trends arise naturally in Lambda cold dark matter (Lambda CDM). This is because (i) disc galaxies in Lambda CDM form at the centre of dark matter haloes spanning a relatively narrow range of virial mass; (ii) cold dark matter halo acceleration profiles are self-similar and have a broad maximum at the centre, reaching values bracketed precisely by amin and a0 in that mass range and (iii) halo mass and galaxy size scale relatively tightly with the baryonic mass of a galaxy in any successful Lambda CDM galaxy formation model. Explaining the MDAR in Lambda CDM does not require modifications to the cuspy inner mass profiles of dark haloes, although these may help to understand the detailed rotation curves of some dwarf galaxies and the origin of extreme outliers from the main relation. The MDAR is just a reflection of the self-similar nature of cold dark matter haloes and of the physical scales introduced by the galaxy formation process.