The origin of the mass discrepancy-acceleration relation in $\Lambda$CDM
  We examine the origin of the mass discrepancy--radial acceleration relation
(MDAR) of disk galaxies. This is a tight empirical correlation between the disk
centripetal acceleration and that expected from the baryonic component. The
MDAR holds for most radii probed by disk 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
$a_{\rm min}$, an effective minimum aceleration probed by kinematic tracers in
isolated galaxies. We use a simple model to show that these trends arise
naturally in $\Lambda$CDM. This is because: (i) disk 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
$a_{\rm min}$ and $a_0$ 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.
