The mass discrepancy acceleration relation in a $\Lambda$CDM context
  The mass discrepancy acceleration relation (MDAR) describes the coupling
between baryons and dark matter (DM) in galaxies: the ratio of
total-to-baryonic mass at a given radius anti-correlates with the acceleration
due to baryons. The MDAR has been seen as a challenge to the $\Lambda$CDM
galaxy formation model, while it can be explained by Modified Newtonian
Dynamics. In this Letter we show that the MDAR arises in a $\Lambda$CDM
cosmology once observed galaxy scaling relations are taken into account. We
build semi-empirical models based on $\Lambda$CDM haloes, with and without the
inclusion of baryonic effects, coupled to empirically motivated structural
relations. Our models can reproduce the MDAR: specifically, a mass-dependent
density profile for DM haloes can fully account for the observed MDAR shape,
while a universal profile shows a discrepancy with the MDAR of dwarf galaxies
with $\rm M^{\star}$$<$$\rm10^{9.5}M_{\odot}$, a further indication suggesting
the existence of DM cores. Additionally, we reproduce slope and normalization
of the baryonic Tully-Fisher relation (BTFR) with 0.17 dex scatter. These
results imply that in $\Lambda$CDM (i) the MDAR is driven by structural scaling
relations of galaxies and DM density profile shapes, and (ii) the baryonic
fractions determined by the BTFR are consistent with those inferred from
abundance-matching studies.
