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.