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The observed tightness of the mass discrepancy-acceleration relation (MDAR)poses a fine-tuning challenge to current models of galaxy formation. We proposethat this relation could arise from collisional interactions between baryonsand dark matter (DM) particles, without the need for modification of gravity orad hoc feedback processes. We assume that these interactions satisfy thefollowing three conditions: (i) the relaxation time of DM particles iscomparable to the dynamical time in disk galaxies; (ii) DM exchanges energywith baryons due to elastic collisions; (iii) the product between the baryon-DMcross section and the typical energy exchanged in a collision is inverselyproportional to the DM number density. We present an example of a particlephysics model that gives a DM-baryon cross section with the desired density andvelocity dependence. Direct detection constraints require our DM particles tobe either very light ($m << m_b$) or very heavy ($m >> m_b$), correspondingrespectively to heating and cooling of DM by baryons. In both cases, ourmechanism applies and an equilibrium configuration can in principle be reached.Here, we focus on the heavy DM/cooling case as it is technically simpler. Underthese assumptions, we find that rotationally-supported disk galaxies couldnaturally settle to equilibrium configurations satisfying a MDAR at all radiiwithout invoking finely tuned feedback processes. We also discuss issuesrelated to the small scale clumpiness of baryons, as well as predictions forpressure-supported systems. We argue in particular that galaxy clusters do notfollow the MDAR despite being DM-dominated because they have not reached theirequilibrium configuration. Finally, we revisit existing phenomenological,astrophysical and cosmological constraints on baryon-DM interactions in lightof the unusual density dependence of the cross section.

Emergence of the mass discrepancy-acceleration relation from dark matter-baryon interactions