Baryon-Interacting Dark Matter: heating dark matter and the emergence of
  galaxy scaling relations
  The empirical scaling relations observed in disk galaxies remain challenging
for models of galaxy formation. The most striking among these is the Mass
Discrepancy-Acceleration Relation (MDAR), which encodes both a tight baryonic
Tully-Fisher relation (BTFR) and the observed diversity of galaxy rotation
curves through the central surface density relation (CSDR). Building on our
earlier work, we propose here that the MDAR is the result of interactions
between baryons and 'Baryon-Interacting Dark Matter' (BIDM), which heat up the
dark matter. Following a bottom-up, hydrodynamical approach, we find that the
MDAR follows if: $i)$ the BIDM equation of state approximates that of an ideal
gas; $ii)$ the BIDM relaxation time is order the Jeans time; $iii)$ the heating
rate is inversely proportional to the BIDM density. Remarkably, under these
assumptions the set of hydrodynamical equations together with Poisson's
equation enjoy an anisotropic scaling symmetry. In the BIDM-dominated regime,
this gives rise to an enhanced symmetry which fully captures the
low-acceleration limit of the MDAR. We then show that, assuming a cored
pseudo-isothermal profile at equilibrium, this set of equations gives rise to
parameters reproducing the MDAR. Specifically, in the flat part of the rotation
curve the asymptotic rotational velocity matches the parametric dependence of
the BTFR. Moreover, in the central region of high-surface brightness galaxies,
the profile reproduces the CSDR. Finally, by studying the time-dependent
approach to equilibrium, we derive a global combination of the BTFR and CSDR,
which matches the expectations in low surface-brightness galaxies. The form of
the heating rate also makes model-independent predictions for various
cosmological observables. We argue that our scenario satisfies existing
observational constraints, and, intriguingly, offers a possible explanation to
the EDGES anomaly.
