The baryonic self similarity of dark matter
  The cosmological simulations indicates that the dark matter haloes have
specific self similar properties. However the halo similarity is affected by
the baryonic feedback, the momentum injected by the supernovae re-shape the
dark matter core and transform it to a flat density core, with a scale length
imposed by the baryonic feedback. Additionally the baryon feedback impose also
an equilibrium condition, which when coupled with the imposed baryonic scale
length induce a new type of similarity. The new self similar solution implies
that the acceleration generated by dark matter is scale free, which in turns
implies that the baryonic acceleration at a reference radius is also scale
free. Constant dark matter and baryonic accelerations at a reference radius
have effectively been observed for a large class of different galaxies, which
is in support of this approach. The new self similar properties implies that
the total acceleration at larger distances is scale free, the transition
between the dark matter and baryons dominated regime occurs at a constant
acceleration, and the maximum of the velocity curve which defines the amplitude
of the velocity curve at larger distances is proportional to $M^{\frac{1}{4}}$.
These results demonstrates that in this self similar model, cold dark matter is
consistent with the basics of MOND phenomenology for the galaxies. In agreement
with the observation the coincidence between the self similar model and MOND is
expected to break at the scale of clusters of galaxies. Some numerical
experiments shows that the behavior of the density near the origin is closely
approximated by a Einasto profile.
