On the absence of a universal surface density, and a maximum Newtonian
  acceleration in dark matter haloes: consequences for MOND
  We study the dark matter (DM) surface density using the SPARC sample and
{compare} it to Donato et al. (2009) result. By means of MCMC method, we infer
the best-fitting parameters for each galaxy. We reobtain the scaling relation
between the surface density and luminosity, and several other scaling laws
relating the dark matter halo properties to that of the galactic disc
properties. We conclude, in contrast with Donato et al. \cite{Donato}, that the
dark matter surface density is not a universal (constant) quantity but
correlates with the luminosity as well as with other galactic disc properties.
A derived posterior probability distribution of $\rho_0 r_0$ shows that the
null hypothesis of constancy is rejected at a very high confidence level. These
results leave little room for the claimed universality of dark matter surface
density. Since MOND has strong prediction on the surface density
\cite{Milgrom2009}, we compared our result with those predictions, finding that
MOND predictions are violated by data. To strengthen the previous result, we
compared our results to another prediction of MOND (Milgrom 2005), the
existence of a maximum Newtonian dark matter acceleration in the halo. Also in
this case, MOND predictions are in contradiction with data. The dark matter
Newtonian acceleration correlates with all the previously presented galactic
disc properties, and data are distributed outside the bound predicted by
Milgrom $\&$ Sanders (Milgrom 2005). We also find that the null hypothesis
(constancy of DM Newtonian acceleration) is rejected at a very high confidence
level.
