Paper detail

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 $ρ_0 r_0$ 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.