The radial dependence of dark matter distribution in M33
The stellar and gaseous mass distributions, as well as the extended rotation curve in the nearby galaxy M33 are used to derive the radial distribution of dark matter density in the halo and to test cosmological models of galaxy formation and evolution. Two methods are examined to constrain dark mass density profiles. The first method deals directly with fitting the rotation curve data in the range of galactocentric distances $0.24\,\text{kpc}\leq r\leq22.72\,\text{kpc}.$ As found in a previous paper by \citet{Corbelli:2014lga}, and using the results of collisionless $\Lambda-$Cold Dark Matter numerical simulations, we confirm that the Navarro-Frenkel-White (hereafter NFW) dark matter profile provides a better fit to the rotation curve data than the cored Burkert profile (hereafter BRK) profile. The second method relies on the local equation of centrifugal equilibrium and on the rotation curve slope. In the aforementioned range of distances we fit the observed velocity profile, using a function which has a rational dependence on the radius, and derive the slope of the rotation curve. Following \citet{Salucci:2010qr} we then infer the effective matter densities. In the radial range $9.53\,\text{kpc}\leq r\leq22.72\,\text{kpc}$ the uncertainties induced by the luminous matter (stars and gas) becomes negligible, because the dark matter density dominates, and we can determine locally the radial distribution of dark matter. With this second method we tested the NFW and the BRK dark matter profiles and confirm that both profiles are compatible with the data even though in this case the cored BRK density profile provides a more reasonable value for the baryonic-to-dark matter ratio.