Dark matter and galaxy rotation curves

Cosmological N-body simulations on structure formation in a Λ−CDM scenario point to a mass density distribution of dark matter, in local objects like galaxies, that are in strong tension with recent observations on low surface brightness galaxies. Modified theories of gravity lack of this problem but also find tensions with observations at larger scales. In this thesis we study the main methods for galaxy rotation curve fitting, from modified theories of gravity such as MOND and f (R) = R n , and considering dark matter halos, such as the one derived from the Λ−CDM numerical simulations and the phenomenological Burkert cored halo profile. To investigate the properties of the dark matter halo that surrounds galaxies, two methods are examined: the standard mass modeling and the local density method. All these methods are applied to the study of the rotation curve of the galaxy M33, which is well extended and measured with an unprecedent high spatial resolution. Later on, we present a unified parameterization of the circular velocity which accurately fits 887 galactic rotation curves without needing in advance the knowledge of the luminous matter components, nor a fixed dark matter halo model. A notable feature of this parametrization is that the associated gravitational potential increases with the distance from the galactic center, giving rise to a length scale indicating a finite size of a galaxy, and after, the keplerian fall-off of the velocity is recovered, making possible for the prediction of the total mass enclosed by the galaxy. As the keplerian regime is reached after a finite length scale, based on isotropy and homogeneity arguments, we considered a static and spherically symmetric Schwarzschild-like space time embedding each galaxy, such that any massive particle moving in geodesic circumferences in the equatorial plane, turns around origin of coordinates with the newly found parameterized velocity formula. Appealing to the General Relativity field equations, for a perfect fluid with pressure anisotropies, we found that the dark matter halo behaves like a cosmological constant in the outer parts of galaxies and controls the distribution shape of the luminous matter component by means of the anisotropic pressure in the azimuthal direction.