In this work we model galactic halos describing the dark matter as a non zero pressure fluid and derive, not impose, a dark matter equation of state by using observational data of the rotation curves of galaxies. In order to reach hydrostatic equilib
rium, as expected for the halo, it is mandatory that dark fluids pressure should not be zero. The equation of state is obtained by solving the matter-geometry system of equations assuming different dark matter density or rotational velocity profiles. The resulting equations of state are, in general, different to a barotropic equation of state. The free parameters of the equation of state are fixed by fitting the observed rotational velocities of a set of galaxies.
We build a spherical halo model for galaxies using a general scalar-tensor theory of gravity in its Newtonian limit. The scalar field is described by a time-independent Klein-Gordon equation with a source that is coupled to the standard Poisson equat
ion of Newtonian gravity. Our model, by construction, fits both the observed rotation velocities of stars in spirals and a typical luminosity profile. As a result, the form of the new Newtonian potential, the scalar field, and dark matter distribution in a galaxy are determined. Taking into account the constraints for the fundamental parameters of the theory (lambda,alpha), we analyze the influence of the scalar field in the dark matter distribution, resulting in shallow density profiles in galactic centers.
