Self-consistent non-spherical isothermal halos embedding zero-thickness disks

We construct self-consistent models of non-spherical isothermal halos embedding a zero-thickness disk, by assuming that the halo distribution function is a Maxwellian, as motivated by the discovery of halos of dark matter from the study of flat rotation curves of spiral galaxies. The approach followed here is fully self-consistent. The halo is taken to be collisionless and stationary and described by the classical Vlasov-Poisson equations. Then the construction of the models requires the solution of the non-linear Poisson equation for the halo potential, in which the gravitational potential of the disk (calculated analytically from the observed mass distribution) acts as an external imposed potential, removing spherical symmetry. The solution is obtained by means of an iterative procedure that generalizes a method introduced in the past to construct spheroidal models of rotating elliptical galaxies. For a typical observed rotation curve the relevant self-consistent models are characterized by two dimensionless parameters, which correspond to the dimensional scales (the disk mass-to-light ratio M/L and the halo central density) of standard disk-halo decompositions. In the past, the study of galaxy rotation curves were performed in a parametric way, by modeling the halo force contribution by means of expressions describing approximately the properties of the regular isothermal sphere and turned out to be unable to produce a unique disk-halo decomposition. Instead, by means of our self-consistent models, the disk-halo degeneracy is removed. Typical rotation curves are fitted by models that are below the so-called maximum-disk prescription. In addition, we quantify the flattening of the spheroidal halo.