Analytical Potentials for Flat Galaxies with Spheroidal Halos
  A family of analytical potential-density pairs for flat galaxies with
spheroidal halos is presented. The potential are obtained by means of the sum
of two independent terms: a potential associated with a thin disc and a
potential associated with a spheroidal halo, which are expressed as
appropriated superpositions of products of Legendre functions, in such a way
that the model implies a linear relationship between the masses of the thin
disc and the spheroidal halo. By taking a particular case for the halo
potential, we found that the circular velocity obtained can be adjusted very
accurately to the observed rotation curves of some specific galaxies, so that
the models are stable against radial and vertical perturbations. Two particular
models for the galaxies NGC4389 and UGC6969 are obtained by adjusting the
circular velocity with data of the observed rotation curve of some galaxies of
the Ursa Mayor Cluster, as reported in Verheijen and Sancisi 2001. The values
of the halo mass and the disc mass for these two galaxies are computed
obtaining a very narrow interval of values for these quantities. Furthermore,
the values of obtained masses are in perfect agreement with the expected order
of magnitude and with the relative order of magnitude between the halo mass and
the disc mass.
