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A family of analytical potential-density pairs for flat galaxies withspheroidal halos is presented. The potential are obtained by means of the sumof two independent terms: a potential associated with a thin disc and apotential associated with a spheroidal halo, which are expressed asappropriated superpositions of products of Legendre functions, in such a waythat the model implies a linear relationship between the masses of the thindisc and the spheroidal halo. By taking a particular case for the halopotential, we found that the circular velocity obtained can be adjusted veryaccurately to the observed rotation curves of some specific galaxies, so thatthe models are stable against radial and vertical perturbations. Two particularmodels for the galaxies NGC4389 and UGC6969 are obtained by adjusting thecircular velocity with data of the observed rotation curve of some galaxies ofthe Ursa Mayor Cluster, as reported in Verheijen and Sancisi 2001. The valuesof the halo mass and the disc mass for these two galaxies are computedobtaining a very narrow interval of values for these quantities. Furthermore,the values of obtained masses are in perfect agreement with the expected orderof magnitude and with the relative order of magnitude between the halo mass andthe disc mass.

Analytical Potentials for Flat Galaxies with Spheroidal Halos