Tensorial solution of the Poisson equation and the dark matter amount and distribution of UGC 8490 and UGC 9753

Abstract

ABSTRACT In the first part of this article we expand three fundamental aspects of the methodology connected to the determination of a relation among the spatial density and the gravitational potential that can be specialized to distinct mass density agglomerations. As a consequence, we obtain general relations for the diagonal entries of a square symmetric matrix without zeros, we provide an expression of the gravitational potential, suitable, to represent several different mass density configurations, and we determine relations for the semi-axes of a triaxial spheroidal mass distribution, as a function of the spheroid mass density, volume density, and radius. In the second part of this paper, we employ the tools developed in the first part, to analyse the mass density content and the inner and global structure of the dark matter haloes of UGC 8490 and UGC 9753, through the fits to the dark matter rotation curves of the two galaxies, assuming a triaxial spheroidal dark matter mass configuration. We employ the Navarro Frenk and White, Burkert, DiCintio, Einasto and Stadel dark matter models, and we obtain that both a cored Burkert and cuspy DiCintio and Navarro Frenk and White inward dark matter distributions could represent equally well the observed data, furthermore we determine an oblate spheroidal dark matter mass density configuration for UGC 8490 and UGC 9753. The latter outcome is confirmed by the estimation of the gravitational torques exerted by the dark matter halo of each analysed galaxy, on the corresponding baryonic components.