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

TL;DR

This paper develops a tensorial method to analyze gravitational potentials and applies it to study the dark matter distribution in two galaxies, finding both cored and cuspy profiles can fit the data and identifying oblate spheroidal shapes.

Contribution

It introduces a tensor-based approach for relating density and potential, and applies this to determine dark matter halo shapes and profiles in specific galaxies.

Findings

Both cored and cuspy dark matter profiles fit the rotation curves.

Dark matter halos are best described as oblate spheroids.

The method provides general relations for mass density and potential configurations.

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 specialised 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 manuscript, 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.