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Register a new userGeneral circular velocity relation of a test particle in a 3D gravitational potential: application to the rotation curves analysis and total mass determination of UGC 8490 and UGC 9753
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In this paper we derive a novel circular velocity relation for a test particle in a 3D gravitational potential applicable to every system of curvilinear coordinates, suitable to be reduced to orthogonal form. As an illustration of the potentiality of the determined circular velocity expression we perform the rotation curves analysis of UGC 8490 and UGC 9753 and we estimate the total and dark matter mass of these two galaxies under the assumption that their respective dark matter halos have spherical, prolate and oblate spheroidal mass distributions. We employ stellar population synthesis models and the total HI density map to obtain the stellar and HI+He+metals rotation curves of both galaxies. The subtraction of the stellar plus gas rotation curves from the observed rotation curves of UGC 8490 and UGC 9753 generates the dark matter circular velocity curves of both galaxies. We fit the dark matter rotation curves of UGC 8490 and UGC 9753 through the newly established circular velocity formula specialised to the spherical, prolate and oblate spheroidal mass distributions, considering the Navarro, Frenk and White, Burkert, Di Cintio, Einasto and Stadel dark matter halos. Our principal findings are the following: globally, cored dark matter profiles Burkert and Einasto prevail over cuspy Navarro, Frenk and White and Di Cintio. Also, spherical/oblate dark matter models fit better the dark matter rotation curves of both galaxies than prolate dark matter halos.
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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.
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