Dynamics of prolate spheroidal mass distributions with varying eccentricity

TL;DR

This paper models the gravitational potential of prolate spheroidal dark matter halos with varying eccentricity, analyzing their effects on galactic dynamics and challenging previous ideas about warp formation.

Contribution

It introduces a method to calculate potentials for radially varying prolate spheroidal mass distributions, including the effects on galactic warps and other astrophysical systems.

Findings

Potential inside a shell remains nearly constant with small eccentricity variation

Prolate halos with variable eccentricity are less conducive to long-lived galactic warps

Results are applicable to other prolate astrophysical structures

Abstract

In this paper we calculate the potential for a prolate spheroidal distribution as in a dark matter halo with a radially varying eccentricity. This is obtained by summing up the shell-by-shell contributions of isodensity surfaces, which are taken to be concentric and with a common polar axis and with an axis ratio that varies with radius. Interestingly, the constancy of potential inside a shell is shown to be a good approximation even when the isodensity contours are dissimilar spheroids, as long as the radial variation in eccentricity is small as seen in realistic systems. We consider three cases where the isodensity contours are more prolate at large radii, or are less prolate, or have a constant eccentricity. Other relevant physical quantities like the rotation velocity, the net orbital and vertical frequency due to the halo and an exponential disc of finite thickness embedded in it are obtained. We apply this to the kinematical origin of Galactic warp, and show that a prolate shaped halo is not conducive to making long-lived warps - contrary to what has been proposed in the literature. The results for a prolate mass distribution with a variable axis ratio obtained are general, and can be applied to other astrophysical systems such as prolate bars, for a more realistic treatment.