Cores and Cusps in the Dwarf Spheroidals

TL;DR

This paper demonstrates that under common assumptions, the inferred dark matter halos of dwarf spheroidal galaxies are generally cusped, with the possibility of cores being non-generic and dependent on specific conditions.

Contribution

It reveals that the typical analysis of dwarf spheroidal galaxies' dark halos inherently favors cusped profiles due to spherical symmetry and isotropy assumptions.

Findings

Dark halos are generally cusped like an isothermal profile.

Cored solutions are non-generic and require specific anisotropy or velocity dispersion conditions.

Spherical symmetry assumptions influence the inferred halo structure.

Abstract

We consider the problem of determining the structure of the dark halo of nearby dwarf spheroidal galaxies (dSphs) from the spherical Jeans equations. Whether the dark halos are cusped or cored at the centre is an important strategic problem in modern astronomy. The observational data comprise the line-of-sight velocity dispersion of a luminous tracer population. We show that when such data are analysed to find the dark matter density with the spherical Poisson and Jeans equations, then the generic solution is a dark halo density that is cusped like an isothermal. Although milder cusps (like the Navarro-Frenk-White 1/r cusp and even cores are possible, they are not generic. Such solutions exist only if the anisotropy parameter beta and the logarithmic slope of the stellar density gamma satisfy the constraint gamma = 2 x beta at the centre or if the radial velocity dispersion falls to zero at the centre. This surprisingly strong statement is really a consequence of the assumption of spherical symmetry, and the consequent coordinate singularity at the origin. So, for example, a dSph with an exponential light profile can exist in Navarro-Frenk- White halo and have a flat velocity dispersion, but anisotropy in general drives the dark halo solution to an isothermal cusp. The identified cusp or core is therefore a consequence of the assumptions (particularly of spherical symmetry and isotropy), and not the data.