Does the Fornax dwarf spheroidal have a central cusp or core?

TL;DR

The paper investigates whether the Fornax dwarf spheroidal’s five globular clusters can remain at substantial distances from the centre in the presence of dynamical friction. It models Fornax with both cuspy and cored dark matter halos consistent with kinematic constraints and uses high-resolution N-body simulations (pkdgrav2) alongside analytic dynamical-friction estimates to track cluster orbits. The main finding is that cuspy halos drive all clusters to the centre within a few Gyr, while constant-density cores halt sinking at the core radius, with the innermost cluster establishing a lower bound on the core size (≈0.24 kpc). If the core is primordial in phase-space, the implied warm dark matter particle mass is about $0.5$ keV, aligning with broader solutions to the substructure problem; these results imply that core formation or modification is needed in Fornax and have implications for dwarf galaxies and DM models alike.

Abstract

The dark matter dominated Fornax dwarf spheroidal has five globular clusters orbiting at ~1 kpc from its centre. In a cuspy CDM halo the globulars would sink to the centre from their current positions within a few Gyrs, presenting a puzzle as to why they survive undigested at the present epoch. We show that a solution to this timing problem is to adopt a cored dark matter halo. We use numerical simulations and analytic calculations to show that, under these conditions, the sinking time becomes many Hubble times; the globulars effectively stall at the dark matter core radius. We conclude that the Fornax dwarf spheroidal has a shallow inner density profile with a core radius constrained by the observed positions of its globular clusters. If the phase space density of the core is primordial then it implies a warm dark matter particle and gives an upper limit to its mass of ~0.5 keV, consistent with that required to significantly alleviate the substructure problem.

Figures (5)

• Figure 1: The initial radial density profiles for the three different haloes used in the simulations. The vertical lines indicate the size of the core of the cored haloes.
• Figure 2: Radial distance of the single globular cluster from the centre of its host halo as a function of time. We start the calculations with the globular at different initial radii for clarity. Solid curves are the analytic estimates, dashed curves are from the numerical simulations.
• Figure 3: Radial distance of the five globular clusters from the centre of their host halo as function of time, as they orbit within a cusped density distribution. The arrow indicates the radius at which $M_{\rm GC} = M(r)$.
• Figure 4: Radial distance of the five globular clusters from the centre of the host halo as function of time within the cored potential. The upper arrow indicates the size of the core and the lower arrow indicates the radius at which $M_{\rm GC} = M(r)$.
• Figure 5: Radial density profile of the dark matter haloes. Only the dark matter is shown, the mass of the globular clusters is neglected. The initial conditions are compared with the final state of the system. An isolated halo, evolved for the same time, has exactly the same density profile as the initial conditions.