The tidal evolution of the Fornax dwarf spheroidal and its globular clusters

The dark matter (DM) content of the Fornax dwarf spheroidal galaxy inferred from its kinematics is substantially lower than expected from LCDM cosmological simulations. We use N-body simulations to examine whether this may be the result of Galactic tides. We find that, despite improved proper motions from the Gaia mission, the pericentric distance of Fornax remains poorly constrained, mainly because its largest velocity component is roughly anti-parallel to the solar motion. Translating Fornax's proper motion into a Galactocentric velocity is thus sensitively dependent on Fornax's assumed distance: the observed distance uncertainty, $\pm 8\%$, implies pericentric distances that vary between $r_{\rm peri}\sim 50$ and $r_{\rm peri}\sim 150$ kpc. Our simulations show that for $r_{\rm peri}$ in the lower range of that estimate, a LCDM subhalo with maximum circular velocity $V_{\rm max}=40$ km s$^{-1}$ (or virial mass $M_{200}\approx 10^{10} M_\odot$, as expected from LCDM) would be tidally stripped to $V_{\rm max} \sim 23$ km s$^{-1}$ over $10$ Gyr. This would reduce the DM mass within the Fornax stellar half-mass radius to about half its initial value, bringing it into agreement with observations. Tidal stripping affects mainly Fornax's DM halo; its stellar component is affected little, losing less than $5\%$ of its initial mass in the process. We also explore the effect of Galactic tides on the dynamical friction decay times of Fornax's population of globular clusters (GC) and find little evidence for substantial changes, compared with models run in isolation. A population of GCs with initial orbital radii between $1$ and $2$ kpc is consistent with the present-day spatial distribution of Fornax GCs, despite assuming a cuspy halo. Neither the DM content nor the spatial distribution of GCs seem inconsistent with a simple model where Fornax inhabits a tidally-stripped cuspy cold DM halo.