Can tides explain the low dark matter density in Fornax?

The low dark matter density in the Fornax dwarf galaxy is often interpreted as being due to the presence of a constant density `core. This interpretation is at odds with dark matter-only simulations of cold dark matter haloes, in which central density distributions follow a steep power-law `cusp. The low density in Fornax can also be explained by the effects of Galactic tides. The latter interpretation has been disfavoured because it is apparently inconsistent with the orbital parameters and star formation history of Fornax. We revisit these arguments using the APOSTLE cosmological hydrodynamics simulations. We show that simulated dwarfs with similar properties to Fornax are able to form stars after infall, so that star formation is not necessarily a good tracer of infall time. We also examine the constraints on the pericentre of Fornax and point out that small pericentres (<50 kpc) are not currently ruled out by the data. Even for large orbital pericentres, we find cases where haloes are stripped prior to infall due to interactions with more massive galaxies. This leads to a reduction in the dark matter density at all radii, while in the inner regions the profile remains cuspy. In the radial range resolved by our simulations, the density profile is consistent with the recent kinematic analysis of Fornax by Read et al. If we extrapolate the profile into the unresolved region, we find that the cuspy profiles in our simulations are consistent with the data within 2-3$sigma$, while dark matter profiles with shallow cusps or cores provide a better fit. We predict that if the reduction of the dark matter density in Fornax occurs, at least in part, due to the action of Galactic tides, then tidal tails should be visible with a surface brightness limit of $sim$35-36 mag arcsec$^2$ and survey areas $gtrsim$ 100 deg$^2$.