The effect of tides on the Sculptor dwarf spheroidal galaxy

Dwarf spheroidal galaxies (dSphs) appear to be some of the most dark matter dominated objects in the Universe. Their dynamical masses are commonly derived using the kinematics of stars under the assumption of equilibrium. However, these objects are satellites of massive galaxies (e.g.\ the Milky Way) and thus can be influenced by their tidal fields. We investigate the implication of the assumption of equilibrium focusing on the Sculptor dSph by means of ad-hoc $N$-body simulations tuned to reproduce the observed properties of Sculptor following the evolution along some observationally motivated orbits in the Milky Way gravitational field. For this purpose, we used state-of-the-art spectroscopic and photometric samples of Sculptor's stars. We found that the stellar component of the simulated object is not directly influenced by the tidal field, while $\approx 30\%-60\%$ the mass of the more diffuse DM halo is stripped. We conclude that, considering the most recent estimate of the Sculptor proper motion, the system is not affected by the tides and the stellar kinematics represents a robust tracer of the internal dynamics. In the simulations that match the observed properties of Sculptor, the present-day dark-to-luminous mass ratio is $\approx 6$ within the stellar half-light radius ($\approx0.3$ kpc) and $>50$ within the maximum radius of the analysed dataset ($\approx1.5^\circ\approx2$ kpc).