Tidal stirring of satellites with shallow density profiles prevents them from being too big to fail

The "too big to fail" problem is revisited by studying the tidal evolution of populations of dwarf satellites with different density profiles. The high resolution cosmological $\rm \Lambda CDM$ "ErisMod" set of simulations is used. These simulations can model both the stellar and dark matter components of the satellites, and their evolution under the action of the tides of a MW-sized host halo at a force resolution better than 10 pc. The stronger tidal mass loss and re-shaping of the mass distribution induced in satellites with $\gamma=0.6$ dark matter density distributions, as those resulting from the effect of feedback in hydrodynamical simulations of dwarf galaxy formation, is sufficient to bring the circular velocity profiles in agreement with the kinematics of MW's dSphs. In contrast, in simulations in which the satellites retain cusps at $z=0$ there are several "massive failures" with circular velocities in excess of the observational constraints. Various sources of deviations in the conventionally adopted relation between the circular velocity at the half light radius and the one dimensional line-of-sight velocity dispersions are found. Such deviations are caused by the response of circular velocity profiles to tidal effects, which also varies depending on the initially assumed inner density profile, and by the complexity of the stellar kinematics, which include residual rotation and anisotropy. In addition tidal effects naturally induce large deviations in the stellar mass-halo mass relation for halo masses below $\rm 10^9 ~ M_{\odot}$, preventing any reliable application of the abundance matching technique to dwarf galaxy satellites.