$S^5$: Tidal Disruption in Crater 2 and Formation of Diffuse Dwarf Galaxies in the Local Group

We present results of a spectroscopic campaign around the diffuse dwarf galaxy Crater 2 (Cra2) and its tidal tails as part of the Southern Stellar Stream Spectroscopic Survey ($S^5$). Cra2 is a Milky Way dwarf spheroidal satellite with extremely cold kinematics, but a huge size similar to the Small Magellanic Cloud, which may be difficult to explain within collisionless cold dark matter. We identify 143 Cra2 members, of which 114 belong to the galaxy's main body and 29 are deemed part of its stellar stream. We confirm that Cra2 is dynamically cold (central velocity dispersion $2.51^{+0.33}_{-0.30}\,{\rm km\,s^{-1}}$) and also discover a $\approx$7$σ$ velocity gradient consistent with its tidal debris track. We separately estimate the stream velocity dispersion to be $5.74^{+0.98}_{-0.83}\,{\rm km\,s^{-1}}$. We develop a suite of $N$-body simulations with both cuspy and cored density profiles on a realistic Cra2 orbit to compare with $S^5$ observations. We find that the velocity dispersion ratio between Cra2 stream and galaxy ($2.30^{+0.41}_{-0.35}$) is difficult to reconcile with a cuspy halo with fiducial concentration and an initial mass predicted by standard stellar mass$-$halo mass relationships. Instead, either a cored halo with relatively small core radius or a low-concentration cuspy model can reproduce this ratio. Despite tidal mass loss, Cra2 is metal-poor ($\langle \rm[Fe/H]\rangle=-2.16\pm0.04$) compared to the stellar mass$-$metallicity relation for its luminosity. Other diffuse dwarf galaxies similar to Cra2 in the Local Group (Antlia 2 and Andromeda 19) also challenge galaxy formation models. Finally, we discuss possible formation scenarios for Cra2, including ram-pressure stripping of a gas-rich progenitor combined with tides.