Dynamical Histories of the Crater II and Hercules Dwarf Galaxies
  We investigate the possibility that the dwarf galaxies Crater II and Hercules
have previously been tidally stripped by the Milky Way. We present
Magellan/IMACS spectra of candidate member stars in both objects. We identify
37 members of Crater II, 25 of which have velocity measurements in the
literature, and we classify 3 stars within that subset as possible binaries. We
find that including or removing these binary candidates does not change the
derived velocity dispersion of Crater II. Excluding the binary candidates, we
measure a velocity dispersion of $\sigma_{V_{los}} = 2.7^{+0.5}_{-0.4}$ \kms,
corresponding to $M/L = 47^{+17}_{-13}$ M$_{\odot}/$L$_{\odot}$. We measure a
mean metallicity of [Fe/H] = $-1.95^{+0.06}_{-0.05}$, with a dispersion of
$\sigma_{\mbox{[Fe/H]}} = 0.18^{+0.06}_{-0.08}$. Our velocity dispersion and
metallicity measurements agree with previous measurements for Crater II, and
confirm that the galaxy resides in a kinematically cold dark matter halo. We
also search for spectroscopic members stripped from Hercules in the possible
extratidal stellar overdensities surrounding the dwarf. For both galaxies, we
calculate proper motions using \textit{Gaia} DR2 astrometry, and use their full
6D phase space information to evaluate the probability that their orbits
approach sufficiently close to the Milky Way to experience tidal stripping.
Given the available kinematic data, we find a probability of $\sim$40% that
Hercules has suffered tidal stripping. The proper motion of Crater II makes it
almost certain to be stripped.
