Tidal disruption of dwarf spheroidal galaxies: the strange case of
  Crater II
  Dwarf spheroidal galaxies of the Local Group obey a relationship between the
line-of-sight velocity dispersion and half-light radius, although there are a
number of dwarfs that lie beneath this relation with suppressed velocity
dispersion. The most discrepant of these (in the Milky Way) is the `feeble
giant' Crater II. Using analytic arguments supported by controlled numerical
simulations of tidally-stripped flattened two-component dwarf galaxies, we
investigate interpretations of Crater II within standard galaxy formation
theory. Heavy tidal disruption is necessary to explain the velocity-dispersion
suppression which is plausible if the proper motion of Crater II is
$(\mu_{\alpha*},\mu_\delta)=(-0.21\pm0.09,-0.24\pm0.09)\mathrm{mas\,yr}^{-1}$.
Furthermore, we demonstrate that the velocity dispersion of tidally-disrupted
systems is solely a function of the total mass loss even for weakly-embedded
and flattened systems. The half-light radius evolution depends more sensitively
on orbital phase and the properties of the dark matter profile. The half-light
radius of weakly-embedded cusped systems rapidly decreases producing some
tension with the Crater II observations. This tension is alleviated by cored
dark matter profiles, in which the half-light radius can grow after tidal
disruption. The evolution of flattened galaxies is characterised by two
competing effects: tidal shocking makes the central regions rounder whilst
tidal distortion produces a prolate tidally-locked outer envelope. After
$\sim70$ per cent of the central mass is lost, tidal distortion becomes the
dominant effect and the shape of the central regions of the galaxy tends to a
universal prolate shape irrespective of the initial shape.
