Cold Fronts and Gas Sloshing in Galaxy Clusters with Anisotropic Thermal
  Conduction
  (Abridged) Cold fronts in cluster cool cores should be erased on short
timescales by thermal conduction, unless protected by magnetic fields that are
"draped" parallel to the front surfaces, suppressing conduction perpendicular
to the fronts. We present MHD simulations of cold front formation in the core
of a galaxy cluster with anisotropic thermal conduction, exploring a parameter
space of conduction strengths parallel and perpendicular to the field lines.
Including conduction has a strong effect on the temperature of the core and the
cold fronts. Though magnetic field lines are draping parallel to the front
surfaces, the temperature jumps across the fronts are nevertheless reduced. The
field geometry is such that the cold gas below the front surfaces can be
connected to hotter regions outside via field lines along directions
perpendicular to the plane of the sloshing motions and along sections of the
front which are not perfectly draped. This results in the heating of this gas
below the front on a timescale of a Gyr, but the sharpness of the density and
temperature jumps may still be preserved. By modifying the density distribution
below the front, conduction may indirectly aid in suppressing Kelvin-Helmholtz
instabilities. If conduction along the field lines is unsuppressed, we find
that the characteristic sharp jumps in X-ray emission seen in observations of
clusters do not form. This suggests that the presence of sharp cold fronts in
hot clusters could be used to place upper limits on conduction in the {\it
bulk} of the ICM. Finally, the combination of sloshing and anisotropic thermal
conduction can result in a larger flux of heat to the core than either process
in isolation. While still not sufficient to prevent a cooling catastrophe in
the very central ($r \sim$ 5 kpc) regions of the cool core, it reduces
significantly the mass of cool gas that accumulates outside those radii.
