The Evaporation and Survival of Cluster Galaxies' Coronae Part II: The
  Effectiveness of Anisotropic Thermal Conduction and Survival of Stripped
  Galactic Tails
  We simulate anisotropic thermal conduction between the intracluster medium
(ICM) and the hot coronal interstellar medium (ISM) gas in cluster galaxies. In
the earlier Paper I (Vijayaraghavan & Sarazin 2017a), we simulated the
evaporation of the hot ISM due to isotropic (possibly saturated) conduction
between the ISM and ICM. We found that hot coronae evaporate on $\sim 10^2$ Myr
timescales, significantly shorter than the $\sim 10^3$ Myr gas loss times due
to ram pressure stripping. No tails of stripped gas are formed. This is in
tension with the observed ubiquity and implied longevity of compact X-ray
coronae and stripped ISM tails, and requires the suppression of evaporation,
possibly due to magnetic fields and anisotropic conduction. We perform a series
of wind tunnel simulations similar to Paper I, now including ISM and ICM
magnetic fields. We simulate the effect of anisotropic conduction for a range
of extreme magnetic field configurations: parallel and perpendicular to the ICM
wind, and continuous and completely disjoint between the ISM and ICM. We find
that when conduction is anisotropic, gas loss due to evaporation is severely
reduced; the overall gas loss rates with and without anisotropic conduction do
not differ by more than $10 - 20\%$. Magnetic fields also prevent stripped
tails from evaporating in the ICM by shielding, and providing few pathways for
heat transport between the ICM and ISM. The morphology of stripped tails and
magnetic fields in the tails and wakes of galaxies are sensitive to the initial
magnetic field configuration.
