  (Abridged) We use the simulations presented in Poole et al. 2006 to examine
the effects of mergers on compact cool cores in X-ray clusters. We propose a
scheme for classifying the morphology of clusters based on their surface
brightness and entropy profiles. Three dominant morphologies emerge: two
hosting compact cores and central temperatures which are cool (CCC systems) or
warm (CWC systems) and one hosting extended cores which are warm (EWC systems).
We find that CCC states are disrupted only after direct collisions between
cluster cores in head-on collisions or during second pericentric passage in
off-axis mergers. By the time they relax, our remnant cores have generally been
heated to warm core (CWC or EWC) states but subsequently recover CCC states.
The only case resulting in a long-lived EWC state is a slightly off-axis 3:1
merger for which the majority of shock heating occurs during the accretion of a
low-entropy stream formed from the disruption of the secondary's core.
Compression prevents core temperatures from falling until after relaxation thus
explaining the observed population of relaxed CWC systems with no need to
invoke AGN feedback. The morphological segregation observed in the L_x-T_x and
beta-r_c scaling relations is reflected in our simulations as well. However,
none of the cases we have studied produce sufficiently high remnant central
entropies to account for the most under-luminous EWC systems observed. Lastly,
systems which initially host central metallicity gradients do not yield merger
remnants with flat metallicity profiles. Taken together, these results suggest
that once formed, compact core systems are remarkably stable against disruption
from mergers. It remains to be demonstrated exactly how the sizable observed
population of extended core systems was formed.
