  We perform N-body simulations of a cluster that forms in a dwarf galaxy and
is then accreted by the Milky Way to investigate how a cluster's structure is
affected by a galaxy merger. We find that the cluster's half mass radius will
respond quickly to this change in potential. When the cluster is placed on an
orbit in the Milky Way with a stronger tidal field the cluster experiences a
sharp decrease in size in response to increased tidal forces. Conversely, when
placed on an orbit with a weaker tidal field the cluster expands since tidal
forces decrease and stars moving outwards due to internal effects remain bound
at further distances than before. In all cases, we find that the cluster's half
mass radius will eventually be indistinguishable from a cluster that has always
lived in the Milky Way on that orbit. These adjustments occur within 1-2 half
mass relaxation times of the cluster in the dwarf galaxy. We also find this
effect to be qualitatively independent of the time that the cluster is taken
from the dwarf galaxy. In contrast to the half mass radius, we show the core
radius of the cluster is not affected by the potential the cluster lives in.
Our work suggests that structural properties of accreted clusters are not
distinct from clusters born in the Milky Way. Other cluster properties, such as
metallicity and horizontal branch morphology, may be the only way to identify
accreted star clusters in the Milky Way.
