Characterization of the velocity anisotropy of accreted globular
  clusters
  Galactic globular clusters (GCs) are believed to have formed in-situ in the
Galaxy as well as in dwarf galaxies later accreted onto the Milky Way. However,
to date, there is no unambiguous signature to distinguish accreted GCs. Using
specifically designed $N$-body simulations of GCs evolving in a variety of
time-dependent tidal fields (describing the potential of a dwarf galaxy-Milky
Way merger), we analyze the effects imprinted to the internal kinematics of an
accreted GC. In particular, we look at the evolution of the velocity
anisotropy. Our simulations show that at early phases, the velocity anisotropy
is determined by the tidal field of the dwarf galaxy and subsequently the
clusters will adapt to the new tidal environment, losing any signature of their
original environment in a few relaxation times. At 10 Gyr, GCs exhibit a
variety of velocity anisotropy profiles, namely, isotropic velocity
distribution in the inner regions and either isotropy or radial/tangential
anisotropy in the intermediate and outer regions. Independently of an accreted
origin, the velocity anisotropy primarily depends on the strength of the tidal
field cumulatively experienced by a cluster. Tangentially anisotropic clusters
correspond to systems that have experienced stronger tidal fields and are
characterized by higher tidal filling factor, $r_{50}/r_j\gtrsim0.17$, higher
mass loss $\gtrsim60\%$ and relaxation times $t_{rel}\lesssim10^9$ Gyr.
Interestingly, we demonstrate that the presence of tidal tails can
significantly contaminate the measurements of velocity anisotropy when a
cluster is observed in projection. Our characterization of the velocity
anisotropy profiles in different tidal environments provides a theoretical
benchmark for the interpretation of the unprecedented amount of
three-dimensional kinematic data progressively available for Galactic GCs.
