On the response of a star cluster to a tidal perturbation
  We study the response of star clusters to individual tidal perturbations
using controlled $N$-body simulations. We consider perturbations by a moving
point mass and by a disc, and vary the duration of the perturbation as well as
the cluster density profile. For fast perturbations (i.e. `shocks'), the
cluster gains energy in agreement with theoretical predictions in the impulsive
limit. For slow disc perturbations, the energy gain is lower, and this has
previously been attributed to adiabatic damping. However, the energy gain due
to slow perturbations by a point-mass is similar to that due to fast shocks,
which is not expected because adiabatic damping should be almost independent of
the nature of the tides. We show that the geometric distortion of the cluster
during slow perturbations is of comparable importance for the energy gain as
adiabatic damping, and that the combined effect can qualitatively explain the
results. The half-mass radius of the bound stars after a shock increases up to
$\sim$7\% for low-concentration clusters, and decreases $\sim$3\% for the most
concentrated ones. The fractional mass loss is a non-linear function of the
energy gain, and depends on the nature of the tides and most strongly on the
cluster density profile, making semi-analytic model predictions for cluster
lifetimes extremely sensitive to the adopted density profile.
