We highlight the impact of cluster-mass-dependent evolutionary rates upon the
evolution of the cluster mass function during violent relaxation, that is,
while clusters dynamically respond to the expulsion of their residual
star-forming gas. Mass-dependent evolutionary rates arise when the mean volume
density of cluster-forming regions is mass-dependent. In that case, even if the
initial conditions are such that the cluster mass function at the end of
violent relaxation has the same shape as the embedded-cluster mass function
(i.e. infant weight-loss is mass-independent), the shape of the cluster mass
function does change transiently {\it during} violent relaxation. In contrast,
for cluster-forming regions of constant mean volume density, the cluster mass
function shape is preserved all through violent relaxation since all clusters
then evolve at the same mass-independent rate.
On the scale of individual clusters, we model the evolution of the ratio
between the dynamical mass and luminous mass of a cluster after gas expulsion.
Specifically, we map the radial dependence of the time-scale for a star cluster
to return to equilibrium. We stress that fields-of-view a few pc in size only,
typical of compact clusters with rapid evolutionary rates, are likely to reveal
cluster regions which have returned to equilibrium even if the cluster
experienced a major gas expulsion episode a few Myr earlier. We provide models
with the aperture and time expressed in units of the initial half-mass radius
and initial crossing-time, respectively, so that our results can be applied to
clusters with initial densities, sizes, and apertures different from ours.Comment: 14 pages, 10 figures, accepted for publication in MNRA
