Mass loss rates and the mass evolution of star clusters
  We describe the interplay between stellar evolution and dynamical mass loss
of evolving star clusters, based on the principles of stellar evolution and
cluster dynamics and on a grid of N-body simulations of cluster models. The
cluster models have different initial masses, different orbits, including
elliptical ones, and different initial density profiles. We use two sets of
cluster models: initially Roche-lobe filling and Roche-lobe underfilling. We
identify four distinct mass loss effects: (1) mass loss by stellar evolution,
(2) loss of stars induced by stellar evolution and (3) relaxation-driven mass
loss before and (4) after core collapse. Both the evolution-induced loss of
stars and the relaxation-driven mass loss need time to build up. This is
described by a delay-function of a few crossing times for Roche-lobe filling
clusters and a few half mass relaxation times for Roche-lobe underfilling
clusters. The relaxation-driven mass loss can be described by a simple power
law dependence of the mass dM/dt =-M^{1-gamma}/t0, (with M in Msun) where t0
depends on the orbit and environment of the cluster. Gamma is 0.65 for clusters
with a King-parameter W0=5 and 0.80 for more concentrated clusters with W0=7.
For initially Roche-lobe underfilling clusters the dissolution is described by
the same gamma=0.80. The values of the constant t0 are described by simple
formulae that depend on the orbit of the cluster. The mass loss rate increases
by about a factor two at core collapse and the mass dependence of the
relaxation-driven mass loss changes to gamma=0.70 after core collapse. We also
present a simple recipe for predicting the mass evolution of individual star
clusters with various metallicities and in different environments, with an
accuracy of a few percent in most cases. This can be used to predict the mass
evolution of cluster systems.
