The evolution of the global stellar mass function (MF) of star clusters is studied based on a large set of N-body simulations of clusters with a range of initial masses, initial concentrations, in circular or elliptical orbits in different tidal envi
ronments. Models with and without initial mass segregation are included. The depletion of low mass stars in initially Roche-volume (tidal) filling clusters starts typically on a time scale of the order of the core collapse time. In clusters that are initially underfilling their Roche-volume it takes longer because the clusters have to expand to their tidal radii before dynamical mass loss becomes important. We introduce the concept of the differential mass function (DMF), which describes the changes with respect to the initial mass function (IMF). We show that the evolution of the DMF can be described by a set of very simple analytic expressions that are valid for a wide range of initial cluster parameters and for different IMFs. The agreement between this description and the models is very good, except for initially Roche-volume underfilling clusters that are severely mass segregated.
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 di
fferent 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.
The analysis of the age distributions of star cluster samples of different galaxies has resulted in two very different empirical models for the dissolution of star clusters: the Baltimore model and the Utrecht model. I describe these two models and t
heir differences. The Baltimore model implies that the dissolution of star clusters is mass independent and that about 90% of the clusters are destroyed each age dex, up to an age of about a Gyr, after which point mass-dependent dissolution from two-body relaxation becomes the dominant mechanism. In the Utrecht model, cluster dissolution occurs in three stages: (i) mass-independent infant mortality due to the expulsion of gas up to about 10 Myr; (ii) a phase of slow dynamical evolution with strong evolutionary fading of the clusters lasting up to about a Gyr; and (iii) a phase dominated by mass dependent-dissolution, as predicted by dynamical models. I describe the cluster age distributions for mass-limited and magnitude-limited cluster samples for both models. I refrain from judging the correctness of these models.
Two aspects of our recent N-body studies of star clusters are presented: (1) What impact does mass segregation and selective mass loss have on integrated photometry? (2) How well compare results from N-body simulations using NBODY4 and STARLAB/KIRA?
The development and progress of the studies of winds and mass loss from hot stars, from about 1965 up to now, is discussed in a personal historical perspective. The present state of knowledge about stellar winds, based on papers presented at this wor
kshop, is described. About ten years ago the mechanisms of the winds were reasonably well understood, the mass loss rates were known, and the predictions of stellar evolution theory with mass loss agreed with observations. However, recent studies especially those based on FUSE observations, have resulted in a significant reduction of the mass loss rates, that disagrees with predictions from radiation driven wind models. The situation is discussed and future studies that can clarify the situation are suggested. I also discuss what is known about the dissolution of star clusters in different environments. The dissolution time can be derived from the mass and age distributions of cluster samples. The resulting dissolution times of clusters in the solar neighborhood (SN) and in interacting galaxies are shorter than predicted by two-body relaxation of clusters in a tidal field. Encounters with giant molecular clouds can explain the fate of clusters in the SN and are the most likely cause of the short lifetime of clusters in interacting galaxies.
