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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.
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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 workshop, 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.
We present radiation-magneto-hydrodynamic simulations of star formation in self-gravitating, turbulent molecular clouds, modeling the formation of individual massive stars, including their UV radiation feedback. The set of simulations have cloud masses between $m_{rm gas}=10^3$~M$_odot$ to $3 times 10^5$~M$_odot$ and gas densities typical of clouds in the local universe ($overline n_{rm gas} sim 1.8times 10^2$~cm$^{-3}$) and 10$times$ and 100$times$ denser, expected to exist in high-redshift galaxies. The main results are: {it i}) The observed Salpeter power-law slope and normalisation of the stellar initial mass function at the high-mass end can be reproduced if we assume that each star-forming gas clump (sink particle) fragments into stars producing on average a maximum stellar mass about $40%$ of the mass of the sink particle, while the remaining $60%$ is distributed into smaller mass stars. Assuming that the sinks fragment according to a power-law mass function flatter than Salpeter, with log-slope $0.8$, satisfy this empirical prescription. {it ii}) The star formation law that best describes our set of simulation is $drho_*/dt propto rho_{gas}^{1.5}$ if $overline n_{gas}<n_{cri}approx 10^3$~cm$^{-3}$, and $drho_*/dt propto rho_{rm gas}^{2.5}$ otherwise. The duration of the star formation episode is roughly $6$ clouds sound crossing times (with $c_s=10$~km/s). {it iii}) The total star formation efficiency in the cloud is $f_*=2% (m_{rm gas}/10^4~M_odot)^{0.4}(1+overline n_{rm gas}/n_{rm cri})^{0.91}$, for gas at solar metallicity, while for metallicity $Z<0.1$~Z$_odot$, based on our limited sample, $f_*$ is reduced by a factor of $sim 5$. {it iv)} The most compact and massive clouds appear to form globular cluster progenitors, in the sense that star clusters remain gravitationally bound after the gas has been expelled.
Context. The asymptotic giant branch (AGB) phase marks the end of the evolution for low- and intermediate-mass stars, which are fundamental contributors to the mass return to the interstellar medium and to the chemical evolution of galaxies. The detailed understanding of mass loss processes is hampered by the poor knowledge of the luminosities and distances of AGB stars. Aims. In a series of papers we are trying to establish criteria permitting a more quantitative determination of luminosities for the various types of AGB stars, using the infrared (IR) fluxes as a basis. An updated compilation of the mass loss rates is also required, as it is crucial in our studies of the evolutionary properties of these stars. In this paper we concentrate our analysis on the study of the mass loss rates for a sample of galactic S stars. Methods. We reanalyze the properties of the stellar winds for a sample of galactic MS, S, SC stars with reliable estimates of the distance on the basis of criteria previously determined. We then compare the resulting mass loss rates with those previously obtained for a sample of C-rich AGB stars. Results. Stellar winds in S stars are on average less efficient than those of C-rich AGB stars of the same luminosity. Near-to-mid infrared colors appear to be crucial in our analysis. They show a good correlation with mass loss rates in particular for the Mira stars. We suggest that the relations between the rates of the stellar winds and both the near-to-mid infrared colors and the periods of variability improve the understanding of the late evolutionary stages of low mass stars and could be the origin of the relation between the rates of the stellar winds and the bolometric magnitudes.
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 environments. 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 discuss the basic physics of hot-star winds and we provide mass-loss rates for (very) massive stars. Whilst the emphasis is on theoretical concepts and line-force modelling, we also discuss the current state of observations and empirical modelling, and address the issue of wind clumping.
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