We present a new version of the fast star cluster evolution code Evolve Me A Cluster of StarS (EMACSS). While previo
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.
Using deep photometric data from WFC@INT and [email protected] we measure the outer number density profiles of 19 stellar clusters located in the inner region of the Milky Way halo (within a Galactocentric distance range of 10-30 kpc) in order to assess the impact of internal and external dynamical processes on the spatial distribution of stars. Adopting power-law fitting templates, with index $-gamma$ in the outer region, we find that the clusters in our sample can be divided in two groups: a group of massive clusters ($ ge 10^5 $ M_sun) that has relatively flat profiles with $2.5 < gamma < 4$ and a group of low-mass clusters ($ le 10^5 $ M_sun), with steep profiles ($gamma > 4$) and clear signatures of interaction with the Galactic tidal field. We refer to these two groups as tidally unaffected and tidally affected, respectively. Our results also show a clear trend between the slope of the outer parts and the half-mass density of these systems, which suggests that the outer density profiles may retain key information on the dominant processes driving the dynamical evolution of Globular Clusters.
The evolution of globular clusters due to 2-body relaxation results in an outward flow of energy and at some stage all clusters need a central energy source to sustain their evolution. Henon provided the insight that we do not need to know the details of the energy production in order to understand the relaxation-driven evolution of the cluster, at least outside the core. He provided two self-similar solutions for the evolution of clusters based on the view that the cluster as a whole determines the amount of energy that is produced in the core: steady expansion for isolated clusters, and homologous contraction for clusters evaporating in a tidal field. We combine these models: the half-mass radius increases during the first half of the evolution, and decreases in the second half; while the escape rate approaches a constant value set by the tidal field. We refer to these phases as `expansion dominated and `evaporation dominated. These simple analytical solutions immediately allow us to construct evolutionary tracks and isochrones in terms of cluster half-mass density, cluster mass and galacto-centric radius. From a comparison to the Milky Way globular clusters we find that roughly 1/3 of them are in the second, evaporation-dominated phase and for these clusters the density inside the half-mass radius varies with the galactocentric distance R as rho_h ~ 1/R^2. The remaining 2/3 are still in the first, expansion-dominated phase and their isochrones follow the environment-independent scaling rho_h ~ M^2; that is, a constant relaxation time-scale. We find substantial agreement between Milky Way globular cluster parameters and the isochrones, which suggests that there is, as Henon suggested, a balance between the flow of energy and the central energy production for almost all globular clusters.
Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber-Jackson relation suggests a strong positive correlation between mass and radius. Objects that are somewhat in between globular clusters and low-mass galaxies, such as ultra-compact dwarf galaxies, have a mass-radius relation consistent with the extension of the relation for bright ellipticals. Here we show that at an age of 10 Gyr a break in the mass-radius relation at ~10^6 Msun is established because objects below this mass, i.e. globular clusters, have undergone expansion driven by stellar evolution and hard binaries. From numerical simulations we find that the combined energy production of these two effects in the core comes into balance with the flux of energy that is conducted across the half-mass radius by relaxation. An important property of this `balanced evolution is that the cluster half-mass radius is independent of its initial value and is a function of the number of bound stars and the age only. It is therefore not possible to infer the initial mass-radius relation of globular clusters and we can only conclude that the present day properties are consistent with the hypothesis that all hot stellar systems formed with the same mass-radius relation and that globular clusters have moved away from this relation because of a Hubble time of stellar and dynamical evolution.
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.
We present an analysis of the spatial distribution of various stellar populations within the Large Magellanic Cloud. We combine mid-infrared selected young stellar objects, optically selected samples with mean ages between ~9 and ~1000 Myr, and existing stellar cluster catalogues to investigate how stellar structures form and evolve within the LMC. For the analysis we use Fractured Minimum Spanning Trees, the statistical Q parameter, and the two-point correlation function. Restricting our analysis to young massive (OB) stars we confirm our results obtained for M33, namely that the luminosity function of the groups is well described by a power-law with index -2, and that there is no characteristic length-scale of star-forming regions. We find that stars in the LMC are born with a large amount of substructure, consistent with a 2D fractal distribution with dimension ~1.8 and evolve towards a uniform distribution on a timescale of ~175 Myr. This is comparable to the crossing time of the galaxy and we suggest that stellar structure, regardless of spatial scale, will be eliminated in a crossing time. This may explain the smooth distribution of stars in massive/dense young clusters in the Galaxy, while other, less massive, clusters still display large amounts of structure at similar ages. By comparing the stellar and star cluster distributions and evolving timescales, we show that infant mortality of clusters (or popping clusters) have a negligible influence on galactic structure. Finally, we quantify the influence of the elongation, differential extinction, and contamination of a population on the measured Q value.
We consider the effect of mass segregation on the observable integrated properties of star clusters. The measurable properties depend on a combination of the dynamical age of the cluster and the physical age of the stars in the cluster. To investigate all possible combinations of these two quantities we propose an analytical model for the mass function of segregated star clusters that agrees with the results of N-body simulations, in which any combination can be specified. For a realistic degree of mass segregation and a fixed density profile we find with increasing age an increase in the measured core radii and a central surface brightness that decreases in all filters more rapidly than what is expected from stellar evolution alone. Within a Gyr the measured core radius increases by a factor of two and the central surface density in all filters of a segregated cluster will be overestimated by a similar factor when not taking into account mass segregation in the conversion from light to mass. We find that the $V-I$ colour of mass segregated clusters decreases with radius by about 0.1-0.2 mag, which could be observable. From recent observations of partially resolved extra-galactic clusters a decreasing half-light radius with increasing wavelength was observed, which was attributed to mass segregation. These observations can not be reproduced by our models. We find that the differences between measured radii in different filters are always smaller than 5%.
Many embedded star clusters do not evolve into long-lived bound clusters. The most popular explanation for this infant mortality of young clusters is the expulsion of natal gas by stellar winds and supernovae, which leaves up to 90% of them unbound. A cluster disruption model has recently been proposed in which this mass- independent disruption of clusters proceeds for another Gyr after gas expulsion. In this scenario, the survival chances of massive clusters are much smaller than in the traditional mass-dependent disruption models. The most common way to study cluster disruption is to use the cluster age distribution, which, however, can be heavily affected by incompleteness. To avoid this, we introduce a new method, based on size-of-sample effects, namely the relation between the most massive cluster, M_max, and the age range sampled. Assuming that clusters are sampled from a power-law initial mass function, with index -2 and that the cluster formation rate is constant, M_max scales with the age range sampled, such that the slope in a log(M_max) vs. log(age) plot is equal to unity. This slope decreases if mass-independent disruption is included. For 90% mass-independent cluster disruption per age dex, the predicted slope is zero. For the solar neighbourhood, SMC, LMC, M33, and M83, based on ages and masses taken from the literature, we find slopes consistent with the expected size-of-sample correlations for the first 100 Myr, hence ruling out the 90% mass-independent cluster disruption scenario. For M51, however, the increase of log(M_max) with log(age) is slightly shallower and for the Antennae galaxies it is flat. This simple method shows that the formation and/or disruption of clusters in the Antennae must have been very different from that of the other galaxies studied here, so it should not be taken as a representative case.
The dissolution time (t_dis) of clusters in a tidal field does not scale with the ``classical expression for the relaxation time. First, the scaling with N, and hence cluster mass, is shallower due to the finite escape time of stars. Secondly, the cluster half-mass radius is of little importance. This is due to a balance between the relative tidal field strength and internal relaxation, which have an opposite effect on t_dis, but of similar magnitude. When external perturbations, such as encounters with giant molecular clouds (GMC) are important, t_dis for an individual cluster depends strongly on radius. The mean dissolution time for a population of clusters, however, scales in the same way with mass as for the tidal field, due to the weak dependence of radius on mass. The environmental parameters that determine t_dis are the tidal field strength and the density of molecular gas. We compare the empirically derived t_dis of clusters in six galaxies to theoretical predictions and argue that encounters with GMCs are the dominant destruction mechanism. Finally, we discuss a number of pitfalls in the derivations of t_dis from observations, such as incompleteness, with the cluster system of the SMC as particular example.
