Star Cluster Survival in Star Cluster Complexes under Extreme Residual Gas Expulsion

After the stars of a new, embedded star cluster have formed they blow the remaining gas out of the cluster. Especially winds of massive stars and definitely the on-set of the first supernovae can remove the residual gas from a cluster. This leads to a very violent mass-loss and leaves the cluster out of dynamical equilibrium. Standard models predict that within the cluster volume the star formation efficiency (SFE) has to be about 33 per cent for sudden (within one crossing-time of the cluster) gas expulsion to retain some of the stars in a bound cluster. If the efficiency is lower the stars of the cluster disperse mostly. Recent observations reveal that in strong star bursts star clusters do not form in isolation but in complexes containing dozens and up to several hundred star clusters, i.e. in super-clusters. By carrying out numerical experiments for such objects placed at distances >= 10 kpc from the centre of the galaxy we demonstrate that under these conditions (i.e. the deeper potential of the star cluster complex and the merging process of the star clusters within these super-clusters) the SFEs can be as low as 20 per cent and still leave a gravitationally bound stellar population. Such an object resembles the outer Milky Way globular clusters and the faint fuzzy star clusters recently discovered in NGC 1023.Comment: 21 pages, 8 figures, accepted by Ap

The dynamical state of the Globular Cluster M10 (NGC 6254)

Studying the radial variation of the stellar mass function in globular clusters (GCs) has proved a valuable tool to explore the collisional dynamics leading to mass segregation and core collapse. In order to study the radial dependence of the luminosity and mass function of M 10, we used ACS/HST deep high resolution archival images, reaching out to approximately the cluster's half-mass radius (rhm), combined with deep WFPC2 images that extend our radial coverage to more than 2 rhm. From our photometry, we derived a radial mass segregation profile and a global mass function that we compared with those of simulated clusters containing different energy sources (namely hard binaries and/or an IMBH) able to halt core collapse and to quench mass segregation. A set of direct N-body simulations of GCs, with and without an IMBH of mass 1% of the total cluster mass, comprising different initial mass functions (IMFs) and primordial binary fractions, was used to predict the observed mass segregation profile and mass function. The mass segregation profile of M 10 is not compatible with cluster models without either an IMBH or primordial binaries, as a source of energy appears to be moderately quenching mass segregation in the cluster. Unfortunately, the present observational uncertainty on the binary fraction in M10 does not allow us to confirm the presence of an IMBH in the cluster, since an IMBH, a dynamically non-negligible binary fraction (~ 5%), or both can equally well explain the radial dependence of the cluster mass function.Comment: 15 pages, 8 figures, accepted for publication on Ap

Lifetimes of tidally limited star clusters with different radii

We study the escape rate, dN/dt, from clusters with different radii in a tidal field using analytical predictions and direct N-body simulations. We find that dN/dt depends on the ratio R=r_h/r_j, where r_h is the half-mass radius and r_j the radius of the zero-velocity surface. For R>0.05, the "tidal regime", there is almost no dependence of dN/dt on R. To first order this is because the fraction of escapers per relaxation time, t_rh, scales approximately as R^1.5, which cancels out the r_h^1.5 term in t_rh. For R<0.05, the "isolated regime", dN/dt scales as R^-1.5. Clusters that start with their initial R, Ri, in the tidal regime dissolve completely in this regime and their t_dis is insensitive to the initial r_h. We predicts that clusters that start with Ri<0.05 always expand to the tidal regime before final dissolution. Their t_dis has a shallower dependence on Ri than what would be expected when t_dis is a constant times t_rh. For realistic values of Ri, the lifetime varies by less than a factor of 1.5 due to changes in Ri. This implies that the "survival" diagram for globular clusters should allow for more small clusters to survive. We note that with our result it is impossible to explain the universal peaked mass function of globular cluster systems by dynamical evolution from a power-law initial mass function, since the peak will be at lower masses in the outer parts of galaxies. Our results finally show that in the tidal regime t_dis scales as N^0.65/w, with w the angular frequency of the cluster in the host galaxy. [ABRIDGED

Theoretical and Observational Agreement on Mass Dependence of Cluster Life Times

Observations and N-body simulations both support a simple relation for the disruption time of a cluster as a function of its mass of the form: t_dis = t_4 * (M/10^4 Msun)^gamma. The scaling factor t_4 seems to depend strongly on the environment. Predictions and observations show that gamma ~ 0.64 +/- 0.06. Assuming that t_dis ~ M^0.64 is caused by evaporation and shocking implies a relation between the radius and the mass of a cluster of the form: r_h ~ M^0.07, which has been observed in a few galaxies. The suggested relation for the disruption time implies that the lower mass end of the cluster initial mass function will be disrupted faster than the higher mass end, which is needed to evolve a young power law shaped mass function into the log-normal mass function of old (globular) clusters.Comment: 2 pages, to appear in "The Formation and Evolution of Massive Young Star Clusters", 17-21 November 2003, Cancun (Mexico

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.Comment: 25 pages, 17 figures, 4 tables, 2 appendices; accepted for publication in MNRA

Monte Carlo Simulations of Globular Cluster Evolution. VI. The Influence of an Intermediate Mass Black Hole

We present results of a series of Monte Carlo simulations investigating the imprint of a central intermediate-mass black hole (IMBH) on the structure of a globular cluster. We investigate the three-dimensional and projected density profiles, and stellar disruption rates for idealized as well as realistic cluster models, taking into account a stellar mass spectrum and stellar evolution, and allowing for a larger, more realistic, number of stars than was previously possible with direct N-body methods. We compare our results to other N-body and Fokker-Planck simulations published previously. We find, in general, very good agreement for the overall cluster structure and dynamical evolution between direct N-body simulations and our Monte Carlo simulations. Significant differences exist in the number of stars that are tidally disrupted by the IMBH, which is most likely an effect of the wandering motion of the IMBH, not included in the Monte Carlo scheme. These differences, however, are negligible for the final IMBH masses in realistic cluster models as the disruption rates are generally much lower than for single-mass clusters. As a direct comparison to observations we construct a detailed model for the cluster NGC 5694, which is known to possess a central surface brightness cusp consistent with the presence of an IMBH. We find that not only the inner slope but also the outer part of the surface brightness profile agree well with observations. However, there is only a slight preference for models harboring an IMBH compared to models without.Comment: 37 pages, 10 figures, Accepted for publication in ApJ Supplement. Substantial additions on modeling NGC 5694 since original versio

The Globular Cluster Luminosity Function and Specific Frequency in Dwarf Elliptical Galaxies

The globular cluster luminosity function, specific globular cluster frequency, S_N, specific globular cluster mass, T_MP, and globular cluster mass fraction in dwarf elliptical galaxies are explored using the full 69 galaxy sample of the HST WFPC2 Dwarf Elliptical Galaxy Snapshot Survey. The GCLFs of the dEs are well-represented with a t_5 function with a peak at M_{V,Z}^0(dE,HST) = -7.3 +/- 0.1. This is ~0.3 magnitudes fainter than the GCLF peaks in giant spiral and elliptical galaxies, but the results are consistent within the uncertainties. The bright-end slope of the luminosity distribution has a power-law form with slope alpha = -1.9 +/- 0.1. The trend of increasing S_N or T_MP with decreasing host galaxy luminosity is confirmed. The mean value for T_MP in dE,N galaxies is about a factor of two higher than the mean value for non-nucleated galaxies and the distributions of T_MP in dE,N and dE,noN galaxies are statistically different. These data are combined with results from the literature for a wide range of galaxy types and environments. At low host galaxy masses the distribution of T_MP for dE,noN and dI galaxies are similar. This supports the idea that one pathway for forming dE,noN galaxies is by the stripping of dIs. The formation of nuclei and the larger values of T_MP in dE,N galaxies may be due to higher star formation rates and star cluster formation efficiencies due to interactions in galaxy cluster environments.Comment: 53 pages, 13 figures, 12 tables, accepted by the Astrophysical Journa

N-body simulations of star clusters

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?Comment: 2 pages, 1 figure with 4 panels (in colour, not well visible in black-and-white; figures screwed in PDF version, ok in postscript; to see further details get the paper source). Conference proceedings for IAUS246 'Dynamical Evolution of Dense Stellar Systems', ed. E. Vesperini (Chief Editor), M. Giersz, A. Sills, Capri, Sept. 2007; v2: references correcte