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

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

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

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

Star clusterings in the Carina complex: UBVRI photometry of NGC 3324 and Loden 165

We report on UBVRI photometry of two $5^{\prime} \times 5^{\prime}$ fields in the region of the young open cluster NGC 3324. One of our fields covers the core region, while the other is closer to the tidal radius of the cluster. Our study provides the first CCD photometry of NGC 3324. We find that the cluster is very young and probably contains several pre Main Sequence (MS) stars. 25 members are identified on the basis of their position in the (U-B) vs (B-V) diagram. We investigate the relation of the red super-giant HD 92207 with NGC 3324, suggesting that it probably does not belong to the cluster. Our second field is close to Loden 165, a possible cluster of stars that has never been studied so far. We show that this object is a probable open cluster, much older than NGC 3324 and much closer to the Sun.Comment: 8 pages, 6 eps figures, in press in Astronomy and Astrophysic

The influence of residual gas expulsion on the evolution of the Galactic globular cluster system and the origin of the Population II halo

We present new results on the evolution of the mass function of the globular cluster system of the Milky Way, taking the effect of residual gas expulsion into account. We assume that gas embedded star clusters start with a power-law mass function with slope \beta=2. The dissolution of the clusters is then studied under the combined influence of residual gas expulsion driven by energy feedback from massive stars, stellar mass-loss, two-body relaxation and an external tidal field. The influence of residual gas expulsion is studied by applying results from a large grid of N-body simulations computed by Baumgardt & Kroupa (2007). In our model, star clusters with masses less than 10^5 M_sun lose their residual gas on timescales much shorter than their crossing time and residual gas expulsion is the main dissolution mechanism for star clusters, destroying about 95% of all clusters within a few 10s of Myr. We find that in this case the final mass function of globular clusters is established mainly by the gas expulsion and therefore nearly independent of the strength of the external tidal field, and that a power-law mass function for the gas embedded star clusters is turned into a present-day log-normal one. Another consequence of residual gas expulsion and the associated strong infant mortality of star clusters is that the Galactic halo stars come from dissolved star clusters. Since field halo stars would come mainly from low-mass, short-lived clusters, our model provides an explanation for the observed abundance variations of light elements among globular cluster stars and the absence of such variations among the halo field stars.Comment: 12 pages, 9 figures, MNRAS accepte

An analytical description of the disruption of star clusters in tidal fields with an application to Galactic open clusters

We present a simple analytical description of the disruption of star clusters in a tidal field, which agrees excellently with detailed N-body simulations. The analytic expression can be used to predict the mass and age histograms of surviving clusters for any cluster initial mass function and any cluster formation history. The method is applied to open clusters in the solar neighbourhood, based on the new cluster sample of Kharchenko et al. From a comparison between the observed and predicted age distributions in the age range between 10 Myr to 3 Gyr we find the following results: (1) The disruption time of a 10^4 M_sun cluster in the solar neighbourhood is about 1.3+/-0.5 Gyr. This is a factor 5 shorter than derived from N-body simulations of clusters in the tidal field of the galaxy. (2) The present starformation rate in bound clusters within 600 pc from the Sun is 5.9+/-0.8 * 10^2 M_sun / Myr, which corresponds to a surface star formation rate in bound clusters of 5.2+/-0.7 10^(-10) M_sun/yr/pc^2. (3) The age distribution of open clusters shows a bump between 0.26 and 0.6 Gyr when the cluster formation rate was 2.5 times higher than before and after. (4) The present star formation rate in bound clusters is half as small as that derived from the study of embedded clusters. The difference suggests that half of the clusters in the solar neighbourhood become unbound within 10 Myr. (5) The most massive clusters within 600 pc had an initial mass of 3*10^4 M_sun. This is in agreement with the statistically expected value based on a cluster initial mass function with a slope of -2, even if the physical upper mass limit is as high as 10^6 M_sun.Comment: 14 pages, 15 figures, to appear in Astronomy & Astrophysic

The ages of Galactic globular clusters in the context of self-enrichment

A significant fraction of stars in globular clusters (about 70%-85%) exhibit peculiar chemical patterns, with strong abundance variations in light elements along with constant abundances in heavy elements. These abundance anomalies can be created in the H-burning core of a first generation of fast-rotating massive stars, and the corresponding elements are conveyed to the stellar surface thanks to rotational induced mixing. If the rotation of the stars is fast enough, this material is ejected at low velocity through a mechanical wind at the equator. It then pollutes the interstellar medium (ISM) from which a second generation of chemically anomalous stars can be formed. The proportion of anomalous stars to normal stars observed today depends on at least two quantities: (1) the number of polluter stars; (2) the dynamical history of the cluster, which may lose different proportions of first- and second-generation stars during its lifetime. Here we estimate these proportions, based on dynamical models for globular clusters. When internal dynamical evolution and dissolution due to tidal forces are accounted for, starting from an initial fraction of anomalous stars of 10% produces a present-day fraction of about 25%, still too small with respect to the observed 70-85%. In the case of gas expulsion by supernovae, a much higher fraction is expected to be produced. In this paper we also address the question of the evolution of the second-generation stars that are He-rich, and deduce consequences for the age determination of globular cluster

Dynamical evolution of the mass function and radial profile of the Galactic globular cluster system

Evolution of the mass function (MF) and radial distribution (RD) of the Galactic globular cluster (GC) system is calculated using an advanced and a realistic Fokker-Planck (FP) model that considers dynamical friction, disc/bulge shocks and eccentric cluster orbits. We perform hundreds of FP calculations with different initial cluster conditions, and then search a wide-parameter space for the best-fitting initial GC MF and RD that evolves into the observed present-day Galactic GC MF and RD. By allowing both MF and RD of the initial GC system to vary, which is attempted for the first time in the present Letter, we find that our best-fitting models have a higher peak mass for a lognormal initial MF and a higher cut-off mass for a power-law initial MF than previous estimates, but our initial total masses in GCs, M_{T,i} = 1.5-1.8x10^8 Msun, are comparable to previous results. Significant findings include that our best-fitting lognormal MF shifts downward by 0.35 dex during the period of 13 Gyr, and that our power-law initial MF models well-fit the observed MF and RD only when the initial MF is truncated at >~10^5 Msun. We also find that our results are insensitive to the initial distribution of orbit eccentricity and inclination, but are rather sensitive to the initial concentration of the clusters and to how the initial tidal radius is defined. If the clusters are assumed to be formed at the apocentre while filling the tidal radius there, M_{T,i} can be as high as 6.9x10^8 Msun, which amounts to ~75 per cent of the current mass in the stellar halo.Comment: To appear in May 2008 issue of MNRAS, 386, L6

The star cluster formation history of the LMC

The Large Magellanic Cloud is one of the nearest galaxies to us and is one of only few galaxies where the star formation history can be determined from studying resolved stellar populations. We have compiled a new catalogue of ages, luminosities and masses of LMC star clusters and used it to determine the age distribution and dissolution rate of LMC star clusters. We find that the frequency of massive clusters with masses M>5000 Msun is almost constant between 10 and 200 Myr, showing that the influence of residual gas expulsion is limited to the first 10 Myr of cluster evolution or clusters less massive than 5000 Msun. Comparing the cluster frequency in that interval with the absolute star formation rate, we find that about 15% of all stars in the LMC were formed in long-lived star clusters that survive for more than 10 Myr. We also find that the mass function of LMC clusters younger than 1 Gyr can be fitted by a power-law mass function with slope \alpha=-2.3, while older clusters follow a significantly shallower slope and interpret this is a sign of the ongoing dissolution of low-mass clusters. Our data shows that for ages older than 200 Myr, about 90% of all clusters are lost per dex of lifetime. The implied cluster dissolution rate is significantly faster than that based on analytic estimates and N-body simulations. Our cluster age data finally shows evidence for a burst in cluster formation about 1 Gyr ago, but little evidence for bursts at other ages.Comment: 18 pages, 6 figures, MNRAS in pres