We present current results from the ongoing WIYN Open Cluster Study radial-velocity survey for 1410 stars in the young (150 Myr) open cluster M35 (NGC 2168) and establish a benchmark for initial conditions in young open clusters. We find for periods ≲ 1000 days a minimum binary frequency of 0.36 – 0.51. We also analyze the spatial, period and eccentricity distributions of the binary systems and find that the period and eccentricity distributions are well approximated by scaled field distributions from Duquennoy & Mayor (1991). With our large sample size and long baseline, we have a unique understanding of the binary population in this young cluster, making it ideal for defining initial conditions for dynamical simulations.

We show that an extended population of stars escaping an evolved cluster and moving along its galactic orbit forms at the final phases of its dynamical evolution. Here we present some results of the numerical simulations for nearest open clusters: Hyades, Pleiades, Praesepe, Alpha Persei, Coma, IC 2391, and IC 2602. We calculated the models of the stellar tails for nearest open clusters and estimated some parameters: sizes, densities, locations relative to the solar neighborhood. Stars of the nearest tails can be observed as moving clusters.

The WIYN open cluster study (WOCS) has been working to yield precise optical (UBRVI) photometry for all stars in the field of a selection of “prototypical” open clusters. Additionally, WOCS has been using radial velocities to obtain orbit solutions for cluster member hard-binary stars (with period less than 1000 days). Recently, WOCS has been expanded to include the near-infrared (JHKs; 2MASS plus new deep ground-based) and mid-infrared ([3.6], [4.5], [5.8], [8.0] micron) photometry from Spitzer/IRAC observations. This multi-wavelength data (0.3–8.0 microns) allows us to identify binaries photometrically, with mass ratios from 1.0–0.3, across a wide range of primary masses. The spectral energy distribution (SED) fitter by Robitaille et al. (2007) is used to fit the fluxes of 10–12 bands to Kurucz stellar models. This technique allows us to explore the soft binary population for the first time. Using this photometric technique, we find that NGC 188 has a binary fraction of 36-49% and provide a star-by-star comparison to the WOCS radial velocity-based hard binary study.

We present a detailed dynamical study of the old (7 Gyr) open cluster NGC 188. Our combined radial-velocity data set spans a baseline of 35 years, a magnitude range of 12 ≤ V ≤ 16.5, and a 1° diameter region on the sky. Our magnitude limits include solar-mass main-sequence stars, subgiants, giants, and blue stragglers, and our spatial coverage extends radially to 11.5 core radii. We have measured radial velocities for 1014 stars in the direction of NGC 188 with a precision of 0.4 km s−1, and have calculated radial-velocity membership probabilities for stars with ≥ 3 measurements. We find 420 stars to be high-probability cluster members, including 137 spectroscopic binaries. These detectable binaries all have orbital periods of less than 104 days, and thus are hard. We have derived orbit solutions for 67 member binary stars, and use our 35 main-sequence binaries with orbit solutions to compare the eccentricity and period distributions with simulated observations of the Hurley et al. (2005) model of M67 (4.5 Gyr). We also compare the spatial distributions of cluster member populations.

Using ISAAC/VLT, we have obtained individual spectra of all NIR-bright stars in the central 2′ × 2′ of the cluster Westerlund 1 (Wd 1) with a resolution of R ≈ 9000 at a central wavelength of 2.30 μm. This allowed us to determine radial velocities of ten post-main-sequence stars, and from these values a velocity dispersion. Assuming virial equilibrium, the dispersion of σ = 8.4 km/s leads to a total dynamical cluster mass of 1.25 × 105M⊙, comparable to the photometric mass of the cluster. There is no extra-virial motion which would have to be interpreted as a signature of cluster expansion or dissolution.

We present a volume-limited sample (d < 850 pc) of open clusters in the Galaxy identified from our studies on galactic open clusters based on data from the all-sky catalogue ASCC-2.5 with absolute proper motions and B, V magnitudes of 2.5 million stars. The astrophysical properties of this sample are discussed.

For 236 of 650 Galactic open clusters identified in the ASCC-2.5 catalogue, we determine tidal radii from a three-parameter fit of King's profiles to the observed integrated density distribution of cluster members. The results are used to calibrate the observed sizes of the remaining clusters to a uniform scale of tidal radii of open clusters in the Solar neighbourhood. The tidal masses are computed from tidal radii. Within a distance of 850 pc where our sample is complete, the observed distributions of cluster masses can be explained by a general mass loss in open clusters with increasing age.

Astronomers have constructed models of globular clusters for over 100 years. These models mainly fall into two categories: (i) static models, such as King's model and its variants, and (ii) evolutionary models. Most attention has been given to static models, which are used to estimate mass-to-light ratios and mass segregation, and to combine data from proper motions and radial velocities. Evolutionary models have been developed for a few objects using the gaseous model, the Fokker-Planck model, Monte Carlo models and N-body models. These models have had a significant role in the search for massive black holes in globular clusters, for example.

In this presentation the problems associated with these various techniques will be summarised, and then we shall describe new work with Giersz's Monte Carlo code, which has been enhanced recently to include the stellar evolution of single and binary stars. We describe in particular recent attempts to model the nearby globular cluster M4, including predictions on the spatial distribution of binary stars and their semi-major axis distribution, to illustrate the effects of about 12 Gyr of dynamical evolution. We also discuss work on an approximate way of predicting the “initial” conditions for such modelling.

Although the overall dynamics of globular clusters involves many complexities, much of their dynamics can be understood on the basis of some simple and straightforward physical arguments. Those arguments are presented here, in an effort to lead the reader through the basic stages of cluster dynamics in a quick and easy way.

An increasing number of photometric observations of multiple stellar populations in Galactic globular clusters is seriously challenging the paradigm of GCs hosting single, simple stellar populations. These multiple populations manifest themselves in a split of different evolutionary sequences as observed in the cluster color-magnitude diagrams. In this paper we will summarize the observational scenario.

We systematically study the effects of collisions on the overall dynamical evolution of dense star clusters using Monte Carlo simulations over many relaxation times. We derive many observable properties of these clusters, including their core radii and the radial distribution of collision products. We also study different aspects of collisions in a cluster taking into account the shorter lifetimes of more massive stars, which has not been studied in detail before. Depending on the lifetimes of the significantly more massive collision products, observable properties of the cluster can be modified qualitatively; for example, even without binaries, core collapse can sometimes be avoided simply because of stellar collisions.

The majority of the inhomogeneities in the chemical composition of Globular Cluster (GC) stars appear due to primordial enrichment by hot-CNO cycled material processed in stars belonging to a first stellar generation. Either massive AGB envelopes subject to hot bottom burning, or the envelopes of massive fastly rotating stars could be the progenitors. In both cases, the stars showing chemical anomalies must have also enhanced helium abundance, and we have proposed that this higher helium could be at the basis of the many different morphologies of GC horizontal branches (HB) for similar ages and metallicities. The helium variations have been beautifully confirmed by the splitting of the main sequence in the clusters ω Cen and NGC 2808, but this effect can show up only for somewhat extreme helium abundances. Therefore it is important to go on using the HB morphology to infer the number ratio of the first to the second generation in as many clusters as possible. We exemplify how it is possible to infer the presence of a He – rich stellar component in different clusters thanks to different HB features (gaps, RR Lyr periods and period distribution, ratio of blue to red stars, blue tails). In many clusters at least 50% of the stars belong to the second stellar generation, and in some cases we suspect that the stars might all belong to the second generation. We shortly examine the problem of the initial mass function required to achieve the observed number ratios and conclude that: 1) the initial cluster must have been much more massive than today's cluster, and 2) formation of the second stellar generation mainly in the central regions of the cluster may help in obtaining the desired values.

We report on the discovery of a surprising observed correlation between the slope of the low-mass stellar global mass function (GMF) of globular clusters (GCs) and their central concentration parameter c = log(rt/rc), i.e. the logarithmic ratio of tidal and core radii. This result is based on the analysis of a sample of twenty Galactic GCs, with solid GMF measurements from deep HST or VLT data, representative of the entire population of Milky Way GCs. While all high-concentration clusters in the sample have a steep GMF, low-concentration clusters tend to have a flatter GMF implying that they have lost many stars via evaporation or tidal stripping. No GCs are found with a flat GMF and high central concentration. This finding appears counter-intuitive, since the same two-body relaxation mechanism that causes stars to evaporate and the cluster to eventually dissolve should also lead to higher central density and possibly core-collapse. Therefore, severely depleted GCs should be in a post core-collapse state, contrary to what is suggested by their low concentration. Several hypotheses can be put forth to explain the observed trend, none of which however seems completely satisfactory. It is likely that GCs with a flat GMF have a much denser and smaller core than suggested by their surface brightness profile and may well be undergoing collapse at present. It is, therefore, likely that the number of post core-collapse clusters in the Galaxy is much larger than thought so far.

Evolution of self-gravitating rotating dense stellar systems (e.g. globular clusters) with embedded black holes is investigated. The interplay between velocity diffusion due to relaxation and black hole star accretion is followed together with cluster differential rotation using 2D+1 Fokker Planck numerical methods. The models can reproduce the Bahcall-Wolf f ∝ E1/4 (∝ r−7/4) cusp inside the zone of influence of the black hole. Angular momentum transport and star accretion processes support the development of central rotation in relaxation time scales, before re-expansion and cluster dissolution due to mass loss in the tidal field of a parent galaxy. Gravogyro and gravothermal instabilities conduce the system to a faster evolution leading to shorter collapse times with respect to models without black hole.

The dissolution time (tdis) 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 tdis, but of similar magnitude. When external perturbations, such as encounters with giant molecular clouds (GMC) are important, tdis 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 tdis are the tidal field strength and the density of molecular gas. We compare the empirically derived tdis 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 tdis from observations, such as incompleteness, with the cluster system of the SMC as particular example.

Massive star clusters in the Magellanic Clouds are observed to follow a striking trend in size with age – older clusters exhibit a much greater spread in core radius than do younger clusters, which are generally compact. We present results from realistic N-body modelling of massive star clusters, aimed at investigating a dynamical origin for the radius-age trend. We find that stellar-mass black holes, formed as remnants of the most massive stars in a cluster, can constitute a dynamically important population. If retained, these objects rapidly form a dense core where interactions are common, resulting in the scattering of black holes into the cluster halo, and the ejection of black holes from the cluster. These processes heat the stellar component, resulting in prolonged core expansion of a magnitude matching the observations. Core expansion at early times does not result from the action of black holes, but can be reproduced by the effects of rapid mass-loss due to stellar evolution in a primordially mass segregated cluster.

We present the results of a survey of N-body simulations aimed at exploring the implications of primordial mass segregation on the dynamical evolution of star clusters. We show that, in a mass-segregated cluster, the effect of early mass loss due to stellar evolution is, in general, more destructive than for an unsegregated cluster with the same density profile and leads to shorter lifetimes, a faster initial evolution toward less concentrated structure and flattening of the stellar initial mass function.

Two aspects of our recent N-body studies of star clusters are presented:

1. 1) What impact does mass segregation and selective mass loss have on integrated photometry?

2. 2) How well do results compare from N-body simulations using NBODY4 and STARLAB/KIRA?

The study of sub-structures in the stellar halo of the Milky Way has made a lot of progress in recent years, especially since surveys like the Sloan Digital Sky Survey became available. In this paper we focus on the newly discovered tidal tails of the Galactic globular cluster NGC 5466. By means of numerical simulations we reproduce the tidal tails, which are the longest tails associated with a globular cluster known (>45°) and hereby finding a possible progenitor of NGC 5466 and analyse its stability. We show that perigalactic passages are the dominant process in the slow dissolution of NGC 5466. Furthermore we use the position of the tails to verify the accuracy of the observationally determined proper motion. The proper motion has to be refined only slightly (within their stated error-margin) to match the location of the tidal tails.

We investigate evolution of star clusters in steady external tidal field by means of N-body simulations. We followed several sets of cluster models whose strength and Coriolis's contribution of the external tidal field are different. We found that the mass loss timescale due to the escape of stars, t_mloss, and its dependence on the two-body relaxation timescale, trh,i, are determined by the strength of the tidal field. The logarithmic slope [≡ dln(tmloss)/dln(trh,i)] approaches unity for the cluster models in weaker tidal fields. We also found that stronger Coriolis force against others, produced by parent galaxy whose density profile is shallower, makes the mass loss timescale longer. This is due to the fact that a fraction of stars whose orbit are nearly regular increases as the Coriolis force becomes stronger.