Dynamical evolution of two-component star clusters

The dynamical evolution of two-component star clusters, each of which is enclosed within a perfectly reflecting sphere, is investigated by numerically solving moment equations derived from the Boltzmann equation. One of the two adopted model clusters evolves, starting from a state of no mass segregation, toward an equilibrium state at a quite slow rate. The other one evolves away from an equilibrium state and its central density increases without limit. The different evolutionary behaviors of the two model clusters are explained by the fact that there exists no equilibrium state for such clusters if the total energy is less than a certain critical value. The critical value increases with increasing total mass fraction of the heavier stars. This is qualitatively the same as Spitzer's theorem (1969) expressed in another way.     

The evolution of star clusters: the resolved-star approach

We present the first results of a new technique to detect, locate, and characterize young dissolving star clusters. Using Hubble Space Telescope/Advanced Camera for Surveys archival images of the nearby galaxy IC2574, we performed stellar PSF photometry and selected the most massive stars as our first test sample. We used a group-finding algorithm on the selected massive stars to find cluster candidates. We then plot the color-magnitude diagrams for each group, and use stellar evolutionary models to estimate their age. So far, we found 79 groups with ages of up to about 100 Myr, displaying various sizes and densities.     

Origin and dynamical evolution of young mass-segregated clusters

A significant degree of mass segregation inconsistent with the effects of standard two-body relaxation has been observed in a number of young star clusters. In this paper we present the results of a survey of N-body simulations aimed at exploring the origin and the dynamical evolution of young mass-segregated star clusters. Our simulations show that large segregated clusters can form from the merger of small clumps that are either initially segregated or in which segregation is produced before the merger is complete; the large cluster produced at the end of the merger process inherits the progenitor clumps’ segregation. We show that, in a young mass-segregated cluster, the effect of early mass loss associated with 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 towards less-concentrated structure and a faster flattening of the stellar initial mass function.     

Dynamical states and dynamical evolution of the selected triple star systems

The general problem of investigating multiple stellar systems is formulated. It is shown that the complete solution of this problem requires 1) a complex of astrometric and astrophysical observations of multiple stars, and the 2) maximum attainable precision of such observations. The conditions under which this precision can be achieved are discussed.The most important characteristics of the dynamical states of multiple systems are the total energy E and the relative energies E_ij of the bodies in these systems. For eight triple systems (ADS 1630, 2926, 6175, 6650, 6811, 7114, 9626, 9909), statistical tests — a method of calculating the uncertainties _E and _Eij from the errors of the observational data — are used to find the probabilities for dynamical states and the values E_tr±E_tr and E_bin±E_bin.Only three triple stars appear certain to be physical systems with a dynamical connection between the components — ADS 6175 and 9909 with the probabilities P>0.80 are dynamical non-hierarchical unstable triple systems with a complicated motions of the components; the final state of these systems is an escape. In the triple system ADS 1630 a qualitative course of the component motions has not been determined because of the larger errors in the observed data. The dynamical evolution of the triple system ADS 9909 is under study.     

Effects of stellar wind,dynamical friction,and star mergers on the dynamical evolution of multiple stars

The dynamical evolution of small stellar groups composed of N=6 components was numerically simulated within the framework of a gravitational N-body problem. The effects of stellar mass loss in the form of stellar wind, dynamical friction against the interstellar medium, and star mergers on the dynamical evolution of the groups were investigated. A comparison with a purely gravitational N-body problem was made. The state distributions at the time of 300 initial system crossing times were analyzed. The parameters of the forming binary and stable triple systems as well as the escaping single and binary stars were studied. The star-merger and dynamical-friction effects are more pronounced in close systems, while the stellar wind effects are more pronounced in wide systems. Star-mergers and stellar wind slow down the dynamical evolution. These factors cause the mean and median semimajor axes of the final binaries as well as the semimajor axes of the internal and external binaries in stable triple systems to increase. Star mergers and dynamical friction in close systems decrease the fraction of binary systems with highly eccentric orbits and the mean component mass ratios for the final binaries and the internal and external binaries in stable triple systems. Star mergers and dynamical friction in close systems increase the fraction of stable triple systems with prograde motions. Dynamical friction in close systems can both increase and decrease the mean velocities of the escaping single stars, depending on the density of the interstellar medium and the mean velocity of the stars in the system.     

On the dynamical evolution of the brown dwarf populationin open clusters

It is by now well established that open clusters contain a considerable fraction of brown dwarfs (BDs). This paper investigates the dynamical evolution of this substellar population by using simulations with Aarseth's (1994) NBODY5 code. A noticeable preferential escape of BDs is found, which may influence the determination of the IMF of substellar objects in dynamically evolved open clusters. This small dynamical-in-origin depletion may not explain, however, the scarcity of BDs observed in some evolved clusters, as the Hyades. On the other hand, BD cooling processes are able to reduce our ability to detect BDs in old clusters in a very significant way. Our results confirm that the probability of observing BDs in open clusters is almost the same over the whole cluster area because they are distributed quite uniformly even at late stages of the evolution of the cluster. This is expected to be a general feature as observed for low-mass stars in well studied open clusters (Pleiades, Praesepe). Our present calculations show that clusters as old as the Pleiades may have lost about 10% of their initial BD population but the number ratio of BDs to normal (not substellar) stars must remain almost unchanged. However, the long-term behavior of the relative percentage of BDs depends strongly on the initial mass function (IMF) assumed in the calculations. Clusters with a Salpeterian IMF evolve to reach relative percentages of BDs as low as 40% for a starting value around 70%. Our results suggest that BDs in clusters escape preferentially by evaporation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of external tidal field on the evolution of the outer regions of multi-mass star clusters

We present N -body simulations (including an initial mass function) of globular clusters in the Galaxy in order to study effects of the tidal field systematically on the properties of the outer parts of globular clusters. Using nbody6 , which correctly takes into account the two-body relaxation, we investigate the development of tidal tails of globular clusters in the Galactic tidal field. For simplicity, we have employed only the spherical components (bulge and halo) of the Galaxy, and ignored the effects of stellar evolution which could have been important in the very early phase of the cluster evolution. The total number of stars in our simulations is about 20 000, which is much smaller than the realistic number of stars. All simulations had been done for several orbital periods in order to understand the development of the tidal tails. In our scaled-down models, the relaxation time is sufficiently short to show the mass segregation effect, but we did not go far enough to see the core collapse, and the fraction of stars lost from the cluster at the end of the simulations is only ∼10 per cent. The radial distribution of extra-tidal stars can be described by a power law with a slope around −3 in surface density. The directions of tidal tails are determined by the orbits and locations of the clusters. We find that the length of tidal tails increases towards the apogalacticon and decreases towards the perigalacticon. This is an anti-correlation with the strength of the tidal field, caused by the fact that the time-scale for the stars to respond to the potential is similar to the orbital time-scale of the cluster. The escape of stars in the tidal tails towards the pericentre could be another reason for the decrease of the length of tidal tails. We find that the rotational angular velocity of tidally induced clusters shows quite different behaviour from that of initially rotating clusters.     

Tidal tails of star clusters

Based on recent findings of a formation mechanism of substructure in tidal tails by Küpper et al., we investigate a more comprehensive set of N -body models of star clusters on orbits about a Milky Way like potential. We find that the predicted epicyclic overdensities arise in any tidal tail no matter which orbit the cluster follows as long as the cluster lives long enough for the overdensities to build up.
The distance of the overdensities along the tidal tail from the cluster centre depends for circular orbits only on the mass of the cluster and the strength of the tidal field, and therefore decreases monotonically with time, while for eccentric orbits the orbital motion influences the distance, causing a periodic compression and stretching of the tails and making the distance oscillate with time. We provide an approximation for estimating the distance of the overdensities in this case.
We describe an additional type of overdensity which arises in extended tidal tails of clusters on eccentric orbits, when the acceleration of the tidal field on the stellar stream is no longer homogeneous. Moreover, we conclude that a pericentre passage or a disc shock is not the direct origin of an overdensity within a tidal tail. Escape due to such tidal perturbations does not take place immediately after the perturbation but is rather delayed and spread over the orbit of the cluster. All observable overdensities are therefore of the mentioned two types. In particular, we note that substructured tidal tails do not imply the existence of dark matter substructures in the haloes of galaxies.     

Analysing the structure of elongated star clusters

We have previously reported a measure     which both quantifies and distinguishes between a (relatively smooth) large-scale radial density gradient and multiscale (fractal) subclustering. Here, we extend the applicability of     to clusters which deviate significantly from an overall circular shape.
    varies systematically as clusters assume a more elongated shape, and it is therefore possible to correct for the effect, if the elongation of the cluster is also quantified.     therefore remains a useful and robust analytical technique for classifying and quantifying the internal structure of star clusters, even when their overall shape is far from circular.
The corrections required are small for individual clusters which are not extremely elongated (not more than three times longer than they are wide) of the same order as the uncertainty in the value of     for a particular cluster type. We therefore recommend that no correction be applied to the calculation of     for individual clusters, unless they are more than three times longer than their width, but that correction for elongation be applied when     is used for statistical analyses of large numbers of observed or simulated clusters.     

Stellar populations in star clusters

Stellar populations contain the most important information about star cluster formation and evolution. Until several decades ago, star clusters were believed to be ideal laboratories for studies of simple stellar populations(SSPs). However, discoveries of multiple stellar populations in Galactic globular clusters have expanded our view on stellar populations in star clusters. They have simultaneously generated a number of controversies, particularly as to whether young star clusters may have the same origin as old globular clusters. In addition, extensive studies have revealed that the SSP scenario does not seem to hold for some intermediate-age and young star clusters either, thus making the origin of multiple stellar populations in star clusters even more complicated. Stellar population anomalies in numerous star clusters are well-documented, implying that the notion of star clusters as true SSPs faces serious challenges. In this review, we focus on stellar populations in massive clusters with different ages. We present the history and progress of research in this active field, as well as some of the most recent improvements, including observational results and scenarios that have been proposed to explain the observations. Although our current ability to determine the origin of multiple stellar populations in star clusters is unsatisfactory, we propose a number of promising projects that may contribute to a significantly improved understanding of this subject.     

Collaborative research of open star clusters

Preliminary results on observations of open clusters are presented. The project has been initiated in the framework of the Uzbek-Taiwan and Taiwan-Baltic collaboration, mainly to upgrade and make use of facilities at Maidanak Observatory. We present detailed, multiwavelength studies of the young cluster NGC 6823 and the associated complex nebulosity, to diagnose the young stellar population and star formation history in the region. In addition, 7 compact open clusters have been monitored for stellar variability. We show how observations like these could feasibly be used to look for exoplanet transit events. We also expect to join the Whole-Earth Telescope effort in future campaigns for asteroseismology.