The early evolution of the star cluster mass function

Several recent studies have shown that the star cluster initial mass function (CIMF) can be well approximated by a power law, with indications for a steepening or truncation at high masses. This contribution considers the evolution of such a mass function due to cluster disruption, with emphasis on the part of the mass function that is observable in the first ∼1 Gyr. A Schechter type function is used for the CIMF, with a power-law index of −2 at low masses and an exponential truncation at M _*. Cluster disruption due to the tidal field of the host galaxy and encounters with giant molecular clouds flattens the low-mass end of the mass function, but there is always a part of the 'evolved Schechter function' that can be approximated by a power law with index −2. The mass range for which this holds depends on age, τ, and shifts to higher masses roughly as  τ^0.6  . Mean cluster masses derived from luminosity-limited samples increase with age very similarly due to the evolutionary fading of clusters. Empirical mass functions are, therefore, approximately power laws with index −2, or slightly steeper, at all ages. The results are illustrated by an application to the star cluster population of the interacting galaxy M51, which can be well described by a model with   M _*= (1.9 ± 0.5) × 10⁵ M_⊙  and a short (mass-dependent) disruption time destroying M _* clusters in roughly a Gyr.     

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.     

Captured older stars as the reason for apparently prolonged star formation in young star clusters

The existence of older stars within a young star cluster can be interpreted to imply that star formation occurs on time-scales longer than a free-fall time of a pre-cluster cloud core. Here, the idea is explored that these older stars are not related to the star formation process forming the young star cluster but rather that the orbits of older field stars are focused by the collapsing pre-cluster cloud core. Two effects appear: the focusing of stellar orbits leads to an enhancement of the density of field stars in the vicinity of the centre of the young star cluster; and due to the time-dependent potential of the forming cluster some of these stars can get bound gravitationally to the cluster. These stars exhibit similar kinematical properties to the newly formed stars and cannot be distinguished from them on the basis of radial velocity or proper motion surveys. Such contaminations may lead to a wrong apparent star formation history of a young cluster. In the case of the ONC, the theoretical number of gravitationally bound older low-mass field stars agrees with the number of observed older low-mass stars.     

Enhanced mergers of galaxies in low-redshift clusters

An ensemble cluster has been formed from a data set comprising a complete magnitude-limited sample of 680 giant galaxies  ( M ⁰ _B ≲−19)  in eight low-redshift clusters, normalized by the velocity dispersions and virial radii for the early-type cluster populations. Distinct galaxy populations have been identified, including an infall population. A majority (50–70 per cent or greater) of the infall population are found to be in interacting or merging systems characterized by slow gravitational encounters. The observed enhancement of galaxy–galaxy encounters in the infall population compared to the field can be explained by gravitational shocking. It is shown that disc galaxy mergers in the infall population integrated over the estimated lifetime of the cluster (∼10 Gyr) can readily account for the present cluster S0 population.     

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.     

Richness dependence of the recent evolution of clusters of galaxies

We revisit the issue of the recent dynamical evolution of clusters of galaxies using a sample of Abell, Corwin & Olowin (ACO) clusters with   z < 0.14  , which has been selected such that it does not contain clusters with multiple velocity components nor strongly merging or interacting clusters, as revealed in X-rays. We use as proxies of the cluster dynamical state the projected cluster ellipticity, velocity dispersion and X-ray luminosity. We find indications for a recent dynamical evolution of this cluster population, which however strongly depends on the cluster richness. Poor clusters appear to be undergoing their primary phase of virialization, with their ellipticity increasing with redshift with a rate  dε/d z ≃ 2.5 ± 0.4  , while the richest clusters show an ellipticity evolution in the opposite direction (with  dε/d z ≃−1.2 ± 0.1  ), which could be due to secondary infall. When taking into account sampling effects due to the magnitude-limited nature of the ACO cluster catalogue we find no significant evolution of the cluster X-ray luminosity, while the velocity dispersion increases with decreasing redshift, independent of the cluster richness, at a rate  dσ _v /d z ≃−1700 ± 400 km s⁻¹  .     

Identifying star clusters in a field: A comparison of different algorithms

Star clusters are often hard to find, as they may lie in a dense field of background objects or, because in the case of embedded clusters, they are surrounded by a more dispersed population of young stars. This paper discusses four algorithms that have been developed to identify clusters as stellar density enhancements in a field, namely stellar density maps from star counts, the nearest neighbour method and the Voronoi tessellation, and the separation of minimum spanning trees. These methods are tested and compared to each other by applying them to artificial clusters of different sizes and morphologies. While distinct centrally concentrated clusters are detected by all methods, clusters with low overdensity or highly hierarchical structure are only reliably detected by methods with inherent smoothing (star counts and nearest neighbour method). Furthermore, the algorithms differ strongly in computation time and additional parameters they provide. Therefore, the method to choose primarily depends on the size and character of the investigated area and the purpose of the study (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)