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.     

Winds from clusters with non-uniform stellar distributions

We present the analytic and numerical models of the 'cluster wind' resulting from the multiple interactions of the winds ejected by the stars of a dense cluster of massive stars. We consider the case in which the distribution of stars (i.e. the number of stars per unit volume) within the cluster is spherically symmetric, has a power-law radial dependence, and drops discontinuously to zero at the outer radius of the cluster. We carry out comparisons between an analytic model (in which the stars are considered in terms of a spatially continuous injection of mass and energy) and 3D gasdynamic simulations (in which we include 100 stars with identical winds, located in 3D space by statistically sampling the stellar distribution function). From the analytic model, we find that for stellar distributions with steep enough radial dependencies, the cluster wind flow develops a very high central density and a non-zero central velocity, and for steeper dependencies, it becomes fully supersonic throughout the volume of the cluster (these properties are partially reproduced by the 3D numerical simulations). Therefore, the wind solutions obtained for stratified clusters can differ dramatically from the case of a homogeneous stellar distribution (which produces a cluster wind with zero central velocity, and a fully subsonic flow within the cluster radius). Finally, from our numerical simulations, we compute predictions of X-ray emission maps and luminosities, which can be directly compared with observations of cluster wind flows.     

Evolutionary synthesis modelling of young star clusters in merging galaxies

The observational properties of globular cluster systems (GCSs) are vital tools to investigate the violent star formation histories of their host galaxies. This violence is thought to have been triggered by galaxy interactions or mergers. The most basic properties of a GCS are its luminosity function (number of clusters per luminosity bin) and color distributions. A large number of observed GCS show bimodal color distributions, which can be translated into a bimodality in either metallicity and/or age. An additional uncertainty comes into play when one considers extinction. These effects can be disentangled either by obtaining spectroscopic data for the clusters or by imaging observations in at least four passbands. This allows us then to discriminate between various formation scenarios of GCSs, e.g. the merger scenario by Ashman and Zepf, and the multi-phase collapse model by Forbes et al. Young and metal-rich star cluster populations are seen to form in interacting and merging galaxies. We analyse multiwavelength broad-band observations of these young cluster systems provided by the ASTROVIRTEL project. This revised version was published online in August 2006 with corrections to the Cover Date.     

3D models of radiatively driven colliding winds in massive O+O star binaries – I. Hydrodynamics

The dynamics of the wind–wind collision in massive stellar binaries are investigated using 3D hydrodynamical models which incorporate gravity, the driving of the winds, the orbital motion of the stars and radiative cooling of the shocked plasma. In this first paper, we restrict our study to main-sequence O+O binaries. The nature of the wind–wind collision region is highly dependent on the degree of cooling of the shocked plasma, and the ratio of the flow time-scale of the shocked plasma to the orbital time-scale. The pre-shock wind speeds are lower in close systems as the winds collide prior to their acceleration to terminal speeds. Radiative inhibition may also reduce the pre-shock wind speeds. Together, these effects can lead to rapid cooling of the post-shock gas. Radiative inhibition is less important in wider systems, where the winds are accelerated to higher speeds before they collide, and the resulting collision region can be largely adiabatic. In systems with eccentric orbits, cold gas formed during periastron passage can persist even at apastron, before being ablated and mixed into its surroundings and/or accelerated out of the system.     

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.     

The formation of a bound star cluster: from the Orion nebula cluster to the Pleiades

Direct N -body calculations are presented of the formation of Galactic clusters using GasEx , which is a variant of the code Nbody6 . The calculations focus on the possible evolution of the Orion nebula cluster (ONC) by assuming that the embedded OB stars explosively drove out 2/3 of its mass in the form of gas about 0.4 Myr ago. A bound cluster forms readily and survives for 150 Myr despite additional mass loss from the large number of massive stars, and the Galactic tidal field. This is the very first time that cluster formation is obtained under such realistic conditions. The cluster contains about 1/3 of the initial 10⁴ stars, and resembles the Pleiades cluster to a remarkable degree, implying that an ONC-like cluster may have been a precursor of the Pleiades. This scenario predicts the present expansion velocity of the ONC, which will be measurable by upcoming astrometric space missions. These missions should also detect the original Pleiades members as an associated expanding young Galactic-field subpopulation. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations.
The results have wide implications, also for the formation of globular clusters and the Galactic-field and halo stellar populations. In view of this, the distribution of binary orbital periods and the mass function within and outside the model ONC and Pleiades is quantified, finding consistency with observational constraints. Advanced mass segregation is evident in one of the ONC models. The calculations show that the primordial binary population of both clusters could have been much the same as is observed in the Taurus–Auriga star-forming region. The computations also demonstrate that the binary proportion of brown dwarfs is depleted significantly for all periods, whereas massive stars attain a high binary fraction.     

The early expansion of cluster cores

The observed properties of young star clusters, such as the core radius and luminosity profile, change rapidly during the early evolution of the clusters. Here we present observations of six young clusters in M51 where we derive their sizes using Hubble Space Telescope ( HST ) imaging and ages using deep Gemini-North spectroscopy. We find evidence for a rapid expansion of the cluster cores during the first 20 Myr of their evolution. We confirm this trend by including data from the literature of both Galactic and extragalactic embedded and young clusters, and possible mechanisms (rapid gas removal, stellar evolutionary mass loss and internal dynamical heating) are discussed. We explore the implications of this result, focussing on the fact that clusters were more concentrated in the past, implying that their stellar densities were much higher and relaxation times ( t _relax) correspondingly shorter. Thus, when estimating if a particular cluster is dynamically relaxed (i.e. when determining if a cluster's mass segregation is due to primordial or dynamical processes), the current relaxation time is only an upper limit, with t _relax likely being significantly shorter in the past.     

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.     

On the X-ray emission from massive star clusters and their evolving superbubbles – II. Detailed analytics and observational effects

In this work, we present a comprehensive X-ray picture of the interaction between a super star cluster and the interstellar medium. In order to do that, we compare and combine the X-ray emission from the superwind driven by the cluster with the emission from the wind-blown bubble. Detailed analytical models for the hydrodynamics and X-ray luminosity of fast polytropic superwinds are presented. The superwind X-ray luminosity models are an extension of the results obtained in Paper I. Here, the superwind polytropic character allows us to parametrize a wide variety of effects, for instance, radiative cooling. Additionally, X-ray properties that are valid for all bubble models taking thermal evaporation into account are derived. The final X-ray picture is obtained by calculating analytically the expected surface brightness and weighted temperature of each component. All of our X-ray models have an explicit dependence on metallicity and admit general emissivities as functions of the hydrodynamical variables. We consider a realistic X-ray emissivity that separates the contributions from hydrogen and metals. The paper ends with a comparison of the models with observational data.     

X-rays from massive OB stars: thermal emission from radiative shocks

Chandra grating spectra of a sample of 15 massive OB stars were analysed under the basic assumption that the X-ray emission is produced in an ensemble of shocks formed in the winds driven by these objects. Shocks develop either as a result of radiation-driven instabilities or due to confinement of the wind by a relatively strong magnetic field, and since they are radiative, a simple model of their X-ray emission was developed that allows a direct comparison with observations. According to our model, the shock structures (clumps, complete or fractional shells) eventually become 'cold' clouds in the X-ray sky of the star. As a result, it is expected that for large covering factors of the hot clumps, there is a high probability for X-ray absorption by the 'cold' clouds, resulting in blueshifted spectral lines. Our analysis has revealed that such a correlation indeed exists for the considered sample of OB stars. As to the temperature characteristics of the X-ray emission plasma, the studied OB stars fall in two groups: (i) one with plasma temperature limited to ∼0.1–0.4 keV and (ii) the other with X-rays produced in plasmas at considerably higher temperatures. We argue that the two groups correspond to different mechanisms for the origin of X-rays: in radiation-driven instability shocks and in magnetically confined wind shocks, respectively.     

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.