Merging time-scales of stellar subclumps in young star-forming regions

Recent observations and hydrodynamical simulations of star formation inside a giant molecular cloud have revealed that, within a star-forming region, stars do not form evenly distributed throughout this region, but rather in small subclumps. It is generally believed that these subclumps merge and form a young star cluster. The time-scale of this merging process is crucial for the evolution and the possible survival of the final star cluster. The key issue is whether this merging process happens faster than the time needed to remove the residual gas of the cloud. A merging time-scale shorter than the gas-removal time would enhance the survival chances of the resulting star cluster. In this paper, we show by means of numerical simulations that the time-scale of the merging is indeed very fast. Depending on the details of the initial subclump distribution, the merging may occur before the gas is expelled from the newly formed cluster via either supernovae or the winds from massive stars. Our simulations further show that the resulting merger objects have a higher effective star formation efficiency than the overall star-forming region and confirm the results that mass-segregated subclumps form mass-segregated merger objects.     

On the mass of dense star clusters in starburst galaxies from spectrophotometry

The mass of unresolved young star clusters derived from spectrophotometric data may well be off by a factor of 2 or more once the migration of massive stars driven by mass segregation is accounted for. We quantify this effect for a large set of cluster parameters, including variations in the stellar initial mass function (IMF), the intrinsic cluster mass, and mean mass density. Gas-dynamical models coupled with the Cambridge stellar evolution tracks allow us to derive a scheme to recover the real cluster mass given measured half-light radius, one-dimensional velocity dispersion and age. We monitor the evolution with time of the ratio of real to apparent mass through the parameter η. When we compute η for rich star clusters, we find non-monotonic evolution in time when the IMF stretches beyond a critical cut-off mass of  25.5 M_⊙  . We also monitor the rise of colour gradients between the inner and outer volume of clusters: we find trends in time of the stellar IMF power indices overlapping well with those derived for the Large Magellanic Cloud cluster NGC 1818 at an age of 30 Myr. We argue that the core region of massive Antennae clusters should have suffered from much segregation despite their low ages. We apply these results to a cluster mass function, and find that the peak of the mass distribution would appear to observers shifted to lower masses by as much as 0.2 dex. The star formation rate derived for the cluster population is then underestimated by from 20 to 50 per cent.     

Black holes and core expansion in massive star clusters

In this study we present the results from realistic N -body modelling of massive star clusters in the Magellanic Clouds. We have computed eight simulations with   N ∼ 10⁵  particles; six of these were evolved for at least a Hubble time. The aim of this modelling is to examine in detail the possibility of large-scale core expansion in massive star clusters, and search for a viable dynamical origin for the radius–age trend observed for such objects in the Magellanic Clouds. We identify two physical processes which can lead to significant and prolonged cluster core expansion – mass-loss due to rapid stellar evolution in a primordially mass-segregated cluster, and heating due to a retained population of stellar mass black holes, formed in the supernova explosions of the most massive cluster stars. These two processes operate over different time-scales and during different periods of a cluster's life. The former occurs only at early times and cannot drive core expansion for longer than a few hundred Myr, while the latter typically does not begin until several hundred Myr have passed, but can result in core expansion lasting for many Gyr. We investigate the behaviour of each of these expansion mechanisms under different circumstances – in clusters with varying degrees of primordial mass segregation, and in clusters with varying black hole retention fractions. In combination, the two processes can lead to a wide variety of evolutionary paths on the radius–age plane, which fully cover the observed cluster distribution and hence define a dynamical origin for the radius–age trend in the Magellanic Clouds. We discuss in some detail the implications of core expansion for various aspects of globular cluster research, as well as the possibility of observationally inferring the presence of a significant population of stellar mass black holes in a cluster.     

Stellar dynamics in young clusters: the formation of massive runaways and very massive runaway mergers

In the present paper we combine an N-body code that simulates the dynamics of young dense stellar systems with a massive star evolution handler that accounts in a realistic way for the effects of stellar wind mass loss. We discuss two topics.

1. The formation and the evolution of very massive stars (with masses >120 M_⊙) is followed in detail. These very massive stars are formed in the cluster core as a consequence of the successive (physical) collisions of the 10–20 most massive stars in the cluster (this process is known as ‘runaway merging’). The further evolution is governed by stellar wind mass loss during core hydrogen and core helium burning (the WR phase of very massive stars). Our simulations reveal that, as a consequence of runaway merging in clusters with solar and supersolar values, massive black holes can be formed, but with a maximum mass ≈70 M_⊙. In low-metallicity clusters, however, it cannot be excluded that the runaway-merging process is responsible for pair-instability supernovae or for the formation of intermediate-mass black holes with a mass of several 100 M_⊙.
2. Massive runaways can be formed via the supernova explosion of one of the components in a binary system (the Blaauw scenario), or via dynamical interaction of a single star and a binary or between two binaries in a star cluster. We explore the possibility that the most massive runaways (e.g. ζ Pup, λ Cep, BD+43°3654) are the product of the collision and merger of two or three massive stars.

     

Analysis of the structure and dynamics of the stellar tails of open star clusters

We have analyzed the formation, structure, and dynamical evolution of the population of stars that escaped from open clusters by numerical simulations using S. Aarseth’s modified NBODY6 code. In the Galactic tidal field, the population of stars that escaped from a cluster is shown to be elongated along the orbit of the cluster symmetrically about its core in the form of stellar tails of increasing sizes. We analyze the parameters of stellar tails as a function of such initial simulation conditions as the number of stars, the cluster density, the eccentricity of the Galactic cluster orbit in the plane of the Galactic disk, and the z velocity component. As a result, we constructed a grid of model stellar tails of open clusters. The grid includes such time-dependent parameters of the stellar tails as the length, the cross section, the number of stars, the velocity distribution, etc. Our simulations allow us to clarify the origin of moving clusters and stellar streams and to assess the role of star clusters in forming the stellar velocity field in the solar neighborhood.     

Role of Gas Dynamical Friction in the Evolution of Embedded Stellar Clusters

Two puzzles associated with open clusters have attracted a lot of attention – their formation, with densities and velocity dispersions that are not too different from those of the star forming regions in the galaxy, given that the observed Star Formation Efficiencies (SFE) are low and, the mass segregation observed/inferred in some of them, at ages significantly less than the dynamical relaxation times in them. Gas dynamical friction has been considered before as a mechanism for contracting embedded stellar clusters, by dissipating their energy. This would locally raise the SFE which might then allow bound clusters to form. Noticing that dynamical friction is inherently capable of producing mass segregation, since here, the dissipation rate is proportional to the mass of the body experiencing the force, we explore further, some of the details and implications of such a scenario, vis-à-vis observations. Making analytical approximations, we obtain a boundary value for the density of a star forming clump of a given mass, such that, stellar clusters born in clumps which have densities higher than this, could emerge bound after gas loss. For a clump of given mass and density, we find a critical mass such that, sub-condensations with larger masses than this could suffer significant segregation within the clump.     

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.     

Constraints on the initial conditions of globular clusters

N -body simulations are made with a variety of initial conditions, in particular clumpy and flattened distributions, to attempt to constrain the possible initial conditions of globular clusters, using the observations that young LMC globular clusters appear relaxed after only 20 to 40 Myr. It is found that violent relaxation is able to erase most of the initial substructure in only ≈ 6 crossing times. However, initially very clumpy distributions (≲ 100 clumps) form clusters that are too concentrated to resemble real globular clusters. Such clusters also often have large clumps in long-lasting (≳ 30 crossing times) orbits which do not appear in observed cluster profiles. It is also found that even modest amounts of initial flattening produce clusters that are too elliptical to resemble real globular clusters. In such a scenario, cloud–cloud collisions and similar energetic processes would be unlikely to produce sufficiently spherical globular clusters. It is suggested that globular clusters form from roughly spherical initial conditions with star formation occurring either smoothly or in many small clumps.     

On a Formation Scenario of Star Clusters

Most formation scenarios of globular clusters assume a molecular cloud as the progenitor of the stellar system. However, it is still unclear, how this cloud is transformed into a star cluster, i.e. how the destructive processes related to gas removal or low star formation effiency can be avoided. Here a scheme of supernova (SN) induced cluster formation is studied. According to this scenario an expanding SN shell accumulates the mass of the cloud. This is accompanied by fragmentation resulting in star formation in the shell. Provided the stellar shell expands sufficiently slow, its self-gravity stops the expansion and the shell recollapses, by this forming a stellar system. I present N-body simulations of collapsing shells which move in a galactic potential on circular and elliptic orbits. It is shown that typical shells (10⁵ M_⊙, 30 pc) evolve to twin clusters over a large range of galactocentric distances. Outside this range single stellar systems are formed, whereas at small galactocentric distances the shells are tidally disrupted. In that case many small fragments formed during the collapse survive as single bound entities. About 1/3 of the twin cluster systems formed on circular orbits merge within 400 Myr. On elliptic orbits the merger rate reduces to less than 4%. Thus, there could be a significant number of twin clusters even in our Galaxy, which, however, might be undetected as twins due to a large phase shift on their common orbit. This revised version was published online in September 2006 with corrections to the Cover Date.     

Mass segregation in young stellar clusters

We investigate the evolutionary effect of dynamical mass segregation in young stellar clusters. Dynamical mass segregation acts on a time-scale of order the relaxation time of a cluster. Although some degree of mass segregation occurs earlier, the position of massive stars in rich young clusters generally reflects the cluster's initial conditions. In particular, the positions of the massive stars in the Trapezium cluster in Orion cannot be due to dynamical mass segregation, but indicate that they formed in, or near, the centre of the cluster. Implications of this for cluster formation and for the formation of high-mass stars are discussed.     

Galaxy evolution in the high-redshift, colour-selected cluster RzCS 052 at z= 1.02

We present deep I and z ' imaging of the colour-selected cluster RzCS 052 and study the colour–magnitude relation of this cluster, its scatter, the morphological distribution on the red sequence, the luminosity and stellar mass functions of red galaxies and the cluster blue fraction. We find that the stellar populations of early-type galaxies in this cluster are uniformly old and that their luminosity function does not show any sign of evolution other than the passive evolution of their stellar populations. We rule out a significant contribution from mergers in the build-up of the red sequence of RzCS 052. The cluster has a large (∼30 per cent) blue fraction and we infer that the evolution of the blue galaxies is faster than an exponentially declining star formation model and that these objects have probably experienced starburst episodes. Mergers are unlikely to be the driver of the observed colour evolution, because of the measured constancy of the mass function, as derived from near-infrared photometry of 32 clusters, including RzCS 052, presented in a related paper. Mechanisms with clustercentric radial dependent efficiencies are disfavoured as well, because of the observed constant blue fraction with clustercentric distance.     

Star formation in the Small Magellanic Cloud: the youngest star clusters

We combined optical Hubble Space Telescope ACS images with mid-infrared Spitzer data of the two young star clusters NGC346 and NGC602 in the Small Magellanic Cloud, to study how local and global conditions may affect the process of star formation. We found that, while general conditions such as metallicity, or the mass or morphological type of the parent galaxy do not strongly affect the process of star formation, local conditions such as the gas and stellar density can affect both how star formation occurs and propagates, and also the evolution of a star cluster from early times.     

The mass-to-light ratio of rich star clusters

We point out a strong time evolution of the mass-to-light conversion factor, η, commonly used to estimate masses of unresolved star clusters from observed cluster spectrophotometric measures. We present a series of gas-dynamical models, coupled with the Cambridge stellar evolution tracks, to compute line-of-sight velocity dispersions and half-light radii weighted by the luminosity. We explore a range of initial conditions, varying in turn the cluster mass and/or density, and the stellar population’s initial mass function. We find that η, and hence the estimated cluster mass, may increase by as much as a factor of three over time-scales of 50 million yr. We apply these results to an hypothetic cluster mass distribution function (d.f.), and show that the d.f. shape may be strongly affected at the low-mass end by this effect. Fitting truncated isothermal (Michie–King) models to the projected light profile leads to over-estimates of the concentration parameter, c, of δ c≈0.3 compared to the same functional fit applied to the projected mass density.     

How well do starlab and nbody4 compare? I. Simple models

N -body simulations are widely used to simulate the dynamical evolution of a variety of systems, among them star clusters. Much of our understanding of their evolution rests on the results of such direct N -body simulations. They provide insight in the structural evolution of star clusters, as well as into the occurrence of stellar exotica. Although the major pure N -body codes starlab/kira and nbody4 are widely used for a range of applications, there is no thorough comparison study yet.
Here, we thoroughly compare basic quantities as derived from simulations performed either with starlab/kira or nbody4 .
We construct a large number of star cluster models for various stellar mass function settings (but without stellar/binary evolution, primordial binaries, external tidal fields, etc.), evolve them in parallel with starlab/kira and nbody4 , analyse them in a consistent way and compare the averaged results quantitatively. For this quantitative comparison, we develop a bootstrap algorithm for functional dependencies.
We find an overall excellent agreement between the codes, both for the clusters' structural and energy parameters as well as for the properties of the dynamically created binaries. However, we identify small differences, like in the energy conservation before core collapse and the energies of escaping stars, which deserve further studies.
Our results reassure the comparability and the possibility to combine results from these two major N -body codes, at least for the purely dynamical models (i.e. without stellar/binary evolution) we performed. Further detailed comparison studies for more complex systems, e.g. including stellar/binary evolution, are required.     

Quantitative analysis of clumps in the tidal tails of star clusters

Tidal tails of star clusters are not homogeneous but show well-defined clumps in observations as well as in numerical simulations. Recently, an epicyclic theory for the formation of these clumps was presented. A quantitative analysis was still missing. We present a quantitative derivation of the angular momentum and energy distribution of escaping stars from a star cluster in the tidal field of the Milky Way and derive the connection to the position and width of the clumps. For the numerical realization we use star-by-star N -body simulations. We find a very good agreement of theory and models. We show that the radial offset of the tidal arms scales with the tidal radius, which is a function of cluster mass and the rotation curve at the cluster orbit. The mean radial offset is 2.77 times the tidal radius in the outer disc. Near the Galactic Centre the circumstances are more complicated, but to lowest order the theory still applies. We have also measured the Jacobi energy distribution of bound stars and showed that there is a large fraction of stars (about 35 per cent) above the critical Jacobi energy at all times, which can potentially leave the cluster. This is a hint that the mass loss is dominated by a self-regulating process of increasing Jacobi energy due to the weakening of the potential well of the star cluster, which is induced by the mass loss itself.     

The lower mass function of young open clusters: clues to (sub)stellar formation

We report the present day mass functions (PDMFs) of 4 young open clusters over a mass range from 30 Jupiter masses to 3M_ . Three of these clusters have been chosen to have a similar age of ∼100 Myr. Their PDMFs are remarkably similar and are comparable to the field mass function. This suggests little impact of initial conditions (stellar density, metallicity) on the mass distribution and raises some issues concerning the currently debated star and brown dwarf formation theories. The fourth cluster is older (600 Myr) which allow us to investigate the effect of the cluster dynamical evolution on the shape of the mass function. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of gas expulsion and initial mass segregation on the stellar mass function of globular star clusters

Recently, De Marchi, Paresce & Pulone studied a sample of 20 globular clusters and found that all clusters with high concentrations have steep stellar mass functions while clusters with low concentration have comparatively shallow mass functions. No globular clusters were found with a flat mass function and high concentration. This seems curious since more concentrated star clusters are believed to be dynamically more evolved and should have lost more low-mass stars via evaporation, which would result in a shallower mass function in the low-mass part.
We show that this effect can be explained by residual-gas expulsion from initially mass segregated star clusters, and is enhanced further through unresolved binaries. If gas expulsion is the correct mechanism to produce the observed trend in the   c –α  -plane, then observation of these parameters would allow to constrain cluster starting conditions such as star formation efficiency and the time-scale of gas expulsion.     

Accretion in stellar clusters and the initial mass function

We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M ∗≳0.5 M_⊙ . The model depends solely on the competitive accretion that occurs in stellar clusters where each star's accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or the stars dominate the gravitational potential. When the cluster is dominated by cold gas, the accretion radius is given by a tidal-lobe radius. This occurs as the cluster collapses towards a ρ  ∝  R ⁻² distribution. Accretion in this regime results in a mass spectrum with an asymptotic limit of γ =−3/2 (where Salpeter is γ =−2.35) . Once the stars dominate the potential and are virialized, which occurs first in the cluster core, the accretion radius is the Bondi–Hoyle radius. The resultant mass spectrum has an asymptotic limit of γ =−2 with slightly steeper slopes ( γ ≈−2.5) if the stars are already mass-segregated. Simulations of accretion on to clusters containing 1000 stars show that, as expected, the low-mass stars accumulate the majority of their masses during the gas-dominated phase whereas the high-mass stars accumulate the majority of their masses during the stellar-dominated phase. This results in a mass spectrum with a relatively shallow γ ≈3/2 power law for low-mass stars and a steeper power law for high-mass stars −2.5≲ γ ≤−2 . This competitive accretion model also results in a mass-segregated cluster.     

The influence of multiple stars on the high-mass stellar initial mass function and age dating of young massive star clusters

The study of young stellar populations has revealed that most stars are in binary or higher order multiple systems. In this study, the influence on the stellar initial mass function (IMF) of large quantities of unresolved multiple massive stars is investigated by taking into account the stellar evolution and photometrically determined system masses. The models, where initial masses are derived from the luminosity and colour of unresolved multiple systems, show that even under extreme circumstances (100 per cent binaries or higher order multiples), the difference between the power-law index of the mass function (MF) of all stars and the observed MF is small (≲0.1). Thus, if the observed IMF has the Salpeter index  α= 2.35  , then the true stellar IMF has an index not flatter than  α= 2.25  . Additionally, unresolved multiple systems may hide between 15 and 60 per cent of the underlying true mass of a star cluster. While already a known result, it is important to point out that the presence of a large number of unresolved binaries amongst pre-main-sequence stars induces a significant spread in the measured ages of these stars even if there is none. Also, lower mass stars in a single-age binary-rich cluster appear older than the massive stars by about 0.6 Myr.     

OB星协和年轻星团的形成与早期演化

ＯＢ星协和年轻星团是恒星形成与早期演化的“化石”，同时也是研究初始重质量函数（ＩＭＦ）的最好场所；文中就ＯＢ星协和年轻星团的形成和早期演化方面的研究进展作了一评述，还论述了ＩＭＦ的测定和研究情况，并对相关的速逃ＯＢ星及蓝离散星问题作了简要介绍。