The formation and evolution of star cluster systems in different environments

The age, mass, and size distributions of star clusters in nearby star-forming galaxies provide important clues to the formation and evolution of cluster systems. In particular, the similarities and differences between these cluster distributions in very different environments can help to disentangle formation and disruption processes. We present the age and mass distributions for clusters younger than ≈1 Gyr in the Magellanic Clouds, which are typical, star-forming irregular galaxies, and compare the results with the more “extreme” environment found in the merging Antennae galaxies. In addition, we describe some new results on the interpretation of ancient globular cluster systems, and present an emerging picture for the life cycle of star clusters.     

Tracing the formation history of intermediate-age star clusters in the Small Magellanic Cloud

Colour–magnitude diagrams (CMDs) are presented for the first time for 10 star clusters projected on to the Small Magellanic Cloud (SMC). The photometry was carried out in the Washington system C and T ₁ filters allowing the determination of ages by means of the magnitude difference between the red giant clump and the main-sequence turnoff (MSTO), and metallicities from the red giant branch (RGB) locus. The clusters all have ages in the range 1.5–4 Gyr and metallicities between  −1.3 < [Fe/H] < −0.6  , with respective errors of ∼0.5 Gyr and 0.3 dex. This increases substantially the sample of intermediate-age clusters in the SMC with well-derived parameters. We combine our results with those for other clusters in the literature to derive as large and homogeneous a data base as possible (totalling 26 clusters) in order to study global effects. We find evidence for two peaks in the age distribution of SMC clusters, at ∼6.5 and 2.5 Gyr, in good agreement with previous hints involving smaller samples. The most recent peak occurs at a time that corresponds to a very close encounter between the Large Magellanic Cloud (LMC) and the SMC according to the recent dynamical models of Bekki et al. that they used to explain the enhancement of LMC clusters with this age. It appears cluster formation may have been similarly stimulated in the SMC by this encounter as well. We also find very good agreement between cluster ages and metallicities and the prediction from a bursting model from Pagel and Tautvaišienė with a burst that occurred 3 Gyr ago. These two lines of evidence together favour a bursting cluster formation history as opposed to a continuous one for the SMC.     

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.     

Probing the evolution of early-type galaxies using multicolour number counts and redshift distributions

We investigate pure luminosity evolution models for early-type (elliptical and S0) galaxies (i.e. no number density change or morphological transition), and examine whether these models are consistent with observed number counts in the B , I and K bands, and redshift distributions of two samples of faint galaxies selected in the I and K bands. The models are characterized by the star formation time-scale τ _SF and the time t _gw when the galactic wind starts to blow, in addition to several other conventional parameters. We find that the single-burst model ( τ _SF=0.1 Gyr and t _gw=0.353 Gyr), which is known to reproduce the photometric properties of early-type galaxies in clusters, is inconsistent with the redshift distributions of early-type galaxies in the field environment, owing to overpredictions of the number of galaxies at z ≳1.4 even with strong extinction which is at work until t _gw. In order for dust extinction to be more effective, we treat τ _SF and t _gw as free parameters, and find that models with τ _SF≳0.5 Gyr and t _gw>1.0 Gyr can be made consistent with both the observed redshift distributions and the number counts, if we introduce strong extinction [ E ( B − V )≥1 as a peak value]. These results suggest that early-type galaxies in the field environment do not have the same evolutionary history as described by the single-burst model.     

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.     

A comparison of optical and near-infrared colours of Magellanic Cloud star clusters with predictions of simple stellar population models

We present integrated JHK _S Two-Micron All-Sky Survey photometry and a compilation of integrated-light optical photoelectric measurements for 84 star clusters in the Magellanic Clouds. These clusters range in age from ≈200 Myr to >10 Gyr, and have [Fe/H] values from −2.2 to −0.1 dex. We find a spread in the intrinsic colours of clusters with similar ages and metallicities, at least some of which is due to stochastic fluctuations in the number of bright stars residing in low-mass clusters. We use 54 clusters with the most-reliable age and metallicity estimates as test particles to evaluate the performance of four widely used simple stellar population models in the optical/near-infrared (near-IR) colour–colour space. All models reproduce the reddening-corrected colours of the old (≥10 Gyr) globular clusters quite well, but model performance varies at younger ages. In order to account for the effects of stochastic fluctuations in individual clusters, we provide composite   B − V , B − J , V − J , V − K _S  and   J − K _S  colours for Magellanic Cloud clusters in several different age intervals. The accumulated masses for most composite clusters are higher than that needed to keep luminosity variations due to stochastic fluctuations below the 10 per cent level. The colours of the composite clusters are clearly distinct in optical–near-IR colour–colour space for the following intervals of age: >10 Gyr, 2–9 Gyr, 1–2 Gyr, and 200 Myr−1 Gyr. This suggests that a combination of optical plus near-IR colours can be used to differentiate clusters of different age and metallicity.     

Westerlund 1: bound or unbound?

The Galactic open cluster Westerlund 1 (Wd 1) represents the ideal local template for extragalactic young massive star clusters, because it is currently the only nearby young cluster with a mass of ～10⁵?M_⊙. Its proximity makes spatially resolved studies of its stellar population feasible, and additionally permits direct comparison of its properties with measurements of velocity dispersion and dynamical mass for spatially unresolved extragalactic clusters. Recently, we published the dynamical mass estimate based on spectra of four red supergiants. We have now identified six additional stars which allow a determination of radial velocity from the wavelength covered in our VLT/ISAAC near-infrared spectra (CO bandhead region near 2.29 μm), significantly improving statistics. Using a combination of stepping and scanning the slit across the cluster center, we covered an area which included the following suitable spectral types: four red supergiants, five yellow hypergiants, and one B-type emission-line star. Our measured velocity dispersion is 9.2 km?s^?1. Together with the cluster size of 0.86 pc, derived from archival near-infrared SOFI-NTT images, this yields a dynamical mass of 1.5×10⁵ M_⊙. Comparing this to the mass derived via photometry, there is no indication that the cluster is currently undergoing dissolution.     

New results on the ages of star clusters in region B of M82

The post-starburst region B in M82 and its massive star cluster component have been the focus of multiple studies, with reports that there is a large population of coeval clusters of age ～1 Gyr, which were created with a Gaussian initial mass distribution. This is in disagreement with other studies of young star clusters, which invariably find a featureless power-law mass distribution. Here, we present Gemini-North optical spectra of seven star clusters in M82-B and show that their ages are all between 10 and 300 Myr (a factor of 3–100 younger than previous photometric results) and that their extinctions range between near zero and 4 mag (A _V ). Using new HST ACS-HRC U-band observations we age date an additional ～30 clusters whose ages/extinctions agree well with those determined from spectroscopy. Completeness tests show that the reported ‘turn-over’ in the luminosity/mass distributions is most likely an artefact, due to the resolved nature of the clusters. We also show that the radial velocities of the clusters are inconsistent with them belonging to a bound region.     

Detecting metal-rich intermediate-age globular clusters in NGC4570 using K-band photometry

Globular cluster systems (GCSs) of most early-type galaxies feature two peaks in their optical colour distributions. Blue-peak globular clusters (GCs) are believed to be old and metal-poor, whereas the ages, metallicities, and the origin of the red-peak GCs are still being debated. We obtained deep K-band photometry and combined it with Hubble Space Telescope observations in g and z to yield a full spectral energy distribution from the optical to the near-infrared. This now allows us to break the age–metallicity degeneracy. We used our evolutionary synthesis models galev for star clusters to compute a large grid of models with different metallicities and a wide range of ages. Comparing these models to our observations revealed a large population of intermediate-age (1–3 Gyr) and metal-rich (≈solar-metallicity) GCs, that will give us further insights into the formation history of this galaxy.     

Open star clusters in the spiral arms of our Galaxy

We consider the age distributions of open star clusters attributed to three segments of Galactic spiral arms. The smoothed distributions of clusters on the age-Galactocentric angle plane show a great nonuniformity. The time dependence of the formation rate of Galactic disk clusters recovered by taking into account selection effects and dynamical evolution of clusters shows that, on average, the formation rate of open star clusters decreases with time. This is in agreement with the increase in star formation rate into the past, as follows from the study of this process by the method of stellar population synthesis. The present time is the epoch of a current maximum of the cluster formation rate. In addition to the current maximum, there have been at least three more maxima with a period of 300–400 Myr and a duration of no more than 300 Myr. The age distributions are consistent with the pattern of star formation governed by the successive passages of density waves through each examined volume of the Galactic disk. The spiral structure becomes more complex when passing from the inner regions of the Galaxy to its outer regions.     

Correlations, spectra, and instability of phase-space density fluctuations in open-cluster models

The dynamical evolution of six open star cluster models is analyzed using the correlation and spectral analysis of phase-space density fluctuations. The two-time and mutual correlation functions are computed for the fluctuations of the phase-space density of cluster models. The data for two-time and two-particle correlations are used to determine the correlation time for phase-space density fluctuations ((0.1–1) τ _v.r., where τ _v.r. is the violent relaxation time of the model) and the average phase velocities of the propagation of such fluctuations in cluster models. These velocities are 2–20 times smaller than the root mean square velocities of the stars in the cluster core. The power spectra and dispersion curves of phase-space density fluctuations are computed using the Fourier transform of mutual correlation functions. The results confirm the presence of known unstable phase-space density fluctuations due to homologous fluctuations of the cluster cores. The models are found to exhibit a number of new unstable phase-space density fluctuations (up to 32–41 pairs of fluctuations with different complex conjugate frequencies in each model; the e-folding time of the amplitude growth of such fluctuations is (0.4–10) τ _v.r. and their phases are distributed rather uniformly). Astrophysical applications of the obtained results (irregular structure of open star clusters, formation and decay of quasi-stationary states in such clusters) are discussed.     

Interpretation of the frequency distribution of isochrone ages of nearby F and G stars

The frequency distribution of isochrone ages of nearby F and G stars is used in a synthetic approach to the history of the star-formation rate (SFR). On the basis of stellar evolutionary sequences, age distributions are calculated for different assumptions on the SFR history. Models with a constant past SFR provide a good fit of the empirical age distributions, unless a feature at ages 4 Gyr. If real, a shoulder in the empirical frequency distribution of isochrone ages at 4–5 Gyr points toward an enhanced SFR during a more or less (1 to 6 Gyr) extended period which ceased with a peak about 4 Gyr ago. It is shown that models with such a nonmonotonous SFR history reproduce the empirical stellar age distribution and, moreover, the age-metallicity relation and the metallicity distribution of nearby stars. An era of enhanced star formation in this time interval is consistent with recently published interpretation of several age-dependent properties in different samples of nearby stars.     

Roche volume filling and the dissolution of open star clusters

From direct N‐body simulations we find that the dynamical evolution of star clusters is strongly influenced by the Roche volume filling factor. We present a parameter study of the dissolution of open star clusters with different Roche volume filling factors and different particle numbers. We study both Roche volume underfilling and overfilling models and compare with the Roche volume filling case. We find that in the Roche volume overfilling limit of our simulations two‐body relaxation is no longer the dominant dissolution mechanism but the changing cluster potential. We call this mechanism “mass‐loss driven dissolution” in contrast to “two‐body relaxation driven dissolution” which occurs in the Roche volume underfilling regime. We have measured scaling exponents of the dissolution time with the two‐body relaxation time. In this experimental study we find a decreasing scaling exponent with increasing Roche volume filling factor. The evolution of the escaper number in the Roche volume overfilling limit can be described by a log‐logistic differential equation. We report the finding of a resonance condition which may play a role for the evolution of star clusters and may be calibrated by the main periodic orbit in the large island of retrograde quasiperiodic orbits in the Poincaré surfaces of section. We also report on the existence of a stability curve which may be of relevance with respect to the structure of star clusters. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Monte Carlo simulations of star clusters – VI. The globular cluster NGC 6397

We describe Monte Carlo models for the dynamical evolution of the nearby globular cluster NGC 6397. The code includes treatments of two-body relaxation, most kinds of three- and four-body interactions involving primordial binaries and those formed dynamically, the Galactic tide and the internal evolution of both single and binary stars. We arrive at a set of initial parameters for the cluster which, after 12 Gyr of evolution, gives a model with a fairly satisfactory match to the surface brightness profile, the velocity dispersion profile and the luminosity function in two fields. We describe in particular those aspects of the evolution which distinguish this cluster from M4, which has a roughly similar mass and Galactocentric distance, but a qualitatively different surface brightness profile. Within the limitations of our modelling, we conclude that the most plausible explanation for the difference is fluctuations: both clusters are post-collapse objects, but sometimes have resolvable cores and sometimes not.     

Population i pulsating stars

On the basis of our age estimations of Population I pulsating stars in our Galaxy (Tsvetkov, 1986a), the mean ages of 6 open star clusters containing 21 Delta Scuti-variables and of 8 star clusters and associations containing 13 classical cepheids, have been evaluated. These mean cluster age estimations weighted according to the probabilities for different evolutionary phases of the pulsating stars, are obtained in the evolutionary track systems of Iben (1967) and Paczyski (1970); the cluster ages are larger in the former system. Our results are compared with those obtained from various methods by other authors. Clusters with classical cepheids and with Delta Scuti-stars have ages, respectively, in the ranges 10⁷–10⁸ years and 10⁶–10⁹ years. It is shown that the use of simple period-age(-colour) relations for Population I pulsating stars gives sufficiently accurate cluster age estimations. By use of our period-age relations for classical cepheids (Tsvetkov, 1986a), the mean ages of 56 other star clusters and associations in our Galaxy, the Magellanic Clouds, and M 31 galaxy have been estimated in both systems of tracks. The results are generally in agreement with those obtained from various methods by other authors. The use of Population I pulsating stars in star clusters and associations is one of the simplest and most easily applied methods for determining cluster ages; but there are some limitations in its application.     

AGB Phase Transition in Globular Clusters: A Tool for Dating Starbursts

A new method to detect and study young star clusters is presented. This is based on the knowledge that the light of stellar populations with ages between ∼ 200 Myr and ∼ 1/2 Gyr is dominated by very red, bright AGB stars. Star clusters undergoing this so-called ‘AGB phase transition’ are featured by very red V-K colours, like those of Magellanic Clouds clusters, while optical colours like B-V remain blue typical for young populations. The best channel for detecting star clusters in this age range is therefore the near IR. From the theoretical side, SSP models including properly the contribution of the bright AGB are required (Maraston, 1998). Using this strategy, we succesfully detected the AGB phase transition among the clusters of the merger remnant galaxy NGC 7252 (see Maraston etal., 2001). This revised version was published online in September 2006 with corrections to the Cover Date.     

Two MASS photometry of open star clusters: King 13 and Berkeley 53

In the present work, we used the near-infrared JHK_s photometric data from the 2-Micron All Sky Survey (2MASS) to determine the morphological and photometric parameters for two rarely studied open star clusters; King 13 and Berkeley 53. Luminosity function, mass function and dynamical relaxation time have been determined for the two clusters. We estimated the distances of 2.11±0.25 Kpc and 3.51±0.21 Kpc for King 13 and Berkeley 53 respectively, and both clusters have the same age 1.00±0.12 Gyr at solar metallicity; z=0.019.     

Five young star clusters in the outer region of the Small Magellanic Cloud

Colour–magnitude diagrams in the Washington system are presented for the first time for five star clusters projected on to the outer region of the Small Magellanic Cloud (SMC). The clusters are found to have ages in the range 0.1–1.0 Gyr, as derived from the fit of isochrones with   Z = 0.004  . This sample increases substantially the number of young clusters in the outer SMC – particularly in the south-east quadrant – with well-derived parameters. We combine our results with those for other clusters in the literature to derive as large and homogeneous a data base as possible (totalling 49 clusters) in order to study global effects. We find no conclusive evidence for a dispersion in the cluster ages and metallicities as a function of their distance from the galaxy centre, in the SMC outer region. L 114 and 115, although very distant, are very young clusters, lying in the bridge of the SMC and therefore most likely formed during the interaction which formed this feature. We also find very good agreement between the cluster age–metallicity relation (AMR) and the prediction from a bursting model from Pagel & Tautvaišienė with a burst that occurred 3 Gyr ago. Comparing the present cluster AMR with that derived by Harris & Zaritsky for field stars in the main body of the SMC, we find that field stars and clusters underwent similar chemical enrichment histories during approximately the last couple of Gyr, but their chemical evolution was clearly different between 4 and 10 Gyr ago.     

Imaging of the protoelliptical NGC 1700 and its globular cluster system

An excellent candidate for a young elliptical, or 'protoelliptical' galaxy is NGC 1700. Here we present new B -, V - and I -band imaging using the Keck telescope, and reanalyse existing V - and I -band images from the Hubble Space Telescope . After subtracting a model of the galaxy from the Keck images, NGC 1700 reveals two symmetric tidal tail-like structures. If this interpretation is correct, it suggests a past merger event involving two spiral galaxies. These tails are largely responsible for the 'boxiness' of the galaxy isophotes observed at a radius of ∼13 kpc.
We also show that the B − I colour distribution of the globular cluster system is bimodal. The mean colour of the blue population is consistent with that of old Galactic globular clusters. Relative to this old, metal-poor population, we find that the red population is younger and more metal-rich. This young population has an age and metallicity similar to that inferred for the central stars, suggesting that both populations are associated with an episode of star formation triggered by the merger that may have formed the galaxy. We find that, although they have large errors, the majority of the age estimates of NGC 1700 are reasonably consistent and we adopt a 'best estimate' for the age of 3.0±1.0 Gyr. This relatively low age places NGC 1700 within the age range where there is a notable lack of obvious candidates for protoellipticals. The total globular cluster specific frequency is rather low for a typical elliptical, even after taking into account the fading of the galaxy over the next 10 Gyr. We speculate that NGC 1700 will eventually form a relatively 'globular cluster poor' elliptical galaxy.     

Final stages of N-body star cluster encounters

We performed numerical simulations of star cluster encounters with Hernquist's treecode on a CRAY YMP-2E computer. We used different initial conditions (relative positions and velocities, cluster sizes, masses and concentration degrees) with the total number of particles per simulation ranging from 4608 to 20 480. Long-term interaction stages (up to 1 Gyr) when the pair coalesces into a single cluster are compared with isolated LMC clusters. Evidence is found that, when seen in a favourable plane, these resulting clusters show elliptical shapes as a result of the disruption of one of the companions. These elliptical shapes are essentially time-independent, but they do depend on the initial structural parameters of the pair components. We also analysed the fraction of stars that are ejected to the field by the interaction. We found that this fraction can be almost 50 per cent for the disrupted cluster. These simulations can represent a possible mechanism with which to explain the ellipticity observed in several star clusters in the Magellanic Clouds.