Integrated photometric properties of magellanic cloud star clusters

Integrated CCD BVR photometric measurements of Magellanic Cloud (MC) star clusters are described and summarized. The integrated colour-magnitude diagrams and colour-age relations for these systems imply that (a) the colour distribution of MC clusters is distinctly bi-modal (although this bi-modality is not simply explained as a distinction between young and old clusters), and (b) the MCs are probably not forming as many (if any) extremely massive clusters at the present as they did early in their lifetimes (i.e., 10 Gyr ago). Structurally, the MC clusters are seen to be intermediate between galactic globular and open clusters and their radial surface brightness profiles can generally be adequately fitted to single-mass King (1966) models (some exceptions do occur, however). Although the distribution of the derived structural parameters of young and old MC clusters are similar, they differ significantly from the distribution of structural parameters observed in intermediate-age clusters, suggesting that these structural properties do not evolve monotonically with time.Visiting astronomer at the Cerro Tololo Interamerican Observatory, National Optical Astronomy Observatories, operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

The initial mass function in clusters: theoretical and observational perspectives

We review the success of current simulations in reproducing the observed initial mass function (IMF) in clusters and show that whereas the two main types of simulation invoke the same physics to explain the point at which the IMF flattens from a Salpeter slope, they reproduce the Salpeter tail itself by quite different means. We highlight the fact that a proper modelling of the thermal properties of star-forming gas is probably crucial in explaining why the IMF is apparently quite insensitive to cloud parameters. We also explore how the mass of a cluster’s most massive star depends on cluster mass and how this issue impacts the relationship between the IMF in individual clusters and the integrated galactic IMF. We emphasise the importance of a careful statistical treatment of data in this area.     

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.     

球状星团的金属丰度特征与其恒星形成史

本文根据球状星团所特有的金属丰度特征,利用星族综合方法,探讨了球状星团诸恒星的形成史。研究表明,这些恒星不可能通过恒星形成率和初始质量函数均不随时间变化的单一恒星形成模式产生。原初云通过恒星演化而得到金属丰度污染的过程和多数恒星的形成过程必须分为两个不同的阶段。 球状星团得到金属丰度污染的过程中,若恒星形成具有通常的初始质量函数,则其恒星形成率必须较低,且初始质量函数不能太陡,从而使污染过程中只形成数量较少的低质量恒星,以保证单个球状星团内金属丰度的均匀性。另一种可能性是污染阶段有非常特殊的初始质量函数,只形成大质量的恒星,从而除提供适量污染外不留下任何痕迹。 多数恒星应是在原初云不同部位得到适当污染后通过局域的短暂的爆发性恒星形成(星暴过程)产生。本文进一步探讨了在Fan和Rees球状星团形成模型的框架下,两相介质中温云块相互碰撞造成星暴过程的可能性。     

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。     

The Jeans mass and the origin of the knee in the IMF

We use numerical simulations of the fragmentation of a  1000 M_⊙  molecular cloud and the formation of a stellar cluster to study how the initial conditions for star formation affect the resulting initial mass function (IMF). In particular, we are interested in the relation between the thermal Jeans mass in a cloud and the knee of the IMF, i.e. the mass separating the region with a flat IMF slope from that typified by a steeper, Salpeter-like, slope. In three isothermal simulations with   M _Jeans= 1, 2  and  5 M_⊙  , the number of stars formed, at comparable dynamical times, scales roughly with the number of initial Jeans masses in the cloud. The mean stellar mass also increases (though less than linearly) with the initial Jeans mass in the cloud. It is found that the IMF in each case displays a prominent knee, located roughly at the mass scale of the initial Jeans mass. Thus clouds with higher initial Jeans masses produce IMFs which are shallow to higher masses. This implies that a universal IMF requires a physical mechanism that sets the Jeans mass to be near  1 M_⊙  . Simulations including a barotropic equation of state as suggested by Larson, with cooling at low densities followed by gentle heating at higher densities, are able to produce realistic IMFs with the knee located at  ≈1 M_⊙  , even with an initial   M _Jeans= 5 M_⊙  . We therefore suggest that the observed universality of the IMF in the local Universe does not require any fine tuning of the initial conditions in star forming clouds but is instead imprinted by details of the cooling physics of the collapsing gas.     

Unresolved Binaries and the Initial Mass Function

In the area of binary stars the important contribution of GAIA will be towards statistical studies of the binary star distribution functions. On the other hand, from the GAIA observations, more than 10 000 masses accurate to 1% can be expected. This improves accuracy of the stellar initial mass function (IMF) still poorly known, particularly for the low-mass stars. A goal of the present study is to simulate a solar vicinity model with 100% binaries for predicting observational distributions. Under the assumption that star formation rate is constant, a random pairing of objects drawn from a pre-assumed single star power-law IMF is generated. Stellar evolution and selection effects are taken into account. Orbital parameters are assumed to be spread according to the common distributions. It is shown that under given assumptions the power-law IMF does lead to quasi-lognormal turnovers for the resulting observational mass function. The described model can be used to estimate, under reasonable assumptions on the IMF shape, the number of binaries of the different types that can be observed with GAIA. This revised version was published online in July 2006 with corrections to the Cover Date.     

A 'super' star cluster grown old: the most massive star cluster in the Local Group

We independently redetermine the reddening and age of the globular cluster (GC) 037−B327 in M31 by comparing independently obtained multicolour photometry with theoretical stellar population synthesis models. 037−B327 has long been known to have a very large reddening value, which we confirm to be   E ( B − V ) = 1.360 ± 0.013  , in good agreement with the previous results. We redetermine its most likely age at  12.4 ± 3.2 Gyr  .
037−B327 is a prime example of an unusually bright early counterpart to the ubiquitous 'super' star clusters presently observed in most high-intensity star-forming regions in the local Universe. In order to have survived for a Hubble time, we conclude that its stellar initial mass function (IMF) cannot have been top-heavy. Using this constraint, and a variety of simple stellar population (SSP) models, we determine a photometric mass of     , somewhat depending on the SSP models used, the metallicity and age adopted and the IMF representation. This mass, and its relatively small uncertainties, makes this object the most massive star cluster of any age in the Local Group. Assuming that the photometric mass estimate thus derived is fairly close to its dynamical mass, we predict that this GC has a (one-dimensional) velocity dispersion of the order of  (72 ± 13) km s⁻¹  . As a surviving 'super' star cluster, this object is of prime importance for theories aimed at describing massive star cluster evolution.     

Monte Carlo simulations of star clusters – III. A million-body star cluster

A revision of Stodółkiewicz's Monte Carlo code is used to simulate the evolution of million-body star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. The evolution of N -body systems influenced by the tidal field of a parent galaxy and by stellar evolution is presented. All models consist of 1 000 000 stars. The process of energy generation is realized by means of appropriately modified versions of Spitzer's and Mikkola's formulae for the interaction cross-section between binaries and field stars and binaries themselves. The results presented are in good agreement with theoretical expectations and the results of other methods. During the evolution, the initial mass function (IMF) changes significantly. The local mass function around the half-mass radius closely resembles the actual global mass function. At the late stages of evolution, the mass of the evolved stars inside the core can be as high as 97 per cent of the total mass in this region. For the whole system, the evolved stars can compose up to 75 per cent of the total mass. The evolution of cluster anisotropy strongly depends on initial cluster concentration, IMF and the strength of the tidal field. The results presented are the first step in the direction of simulating the evolution of real globular clusters by means of the Monte Carlo method.     

Stellar contents and star formation in the young star cluster Be 59

We present   UBV  I _c   CCD photometry of the young open cluster Be 59 with the aim to study the star formation scenario in the cluster. The radial extent of the cluster is found to be ∼10 arcmin (2.9 pc). The interstellar extinction in the cluster region varies between   E ( B − V ) ≃ 1.4  to 1.8 mag. The ratio of total-to-selective extinction in the cluster region is estimated as  3.7 ± 0.3  . The distance of the cluster is found to be  1.00 ± 0.05 kpc  . Using near-infrared (NIR) colours and slitless spectroscopy, we have identified young stellar objects (YSOs) in the open cluster Be 59 region. The ages of these YSOs range between <1 and ∼2 Myr, whereas the mean age of the massive stars in the cluster region is found to be ∼2 Myr. There is evidence for second-generation star formation outside the boundary of the cluster, which may be triggered by massive stars in the cluster. The slope of the initial mass function, Γ, in the mass range  2.5 < M /M_⊙≤ 28  is found to be  −1.01 ± 0.11  which is shallower than the Salpeter value (−1.35), whereas in the mass range  1.5 < M /M_⊙≤ 2.5  the slope is almost flat. The slope of the K -band luminosity function is estimated as  0.27 ± 0.02  , which is smaller than the average value (∼0.4) reported for young embedded clusters. Approximately 32 per cent of Hα emission stars of Be 59 exhibit NIR excess indicating that inner discs of the T Tauri star (TTS) population have not dissipated. The Midcourse Space Experiment (MSX) and IRAS-HIRES images around the cluster region are also used to study the emission from unidentified infrared bands and to estimate the spatial distribution of optical depth of warm and cold interstellar dust.     

Optical and submillimetre observations of Bok globules – tracing the magnetic field from low to high density

Although the stellar initial mass function (IMF) has only been directly determined in star clusters, it has been manifoldly applied on galaxy-wide scales. But taking the clustered nature of star formation into account the galaxy-wide IMF is constructed by adding all IMFs of all young star clusters leading to an integrated galactic initial mass function (IGIMF). The IGIMF is top-light compared to the canonical IMF in star clusters and steepens with decreasing total star formation rate (SFR). This discrepancy is marginal for large disc galaxies but becomes significant for Small Magellanic Cloud type galaxies and less massive ones. We here construct IGIMF-based relations between the total far- and near-ultraviolet luminosities of galaxies and the underlying SFR. We make the prediction that the Hα luminosity of star-forming dwarf galaxies decreases faster with decreasing SFR than the ultraviolet (UV) luminosity. This turn-down of the Hα/UV-flux ratio should be evident below total SFRs of  10⁻² M_⊙ yr⁻¹  .     

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.     

Determination of the IMF on the basis of a recently derived SFR history in the solar neighbourhood

The initial mass function (IMF) in the solar neighbourhood is determined on the basis of a recently derived history of the star formation rate (SFR) which shows the presence of a star formation burst about 8 Gyr ago. The observed present-day mass function (PDMF) is considered, and the average past distribution of stars of a given mass is estimated. Two cases are considered, namely (i) constant SFR, and (ii) variable SFR as derived from the new metallicity distribution of G dwarfs. The resulting IMF is compared with previous determinations by Scalo and Kroupa et al., and the variation with stellar mass of the slope of the IMF is compared with reference determinations in the literature.     

On the Past Star Formation Rate in the Solar Neighbourhood

The present day mass function (PDMF) is derived from the data material of the immediate solar neighbourhood. From the comparison of the lower mass part (R<R) and the high mass part of the PDMF it is estimated that the mean past star formation rate related to the present one is in the range 0.08—2.0, supposed the initial mass function (IMF) is time independent. References to probable time dependences of the IMF are summarized. Using the PDMF as a constraint on the temporal variation of the IMF, unplausibilities for the star formation rate result if the IMF monotonously flattens in time uniform over the whole mass range.     

Stellar Mass—Halo Mass Relation and Star Formation Efficiency in High-Mass Halos

We study relation between stellar mass and halo mass for high-mass halos using a sample of galaxy clusters with accurate measurements of stellar masses from optical and ifrared data and total masses from X-ray observations. We find that stellar mass of the brightest cluster galaxies (BCGs) scales as M_*,BCG ∝ M ₅₀₀ ^αBCG with the best fit slope of α_BCG ≈ 0.4 ± 0.1. We measure scatter of M_*,BCG at a fixed M₅₀₀ of ≈0.2 dex. We show that stellar mass-halo mass relations from abundance matching or halo modelling reported in recent studies underestimate masses of BCGs by a factor of ～2?4. We argue that this is because these studies used stellar mass functions (SMF) based on photometry that severely underestimates the outer surface brightness profiles of massive galaxies. We show that M_*?M relation derived using abundance matching with the recent SMF calibration by Bernardi et al. (2013) based on improved photometry is in a much better agreement with the relation we derive via direct calibration for observed clusters. The total stellar mass of galaxies correlates with total mass M₅₀₀ with the slope of ≈0.6 ± 0.1 and scatter of 0.1 dex. This indicates that efficiency with which baryons are converted into stars decreases with increasing cluster mass. The low scatter is due to large contribution of satellite galaxies: the stellar mass in satellite galaxies correlates with M₅₀₀ with scatter of ≈0.1 dex and best fit slope of α_sat ≈ 0.8 ± 0.1. We show that for a fixed choice of the initial mass function (IMF) total stellar fraction in clusters is only a factor of 3?5 lower than the peak stellar fraction reached in M ≈ 10¹²M_⊙ halos. The difference is only a factor of ～1.5?3 if the IMF becomes progressively more bottom heavy with increasing mass in early type galaxies, as indicated by recent observational analyses. This means that the overall efficiency of star formation in massive halos is only moderately suppressed compared to L_* galaxies and is considerably less suppressed than previously thought. The larger normalization and slope of the M_*?M relation derived in this study shows that feedback and associated suppression of star formation in massive halos should be weaker than assumed in most of the current semi-analytic models and simulations.     

Star cluster formation and star formation: the role of environment and star-formation efficiencies

By analyzing global starburst properties in various kinds of starburst and post-starburst galaxies and relating them to the properties of the star cluster populations they form, I explore the conditions for the formation of massive, compact, long-lived star clusters. The aim is to determine whether the relative amount of star formation that goes into star cluster formation as opposed to field star formation, and into the formation of massive long-lived clusters in particular, is universal or scales with star-formation rate, burst strength, star-formation efficiency, galaxy or gas mass, and whether or not there are special conditions or some threshold for the formation of star clusters that merit to be called globular clusters a few billion years later.     

The origin of intergalactic thermonuclear supernovae

The population synthesis method is used to study the possibility of explaining the appreciable fraction of the intergalactic type-Ia supernovae (SN Ia), 20 ₋₁₅ ⁺¹² %, observed in galaxy clusters (Gal-Yam et al. 2003) when close white dwarf binaries merge in the cores of globular clusters. In a typical globular cluster, the number of merging double white dwarfs does not exceed ∼10⁻¹³ per year per average cluster star in the entire evolution time of the cluster, which is a factor of ∼3 higher than that in a Milky-Way-type spiral galaxy. From 5 to 30% of the merging white dwarfs are dynamically expelled from the cluster with barycenter velocities up to 150 km s⁻¹. SN Ia explosions during the mergers of double white dwarfs in dense star clusters may account for ∼1% of the total rate of thermonuclear supernovae in the central parts of galaxy clusters if the baryon mass fraction in such star clusters is ∼0.3%.     

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.     

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.