The age determination of young clusters in the large magellanic cloud by means of integrated photometry

The relationt=t(Q), obtained from theoretical integrated colours (B-V)₀ and (U-B)₀ for Pop. I clusters, has been employed to date a group of 13 young clusters in the LMC. The comparison with the ages derived by the t.o.p. method shows that the theoretical integrated colour indices of clusters, with evolved stars in the mass range 5–15M , are systematically bluer than the observed ones.The analysis performed indicate that, in order to reconcile observed and computed colours, the maximum effective temperature of evolved stars should be suitably lowered. The hypothesis has been advanced that such changes can be obtained by the inclusion of the mass loss in the computation of evolutionary tracks.     

疏散星团的质量分层

对疏散星团质量分层的有关问题做了简要的评述,包括空间质量分层和速度质量分层的表现形式和探测途径,质量分层形成机制的研究现状.最后概要介绍了2MASS测光资料对探讨疏散星团质量分层效应的作用.     

A Numerical Simulation Study of Mass Segregation in Embedded Stellar Clusters

The initial condition of the formation of massive stars is still unclear at present. In particular, it is still debatable whether or not massive stars are formed in the cluster center. Some people considered from the viewpoint of time scale and thought that the mass segregation phenomena in embedded clusters means that the massive stars can only be born in the cluster center. In this paper we used the Monte Carlo method to make numerical simulation of the dynamical evolution of embedded clusters and the result is compared with the observations. It is assumed that at the initial time massive stars are randomly distributed. It was found that, due to the random motions of massive stars, temporary mass segregation may exist at certain times in the course of evolution of a given embedded cluster, and this phenomenon may be very prominent in some of them. It is pointed out that massive star formation in the center is not the only explanation for mass segregation in embedded clusters. In addition, dynamical friction from the gas can effectively reduce the time scale of the dynamical mass segregation. In consequence, the probability of temporary mass segregation is increased.     

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.     

星系团的分层效应

对星系团各类分层效应的有关问题做了概要的评述,包括成员星系在位置空间和(或)速度空间中的形态分层、光度(质量)分层和元素丰度分层的表现形式和探测途径,分层效应可能的形成机制及其对星系和星系团的结构和演化的影响。     

Using the minimum spanning tree to trace mass segregation

We present a new method to detect and quantify mass segregation in star clusters. It compares the minimum spanning tree (MST) of massive stars with that of random stars. If mass segregation is present, the MST length of the most massive stars will be shorter than that of random stars. This difference can be quantified (with an associated significance) to measure the degree of mass segregation. We test the method on simulated clusters in both 2D and 3D and show that the method works as expected.
We apply the method to the Orion Nebula Cluster (ONC) and show that the method is able to detect the mass segregation in the Trapezium with a 'mass segregation ratio (MSR)'  Λ_MSR= 8.0 ± 3.5  (where  Λ_MSR= 1  is no mass segregation) down to  16 M_⊙  , and also that the ONC is mass segregated at a lower level  (∼2.0 ± 0.5)  down to  5 M_⊙  . Below  5 M_⊙  we find no evidence for any further mass segregation in the ONC.     

Colour gradients in globular clusters

Radial colour gradients in the globular clusters NGC 2808, NGC 1851, NGC 5139, NGC 5139, NGC 6388, NGC 6441, NGC 6541, NGC 6723, and NGC 7099 were searched byB-V and DDO photoelectric photometry, using a set of circular diaphragms. Two of the observed globular clusters, NGC 5139 (Cen) and NGC 7099 (M30), showedB-V and C(45–48) colour gradients; the colour C(42–45) is essentially constant in these clusters, which means that the physical reason for those gradients cannot be attributed to chemical composition variations, since C(42–45) is a good metal abundance indicator.B-V colours in the external regions of NGC 5139 and NGC 7099 were obtained by synthesizing the observed HR diagrams of these clusters. The ages and the relaxation times for NGC 5139 and NGC 7099 indicate that mass segregation must have taken place in both clusters, which is probably related to the observed colour gradients.     

Integrated magnitudes and colors of open clusters

The integratedUBV characteristics of 50 galactic clusters, computed for the clusters' physical members only (segregated on the basis of the proper motions or radial velocities) are discussed.On the basis of a comparison between the empirically-obtained dependences and their theoretical counterparts (Searleet al., 1973) a suggestion has been made that the number of the massive stars (with masses>10M ) in the initial mass function must be considerably greater.Evolutionary effects on integrated parameters and their dependences have been discussed. An attempt at an evolutionary interpretation of the integrated luminosity function for galactic clusters, obtained by Starikova (1962) in the light of the self-obtained dependences has been made.     

The system of old clusters in the magellanic clouds

IntegratedUBV colours have been computed for synthetic clusters older than one billion years and for two chemical composition: (a)Y=0.30;Z=10^–4 and (b)Y=0.30;Z=10^–2, taking into account the contribution to the integrated light of Main Sequence, subgiant, red giant and horizontal branch stars. It has been found that integrated colours depend onZ and allow an estimate of the metal content, however not generally. Horizontal branch stars contribute to the integrated colours of clusters not significantly and the contribution of stars in more advanced phases (e.g., asymptotic branch stars) is almost negligible.Old clusters in LMC and SMC have been studied in terms of colour calibrations and this analysis has been supplemented, when possible, by photometric and spectroscopic data of individual stars. It was found that in the LMC clusters withZ=10^–2 andt>5×10⁹ yr are lacking, clusters with relatively blue colours are similar, both in age and chemical composition, to the halo galactic globular clusters. Moreover, there is a group of clusters with 1×10⁹t5×10⁹. In the SMC clusters withZ=10^–2 andt>5×10⁹ yr are lacking and clusters with 1×10⁹t5×10⁹ are rare. Clusters with relatively blue colours are interpreted with the following parameters:t=5×10⁹ yr, 10^–4Z10^–3 andY=0.20.The implication of these results on the chemical history of the two galaxies is discussed.     

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.     

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.     

Dark matter influence on velocity dispersion profiles of clusters of galaxies

We have performed a series ofN-body experiments including the effects of a massive dominant background which follows Schuster's density law in order to simulate clusters of galaxies in which a smoothly distributed dark component is present. The existence of this background is inferred from the weak luminosity segregation observed in clusters which, however, show several characteristics of well-relaxed systems. The comparison of the velocity dispersion profiles of three clusters of galaxies (Coma, Perseus, and Virgo) with those obtained in the numerical experiments allows us to place some constraints on both the distribution and amount of distributed dark material in these clusters. The profiles are rather insensitive to variations in the ratio of the background mass to the mass attached to galaxies (M _b/M_g), but exhibit a strong dependence on their relative concentration. We conclude that highly concentrated background models are not consistent with observations. We find a maximum value for the ratio of the gravitational radius of the galaxies and the background (R _g/R_b) (approximately 0.6) and using previous results (Navarroet al., 1986) we conclude that virial theorem masses underestimate the total mass (M _b+M _g) of the clusters. As a final result, we derive a minimum value for theM _b/M_g ratio. All these conclusions could apply in general if Coma, Perseus, and Virgo constitute a fair sample of the rich clusters of galaxies in the Universe.     

Note on the spatial distribution of old open clusters

Using the sample of 74 old open clusters compiled by Friel (1995) the increase of the mean distance from the galactic plane with cluster age has been determined. The result is in a qualitative agreement with the hypothesis of scattering of the clusters during encounters with massive molecular clouds and by spiral arms. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Mass segregation in young clusters: observational biases

We investigate the validity of the mass-segregation indicators most commonly used in the analysis of young stellar clusters. We construct and analyze synthetic massive clusters with a standard, fully sampled stellar initial mass function and a King density distribution function. We find that the commonly used indicators are highly sensitive to the effects of incompleteness in observational data, and that completeness determinations do not provide satisfactory corrections, leading to results that may be severely biased toward mass segregation.     

The globular clusters–stellar haloes connection in early-type galaxies

This paper explores if, and to what an extent, the stellar populations of early-type galaxies can be traced through the colour distribution of their globular cluster (GC) systems. The analysis, based on a galaxy sample from the Virgo Advanced Camera for Surveys data, is an extension of a previous approach that has been successful in the cases of the giant ellipticals NGC 1399 and NGC 4486, and assumes that the two dominant GC populations form along diffuse stellar populations sharing the cluster chemical abundances and spatial distributions. The results show that (a) integrated galaxy colours can be matched to within the photometric uncertainties and are consistent with a narrow range of ages; (b) the inferred mass to luminosity ratios and stellar masses are within the range of values available in the literature; (c) most GC systems occupy a thick plane in the volume space defined by the cluster formation efficiency, total stellar mass and projected surface mass density. The formation efficiency parameter of the red clusters shows a dependency with projected stellar mass density that is absent for the blue globulars. In turn, the brightest galaxies appear clearly detached from that plane as a possible consequence of major past mergers; (d) the stellar mass–metallicity relation is relatively shallow but shows a slope change at   M _*≈ 10¹⁰ M_⊙  . Galaxies with smaller stellar masses show predominantly unimodal GC colour distributions. This result may indicate that less massive galaxies are not able to retain chemically enriched interstellar matter.     

Stellar contents of two young open clusters: NGC 663 and 654

UBVRI CCD photometry in a wide field around two young open clusters, NGC 663 and 654, has been carried out. Hα and polarimetric observations for the cluster NGC 654 have also been obtained. We use the photometric data to construct colour–colour and colour–magnitude diagrams, from which we can investigate the reddening, age, mass and evolutionary states of the stellar contents of the these clusters. The reddening across the cluster regions is found to be variable. There is evidence for anomalous reddening law in both clusters; however, more infrared and polarimetric data are needed to conclude about the reddening law. Both clusters are situated at about a distance of 2.4 kpc. Star formation in both clusters is found to be a continuous process. In the case of NGC 663, star formation seems to have taken place sequentially, in the sense that formation of low-mass stars precedes the formation of most massive stars. Whereas, in the case of NGC 654, formation of low-mass stars did not cease after the formation of most massive stars in the cluster.     

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.     

Galaxies and Star Clusters – From the Computer to the Real World

G01 New evidence for a connection between massive black holes and ULX G02 Long‐Term Evolution of Massive Black Hole Binaries G03 NBODY Meets Stellar Population Synthesis G04 N‐body modelling of real globular star clusters G05 Fokker‐Planck rotating models of globular clusters with black hole G06 Observational Manifestation of chaos in spiral galaxies: quantitative analysis and qualitative explanation G07 GRAPE Clusters: Beyond the Million‐Body Problem G08 Orbital decay of star clusters and Massive Black Holes in cuspy galactic nuclei G09 An Edge‐on Disk Galaxy Catalog G10 Complexes of open clusters in the Solar neighborhood G11 Search for and investigation of new stellar clusters using the data from huge stellar catalogues G12 Computing 2D images of 3D galactic disk models G13 Outer Pseudoring in the Galaxy G14 Where are tidal‐dwarf galaxies? G15 Ultra compact dwarf galaxies in nearby clusters G16 Impact of an Accretion Disk on the Structure of a stellar cluster in active galactic nuclei G17 Order and Chaos in the edge‐on profiles of disk galaxies G18 On the stability of OB‐star configurations in the Orion Nebula cluster G19 Older stars captured in young star clusters by cloud collapse G20 General features of the population of open clusters within 1 kpc from the Sun G21 Unstable modes in thin stellar disks G22 From Newton to Einstein – Dynamics of N‐body systems G23 On the relation between the maximum stellar mass and the star cluster mass     

Binary population synthesis for blue stragglers

In this talk, we will simply show the consequences of binary population synthesis for blue stragglers, such as the integrated spectral energy distribution (ISED), the color-magnitude diagram, the specific frequency, and the influences on colors. Blue stragglers have been found in all stellar populations and they are an important population component in both stellar evolution and star clusters. Much evidence shows that blue stragglers are relevant to primordial binaries. The binary population synthesis study shows that primordial binary evolution may produce blue stragglers at any given times. The specific frequency in this way decreases with time first, then increases when the age is larger than 10 Gyr, while that from angular momentum loss induced by magnetic braking in low-mass binaries increases with time and exceeds that of primordial binary evolution in a population older than 3 Gyr. Meanwhile, blue stragglers resulting from primordial binary evolution are dominant contributors to the ISEDs in ultraviolet and blue bands in a population between 0.3 and 2.0 Gyr. The mass fraction of the lost matter from the primary accreted by the secondary, β, significantly affects on the final results, e.g. the specific frequency of blue stragglers decreasing with β, blue stragglers produced from a high value of β being more massive, then contributing more to the ISEDs of the host clusters. For old open clusters, it is appropriate to adopt a higher value of β when the primary is in HG at the onset of mass transfer. Our study also shows that, for most Galactic open clusters, the specific frequency of blue stragglers obtained from our simulations is much lower than that of observations, which has been discussed in this talk.