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.     

Study of the nearest open clusters and the associated moving clusters by numerical simulations

In our previous papers, we showed that at the final phases of the dynamical evolution of an open cluster, an extended population of stars elongated along its Galactic orbit, the stellar tail of the cluster, is formed. The tail stars that escaped from the cluster at different times move in a common orbit with low relative velocities. Experiencing a weak interaction with Galactic field stars, these objects, the relics of open clusters, can exist for a fairly long time. In this paper, we investigate the structures of such stellar tails in the nearest open clusters: Hyades, Pleiades, Praesepe, Alpha Persei, Coma, IC 2391, and IC 2602. To this end, we performed several numerical simulations of the dynamical evolution of these clusters in the tidal field of the Galaxy. Our computations of the dynamical evolution were based on known cluster age estimates and real Galactic orbits. The initial conditions were chosen in such a way that the parameters of the simulated clusters corresponded to their observed parameters. As a result, we obtained models of the stellar tails for the nearest open clusters and estimated such parameters of the tails as their sizes, densities, locations relative to the solar neighborhood, and others.     

Direct N-body modelling of stellar populations: blue stragglers in M67

We present a state-of-the-art N -body code which includes a detailed treatment of stellar and binary evolution as well as the cluster dynamics. This code is ideal for investigating all aspects relating to the evolution of star clusters and their stellar populations. It is applicable to open and globular clusters of any age. We use the N -body code to model the blue straggler population of the old open cluster M67. Preliminary calculations with our binary population synthesis code show that binary evolution alone cannot explain the observed numbers or properties of the blue stragglers. On the other hand, our N -body model of M67 generates the required number of blue stragglers and provides formation paths for all the various types found in M67. This demonstrates the effectiveness of the cluster environment in modifying the nature of the stars it contains, and highlights the importance of combining dynamics with stellar evolution. We also perform a series of N =10 000 simulations in order to quantify the rate of escape of stars from a cluster subject to the Galactic tidal field.     

疏散星团中的耀星及其演化学意义

耀星是红矮星早期演化的一个必经阶段，这个阶段的持续时间取决于恒星的质量。在年轻和比较年轻的疏散星闭中，都含有大量耀星，它们的光度分布是疏散星闭年龄的标志。在昴生闭中已发现大量耀星，对它们的自行，测光和分光资料进行深入的统计研究，对于解决疏散星闭及矮星起源和演化问题，有着极其重要的价值。     

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.     

Evidence of recent changes in the local Galactic IMF of stars and substars

This paper calculates the stellar–substellar initial mass function (IMF) based on data from low-luminosity stars and substars. We find the mass spectrum for the stars and substars less than 10 million years in age, and we estimate the low-mass part of the stellar–substellar IMF for 10 million years ago.     

Numerical experiments on the escape from non-isolated clusters and the formation of multiple stars

Isolated and non isolated clusters with a mass distribution have been studied by numerical techniques. The rates of escape of stars and of kinetic energy are compared with Hénon's theoretical expressions. Multiple encounters play a very important role in the escape phenomenon, at least for clusters with a small number of stars. This leads to a theoretical underestimate of the rates of escape when the stars have equal masses and to an overestimate when masses are unequal.For non isolated clusters, the tidal field of the Galaxy is responsible for one half of the rate of escape of the stars. The energy of a star escaping because of the tidal effect grown slowly while that of a star escaping after an encounter increases very rapidly. The stars escaping because of the tidal effect leave the cluster in the vicinity of the equilibrium points.Encounters and the tidal field are not efficient enought to explain why very old open clusters are not observed. Other escape mechanisms have to be considered.Very stable subsystems are formed which are not destroyed under the influence of the galactic tide. Separation between stars can be as low as 100 UA.     

The galactic evolution of lithium

Measurements of lithium in stars of different galactic populations such as young open clusters ( Per, Pleiades, Praesepe, Coma, Hyades), very young stellar associations (Taurus-Auriga, Chamaeleon, Ophiuchus clouds), intermediate and old open clusters (NGC 752, M 67, NGC 188), old disc stars and halo stars give us the observational framework from which the galactic evolution of lithium has to be inferred. This element is produced mainly via three mechanisms: primordial nucleosynthesis, spallation reactions in the interstellar medium and thermonuclear reactions in some particular stellar evolutionary stages (novae, red giants). The complicated nucleosynthesis and the fact that astration of lithium in stars is not well understood, makes a direct interpretation of the lithium evolutionary abundance curve difficult. The constraints set by recent lithium measurements in very old open clusters and metal-deficient stars on galactic lithium production mechanisms are discussed. Current problems in the determination of the primordial lithium abundance are briefly reviewed.     

Flare star activity in the open cluster Alpha Persei

The results from a flare star investigation in the open cluster Alpha Persei are presented. Photographic flare star monitoring and CCD photometry of the discovered 4 new flare stars are made. The flare star activity phenomenon is restricted to the classical flare stars (UV Ceti type) as classified in the GCVS. The V/V‐I diagramme of the members of the cluster with the locations of the considered flare stars is given. Most of the flare stars are probable cluster members. The flare frequency determined from the Rozhen flare star monitoring is very low–one flare event occurs for 38.5 hours effective observing time. Comparison with the flare activity of the Pleiades is made because of the small difference in the age and distance of the clusters.     

Scaling of N-body calculations

We report results of collisional N -body simulations aimed at studying the N dependence of the dynamical evolution of star clusters. Our clusters consist of equal-mass stars and are in virial equilibrium. Clusters moving in external tidal fields and clusters limited by a cut-off radius are simulated. Our main focus is to study the dependence of the lifetimes of the clusters on the number of cluster stars and the chosen escape condition.
We find that star clusters in external tidal fields exhibit a scaling problem in the sense that their lifetimes do not scale with the relaxation time. Isolated clusters show a similar problem if stars are removed only after their distance to the cluster centre exceeds a certain cut-off radius. If stars are removed immediately after their energy exceeds the energy necessary for escape, the scaling problem disappears.
We show that some stars that gain the energy necessary for escape are scattered to lower energies before they can leave the cluster. As the efficiency of this process decreases with increasing particle number, it causes the lifetimes not to scale with the relaxation time. Analytic formulae are derived for the scaling of the lifetimes in the different cases.     

Numerical simulations of the Hyades dynamics and the nature of the moving Hyades cluster

We present our numerical simulations of the dynamical evolution of the Hyades open cluster. The simulations were performed usinga modified NBODY6 algorithm that included tidal forces and a realistic orbit of the cluster in a gravitational field described by the Miyamoto-Nagai potential. Our goal was to study the nature of movingclu sters. We show that the stars that were earlier cluster members could be later identified within a sphere of 50 pc in diameter around the Sun. The number of such stars for the chosen initial mass and virial radius of the cluster does not exceed ten. The maximum space velocity of these stars relative to the core of the current cluster does not exceed 3 km s^?1. Our numerical simulations confirm the assumption that some of the moving clusters near the Sun could consist of stars that have escaped from open clusters in the course of their dynamical evolution.     

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.     

Dynamics of very rich open clusters

The oldest open clusters in our Galaxy set the lower limit to the age of the Galactic Disk (9–10 Gyr). Although they appear to be very rich now, it is clear that their primordial populations were much larger. Often considered as transitional objects, these populous open clusters show structural differences with respect to globular clusters so their dynamics and characteristic evolutionary time scales can also be different. On the other hand, their large membership lead to different dynamical evolution as compared with average open clusters. In this paper, the differential features of the evolution of rich open clusters are studied using N-body simulations, including several of the largest (10⁴ stars) published direct collisional N-body calculations so far, which were performed on a CRAY YMP. The disruption rate of rich open clusters is analysed in detail and the effect of the initial spatial distribution of the stars in the cluster on its dynamics is studied. The results show that cluster life-time depends on this initial distribution, decreasing when it is more concentrated. The effect of stellar evolution on the dynamical evolution of rich clusters is an important subject that also has been considered here. We demonstrate that the cluster's life-expectancy against evaporation increases because of mass loss by evolving high-mass stars. This revised version was published online in July 2006 with corrections to the Cover Date.     

The empirical upper limit for mass loss of cool main sequence stars

The knowledge of mass loss rates due to thermal winds in cool dwarfs is of crucial importance for modeling the evolution of physical parameters of main sequence single and binary stars. Very few, sometimes contradictory, measurements of such mass loss rates exist up to now. We present a new, independent method of measuring an amount of mass lost by a star during its past life. It is based on the comparison of the present mass distribution of solar type stars in an open cluster with the calculated distribution under an assumption that stars with masses lower than M_lim have lost an amount of mass equal to ΔM. The actual value of ΔM or its upper limit is found from the best fit. Analysis of four clusters: Pleiades, NGC 6996, Hyades and Praesepe gave upper limits for ΔM in three of them and the inconclusive result for Pleiades. The most restrictive limit was obtained for Praesepe indicating that the average mass loss rate of cool dwarfs in this cluster was lower than 6 × 10^–11 M_⊙/yr. With more accurate mass determinations of the solar type members of selected open clusters, including those of spectral type K, the method will provide more stringent limits for mass loss of cool dwarfs. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

The origin of the initial mass function and its dependence on the mean Jeans mass in molecular clouds

We investigate the dependence of stellar properties on the mean thermal Jeans mass in molecular clouds. We compare the results from the two largest hydrodynamical simulations of star formation to resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical except for the radii of the clouds, which are chosen so that the mean densities and mean thermal Jeans masses of the clouds differ by factors of 9 and 3, respectively.
We find that the denser cloud, with the lower mean thermal Jeans mass, produces a higher proportion of brown dwarfs and has a lower characteristic (median) mass of the stars and brown dwarfs. This dependence of the initial mass function (IMF) on the density of the cloud may explain the observation that the Taurus star-forming region appears to be deficient in brown dwarfs when compared with the Orion Trapezium cluster. The new calculation also produces wide binaries (separations >20 au), one of which is a wide binary brown dwarf system.
Based on the hydrodynamical calculations, we develop a simple accretion/ejection model for the origin of the IMF. In the model, all stars and brown dwarfs begin with the same mass (set by the opacity limit for fragmentation) and grow in mass until their accretion is terminated stochastically by their ejection from the cloud through dynamically interactions. The model predicts that the main variation of the IMF in different star-forming environments should be in the location of the peak (due to variations in the mean thermal Jeans mass of the cloud) and in the substellar regime. However, the slope of the IMF at high masses may depend on the dispersion in the accretion rates of protostars.     

A revisit to agglomerates of early‐type Hipparcos stars

We study the spatial structure and sub‐structure of regions rich in Hipparcos stars with blue B_T – V_T colours. These regions, which comprise large stellar complexes, OB associations, and young open clusters, are tracers of on‐going star formation in the Galaxy. The DBSCAN (Density‐Based Spatial Clustering of Applications with Noise) data clustering algorithm is used to look for spatial overdensities of early‐type stars. Once an overdensity, “agglomerate”, is identified, we carry out a data and bibliographic compilation of their star member candidates. The actual membership in agglomerate of each early‐type star is studied based on its heliocentric distance, proper motion, and previous spectro‐photometric information. We identify 35 agglomerates of early‐type Hipparcos stars. Most of them are associated to previously known clusters and OB associations. The previously unknown P Puppis agglomerate is subject of a dedicated study with Virtual Observatory tools. It is actually a new, nearby, young open cluster (d ∼ 470 pc, age ∼ 20 Ma) with a clear radial density gradient.We list P Puppis and other six agglomerates (including NGC 2451 A, vdBH 23, and Trumpler 10) as new sites for substellar searches because of their youth, closeness, and spatial density. We investigate in detail the sub‐structure in the Orion, CMa‐Pup and Pup‐Vel OB complexes (“super‐agglomerates”). We confirm or discover some stellar overdensities in the Orion complex, like the 25 Ori group, the Horsehead region (including the σ Orionis cluster), and the η Orionis agglomerate. Finally, we derive accurate parallactic distances to the Pleiades, NGC 2451 A, and IC 2391, describe several field early‐type stars at d < 200 pc, and discuss the incompleteness of our search. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Faint stars in the Ursa Minor dwarf spheroidal galaxy: implications for the low-mass stellar initial mass function at high redshift

The stellar initial mass function at high redshift is an important defining property of the first stellar systems to form and may also play a role in various dark matter problems. We here determine the faint stellar luminosity function in an apparently dark-matter-dominated external galaxy in which the stars formed at high redshift. The Ursa Minor dwarf spheroidal galaxy is a system with a particularly simple stellar population—all of the stars being old and metal-poor—similar to that of a classical halo globular cluster. A direct comparison of the faint luminosity functions of the UMi dSph and of similar metallicity, old globular clusters is equivalent to a comparison of the initial mass functions and is presented here, based on deep HST WFPC2 and STIS imaging data. We find that these luminosity functions are indistinguishable, down to a luminosity corresponding to ∼0.3 M_⊙. Our results show that the low-mass stellar IMF for stars that formed at very high redshift is apparently invariant across environments as diverse as those of an extremely low-surface-brightness, dark-matter-dominated dwarf galaxy and a dark-matter-free, high-density globular cluster within the Milky Way.     

Untersuchungen über den Aufbau offener Sternhaufen

From strip counts in 20 open star clusters the characteristic parameters of their structure are derived. At the boundaries of the clusters the relative potential amounts to 0.32 on the average. The effective mean distance of the stars from the centre of the cluster introduced by SCHWARZSCHILD corresponds nearly to the radius of the cluster. The counts in two clusters allow to continue the cumulative mass functions up to Mv ≈ 8, and their exponential convergence is used for the determination of the cluster masses. The same has been done for the Pleiades and seven clusters according to the counts of VAN DEN BERGH and SHER . The mean velocities and the mean periods of revolution T of the cluster stars are of the order 0.90 km/s and 12 · 10⁶ years respectively. Between the latter and the mean (mass) density the relation T ≈≈ 20 · 10⁶ is valid. During 1 · 10⁹ years the mean cluster loses 50% of its stars by relaxation.