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1.
In this paper a cluster is modelled as a smooth potential (due to the cluster stars) plus the steady tidal field of the Galaxy. In this model there is a minimum energy below which stars cannot escape. Above this energy, however, the time-scale on which a star escapes varies with the orbital parameters of the star (mainly its energy) in a way which we attempt to quantify, with both theoretical arguments and computer simulations. Within the limitations of the model we show that the time-scale is long enough to complicate the interpretation of full N -body simulations of clusters, and that stars above the escape energy may remain bound to the cluster for about a Hubble time.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
Dynamical evolution of globular clusters in the Large Magellanic Cloud (LMC) is investigated by means of N-body simulations; particular attention is paid to time evolution in the ellipticitical figure of globular clusters. The simulations were started with a binary globular cluster. It merged into a single cluster with ellipticity of about 0.3. The simulations were continued until the cluster became rounder due to the effects of two body relaxation and of tidal field of LMC. It is found that the outward angular momentum transport due to the gravothermal contraction makes the inner region rounder; the ellipticity at about the initial half-mass radius (r h) decreases with the e-folding time of 20 relaxation times. On the other hand, the outer region becomes rounder due to the stripping of stars by the tidal field; the ellipticity at about 3r h decreases with the e-folding time of 80 crossing times therein, though the time scale depends on the direction of the tidal field relative to the spin of the cluster. These two effects are comparable at about the half-mass radius. Taking account of such theoretical results we reanalyzed observed data for the ellipticity at about the half-mass radius of LMC clusters. We estimated the relaxation time and crossing time for each of the observed clusters, from which we calculated the effective time of getting round of the cluster. We plotted the observed ellipticity of the clusters against their non-dimensional age — i.e., the age normalized by the effective time. We found that observed ellipticity distribution is consistent with our picture.  相似文献   

5.
We consider the use of N -body simulations for studying the evolution of rich star clusters (i.e. globular clusters).The dynamical processes included in this study are restricted to gravitational (point-mass) interactions, the steady tidal field of a galaxy, and instantaneous mass loss resulting from stellar evolution. With evolution driven by these mechanisms, it is known that clusters fall roughly into two broad classes: those that dissipate promptly in the tidal field, as a result of mass loss; and those that survive long enough for their evolution to become dominated by two-body relaxation.
The time-scales of the processes we consider scale in different ways with the number of stars in the simulation, and the main aim of the paper is to suggest how the scaling of a simulation should be done so that the results are representative of the evolution of a 'real' cluster. We investigate three different ways of scaling time. One of these is appropriate to the first type of cluster, i.e. those that dissipate rapidly; similarly, a second scaling is appropriate only to the second (relaxation-dominated) type. We also develop a hybrid scaling, which is a satisfactory compromise for both types of cluster. Finally we present evidence that the widely used Fokker–Planck method produces models that are in good agreement with N -body models of those clusters that are relaxation-dominated, at least for N -body models with several thousand particles, but that the Fokker–Planck models evolve too fast for clusters that dissipate promptly.  相似文献   

6.
Tidal tails of star clusters are not homogeneous but show well-defined clumps in observations as well as in numerical simulations. Recently, an epicyclic theory for the formation of these clumps was presented. A quantitative analysis was still missing. We present a quantitative derivation of the angular momentum and energy distribution of escaping stars from a star cluster in the tidal field of the Milky Way and derive the connection to the position and width of the clumps. For the numerical realization we use star-by-star N -body simulations. We find a very good agreement of theory and models. We show that the radial offset of the tidal arms scales with the tidal radius, which is a function of cluster mass and the rotation curve at the cluster orbit. The mean radial offset is 2.77 times the tidal radius in the outer disc. Near the Galactic Centre the circumstances are more complicated, but to lowest order the theory still applies. We have also measured the Jacobi energy distribution of bound stars and showed that there is a large fraction of stars (about 35 per cent) above the critical Jacobi energy at all times, which can potentially leave the cluster. This is a hint that the mass loss is dominated by a self-regulating process of increasing Jacobi energy due to the weakening of the potential well of the star cluster, which is induced by the mass loss itself.  相似文献   

7.
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.  相似文献   

8.
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.  相似文献   

9.
银晕外区存在众多星流,它们或源自银河系的矮伴星系,或源自晕族球状星团,常分别称为矮星系星流和球状星团潮汐尾。星流可以利用各类示踪星,并通过不同的途径加以探测,对若干代表性矮星系星流和球状星团潮汐尾的探测进展做了简要的介绍。  相似文献   

10.
Based on recent findings of a formation mechanism of substructure in tidal tails by Küpper et al., we investigate a more comprehensive set of N -body models of star clusters on orbits about a Milky Way like potential. We find that the predicted epicyclic overdensities arise in any tidal tail no matter which orbit the cluster follows as long as the cluster lives long enough for the overdensities to build up.
The distance of the overdensities along the tidal tail from the cluster centre depends for circular orbits only on the mass of the cluster and the strength of the tidal field, and therefore decreases monotonically with time, while for eccentric orbits the orbital motion influences the distance, causing a periodic compression and stretching of the tails and making the distance oscillate with time. We provide an approximation for estimating the distance of the overdensities in this case.
We describe an additional type of overdensity which arises in extended tidal tails of clusters on eccentric orbits, when the acceleration of the tidal field on the stellar stream is no longer homogeneous. Moreover, we conclude that a pericentre passage or a disc shock is not the direct origin of an overdensity within a tidal tail. Escape due to such tidal perturbations does not take place immediately after the perturbation but is rather delayed and spread over the orbit of the cluster. All observable overdensities are therefore of the mentioned two types. In particular, we note that substructured tidal tails do not imply the existence of dark matter substructures in the haloes of galaxies.  相似文献   

11.
恒星的Al元素丰度可以为探索星团和星系的化学演化提供重要线索.通过系统分析银河系薄盘、厚盘、核球、银晕以及M4、M5等球状星团中恒星的[Al/Fe]随恒星金属丰度[Fe/H]的变化趋势,得出银河系薄盘、厚盘和核球恒星的[Al/Fe]随着[Fe/H]的增加而缓慢下降,而球状星团M4和M5恒星的[Al/Fe]随[Fe/H]增加没有下降趋势,这暗示Ia超新星对M4和M5恒星元素丰度的贡献比较小.详细研究了银河系恒星[Al/Fe]与[Mg/Fe]、[Na/Fe]的相关性,结果表明银河系场星的[Al/Fe]与[Mg/Fe]正相关,但在球状星团M4和M5恒星中未见此相关性;银河系盘星及M4和M5等球状星团恒星的[Al/Fe]与[Na/Fe]都存在正相关.  相似文献   

12.
The new approach outlined in Paper I to follow the individual formation and evolution of binaries in an evolving, equal point-mass star cluster is extended for the self-consistent treatment of relaxation and close three- and four-body encounters for many binaries (typically a few per cent of the initial number of stars in the cluster mass). The distribution of single stars is treated as a conducting gas sphere with a standard anisotropic gaseous model. A Monte Carlo technique is used to model the motion of binaries, their formation and subsequent hardening by close encounters, and their relaxation (dynamical friction) with single stars and other binaries. The results are a further approach towards a realistic model of globular clusters with primordial binaries without using special hardware. We present, as our main result, the self-consistent evolution of a cluster consisting of 300 000 equal point-mass stars, plus 30 000 equal-mass binaries over several hundred half-mass relaxation times, well into the phase where most of the binaries have been dissolved and evacuated from the core. The cluster evolution is about three times slower than found by Gao et al. Other features are rather comparable. At every moment we are able to show the individual distribution of binaries in the cluster.  相似文献   

13.
We examine the longitudinal distribution of the stars escaping from a cluster along tidal tails. Using both theory and simulations, we show that, even in the case of a star cluster in a circular galactic orbit, when the tide is steady, the distribution exhibits maxima at a distance of many tidal radii from the cluster.  相似文献   

14.
We present an analysis of the spatial distribution of various stellar populations within the Large Magellanic Cloud (LMC). We combine mid-infrared selected young stellar objects, optically selected samples with mean ages between ∼9 and ∼1000 Myr and existing stellar cluster catalogues to investigate how stellar structures form and evolve within the LMC. For the analysis we use Fractured Minimum Spanning Trees, the statistical Q parameter and the two-point correlation function. Restricting our analysis to young massive (OB) stars, we confirm our results obtained for M33, namely that the luminosity function of the groups is well described by a power law with index −2, and that there is no characteristic length-scale of star-forming regions. We find that stars in the LMC are born with a large amount of substructure, consistent with a two-dimensional fractal distribution with dimension     and evolve towards a uniform distribution on a time-scale of ∼175 Myr. This is comparable to the crossing time of the galaxy, and we suggest that stellar structure, regardless of spatial scale, will be eliminated in a crossing time. This may explain the smooth distribution of stars in massive/dense young clusters in the Galaxy, while other, less massive, clusters still display large amounts of structure at similar ages. By comparing the stellar and star cluster distributions and evolving time-scales, we show that infant mortality of clusters (or 'popping clusters') has a negligible influence on the galactic structure. Finally, we quantify the influence of the elongation, differential extinction and contamination of a population on the measured Q value.  相似文献   

15.
We analyse the angular momentum evolution from the red giant branch (RGB) to the horizontal branch (HB) and along the HB. Using rotation velocities for stars in the globular cluster M13, we find that the required angular momentum for the fast rotators is up to 1–3 orders of magnitude (depending on some assumptions) larger than that of the Sun. Planets of masses up to 5 times Jupiter's mass and up to an initial orbital separation of ~2 au are sufficient to spin-up the RGB progenitors of most of these fast rotators. Other stars have been spun-up by brown dwarfs or low-mass main-sequence stars. Our results show that the fast rotating HB stars have been probably spun-up by planets, brown dwarfs or low-mass main-sequence stars while they evolved on the RGB. We argue that the angular momentum considerations presented in this paper further support the 'planet second parameter' model. In this model, the 'second parameter' process, which determines the distribution of stars on the HB, is interaction with low-mass companions, in most cases with gas-giant planets, and in a minority of cases with brown dwarfs or low-mass main-sequence stars. The masses and initial orbital separations of the planets (or brown dwarfs or low-mass main-sequence stars) form a rich spectrum of different physical parameters, which manifests itself in the rich varieties of HB morphologies observed in the different globular clusters.  相似文献   

16.
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.  相似文献   

17.
We performed high-resolution simulations of two stellar collisions relevant for stars in globular clusters. We considered one head-on collision and one off-axis collision between two 0.6-M⊙ main-sequence stars. We show that a resolution of about 100 000 particles is sufficient for most studies of the structure and evolution of blue stragglers. We demonstrate conclusively that collision products between main-sequence stars in globular clusters do not have surface convection zones larger than 0.004 M⊙ after the collision, nor do they develop convection zones during the 'pre-main-sequence' thermal relaxation phase of their post-collision evolution. Therefore, any mechanism which requires a surface convection zone (i.e. chemical mixing or angular momentum loss via a magnetic wind) cannot operate in these stars. We show that no disc of material surrounding the collision product is produced in off-axis collisions. The lack of both a convection zone and a disc proves a continuing problem for the angular momentum evolution of blue stragglers in globular clusters.  相似文献   

18.
We present 3D hydrodynamical simulations of ram-pressure stripping of a disc galaxy orbiting in a galaxy cluster. In this paper, we focus on the properties of the galaxies' tails of stripped gas. The galactic wakes show a flaring width, where the flaring angle depends on the gas disc's cross-section with respect to the galaxy's direction of motion. The velocity in the wakes shows a significant turbulent component of a few     . The stripped gas is deposited in the cluster rather locally, i.e. within     from where it was stripped. We demonstrate that the most important quantity governing the tail density, length and gas mass distribution along the orbit is the galaxy's mass-loss per orbital length. This in turn depends on the ram pressure as well as the galaxy's orbital velocity.
For a sensitivity limit of     in projected gas density, we find typical tail lengths of     . Such long tails are seen even at large distances (0.5 to     ) from the cluster centre. At this sensitivity limit, the tails show little flaring, but a width similar to the gas disc's size.
Morphologically, we find good agreement with the H  i tails observed in the Virgo cluster by Chung et al. 2007 . However, the observed tails show a much smaller velocity width than predicted from the simulation. The few known X-ray and Hα tails are generally much narrower and much straighter than the tails in our simulations. Thus, additional physics like a viscous intracluster medium (ICM), the influence of cooling and tidal effects may be needed to explain the details of the observations.
We discuss the hydrodynamical drag as a heat source for the ICM but conclude that it is not likely to play an important role, especially not in stopping cooling flows.  相似文献   

19.
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.  相似文献   

20.
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.  相似文献   

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