Parameters of core collapse

This paper considers the phenomenon of deep core collapse in collisional stellar systems, with stars of equal mass. The collapse takes place on some multiple,  ξ⁻¹  , of the central relaxation time, and produces a density profile in which  ρ∝ r ^−α  , where α is a constant. The parameters α and ξ have usually been determined from simplified models, such as gas and Fokker–Planck models, often with the simplification of isotropy. Here we determine the parameters directly from N -body simulations carried out using the newly completed GRAPE-6.     

The evolution of substructure – III. The outskirts of clusters

We present an investigation of satellite galaxies in the outskirts of galaxy clusters taken from a series of high-resolution N -body simulations. We focus on the so-called backsplash population, i.e. satellite galaxies that once were inside the virial radius of the host but now reside beyond it. We find that this population is significant in number and needs to be appreciated when interpreting the various galaxy morphology environmental relationships and decoupling the degeneracy between nature and nurture. Specifically, we find that approximately half of the galaxies with current cluster-centric distance in the interval 1–2 virial radii of the host are backsplash galaxies that once penetrated deep into the cluster potential, with 90 per cent of these entering to within 50 per cent of the virial radius. These galaxies have undergone significant tidal disruption, losing on average 40 per cent of their mass. This results in a mass function for the backsplash population different from those galaxies infalling for the first time. We further show that these two populations are kinematically distinct and should be observable within existent spectroscopic surveys.     

Merging time-scales of stellar subclumps in young star-forming regions

Recent observations and hydrodynamical simulations of star formation inside a giant molecular cloud have revealed that, within a star-forming region, stars do not form evenly distributed throughout this region, but rather in small subclumps. It is generally believed that these subclumps merge and form a young star cluster. The time-scale of this merging process is crucial for the evolution and the possible survival of the final star cluster. The key issue is whether this merging process happens faster than the time needed to remove the residual gas of the cloud. A merging time-scale shorter than the gas-removal time would enhance the survival chances of the resulting star cluster. In this paper, we show by means of numerical simulations that the time-scale of the merging is indeed very fast. Depending on the details of the initial subclump distribution, the merging may occur before the gas is expelled from the newly formed cluster via either supernovae or the winds from massive stars. Our simulations further show that the resulting merger objects have a higher effective star formation efficiency than the overall star-forming region and confirm the results that mass-segregated subclumps form mass-segregated merger objects.     

Star clusters with primordial binaries – I. Dynamical evolution of isolated models

In order to interpret the results of complex realistic star cluster simulations, which rely on many simplifying approximations and assumptions, it is essential to study the behaviour of even more idealized models, which can highlight the essential physical effects and are amenable to more exact methods. With this aim, we present the results of N -body calculations of the evolution of equal-mass models, starting with primordial binary fractions of 0–100 per cent, with values of N ranging from 256 to 16 384. This allows us to extrapolate the main features of the evolution to systems comparable in particle number with globular clusters.
In this range, we find that the steady-state 'deuterium main sequence' is characterized by a ratio of the core radius to half-mass radius that follows qualitatively the analytical estimate by Vesperini & Chernoff, although the N dependence is steeper than expected. Interestingly, for an initial binary fraction f greater than 10 per cent, the binary heating in the core during the post-collapse phase almost saturates (becoming nearly independent of f ), and so little variation in the structural properties is observed. Thus, although we observe a significantly lower binary abundance in the core with respect to the Fokker–Planck simulations by Gao et al., this is of little dynamical consequence.
At variance with the study of Gao et al., we see no sign of gravothermal oscillations before 150 half-mass relaxation times. At later times, however, oscillations become prominent. We demonstrate the gravothermal nature of these oscillations.     

On the onset of runaway stellar collisions in dense star clusters – I. Dynamics of the first collision

We study the circumstances under which first collisions occur in young and dense star clusters. The initial conditions for our direct N -body simulations are chosen such that the clusters experience core collapse within a few million years, before the most massive stars have left the main sequence. It turns out that the first collision is typically driven by the most massive stars in the cluster. Upon arrival in the cluster core, by dynamical friction, massive stars tend to form binaries. The enhanced cross-section of the binary compared to a single star causes other stars to engage the binary. A collision between one of the binary components and the incoming third star is then mediated by the encounters between the binary and other cluster members. Due to the geometry of the binary–single star engagement the relative velocity at the moment of impact is substantially different than in a two-body encounter. This may have profound consequences for the further evolution of the collision product.     

Black holes and core expansion in massive star clusters

In this study we present the results from realistic N -body modelling of massive star clusters in the Magellanic Clouds. We have computed eight simulations with   N ∼ 10⁵  particles; six of these were evolved for at least a Hubble time. The aim of this modelling is to examine in detail the possibility of large-scale core expansion in massive star clusters, and search for a viable dynamical origin for the radius–age trend observed for such objects in the Magellanic Clouds. We identify two physical processes which can lead to significant and prolonged cluster core expansion – mass-loss due to rapid stellar evolution in a primordially mass-segregated cluster, and heating due to a retained population of stellar mass black holes, formed in the supernova explosions of the most massive cluster stars. These two processes operate over different time-scales and during different periods of a cluster's life. The former occurs only at early times and cannot drive core expansion for longer than a few hundred Myr, while the latter typically does not begin until several hundred Myr have passed, but can result in core expansion lasting for many Gyr. We investigate the behaviour of each of these expansion mechanisms under different circumstances – in clusters with varying degrees of primordial mass segregation, and in clusters with varying black hole retention fractions. In combination, the two processes can lead to a wide variety of evolutionary paths on the radius–age plane, which fully cover the observed cluster distribution and hence define a dynamical origin for the radius–age trend in the Magellanic Clouds. We discuss in some detail the implications of core expansion for various aspects of globular cluster research, as well as the possibility of observationally inferring the presence of a significant population of stellar mass black holes in a cluster.     

On the dissolution of star clusters in the Galactic Centre – I. Circular orbits

We present N -body simulations of dissolving star clusters close to Galactic Centres. For this purpose, we developed a new N -body program called nbody6gc based on Aarseth's series of N -body codes. We describe the algorithm in detail. We report about the density wave phenomenon in the tidal arms which has been recently explained by Küpper, Macleod & Heggie. Standing waves develop in the tidal arms. The wave knots or clumps develop at the position, where the emerging tidal arm hits the potential wall of the effective potential and is reflected. The escaping stars move through the wave knots further into the tidal arms. We show the consistency of the positions of the wave knots with the theory in Just et al. We also demonstrate a simple method to study the properties of tidal arms. By solving many eigenvalue problems along the tidal arms, we numerically construct a one-dimensional coordinate system whose direction is always along a principal axis of the local tensor of inertia. Along this coordinate system, physical quantities can be evaluated. The half-mass or dissolution times of our models are almost independent of the particle number which indicates that two-body relaxation is not the dominant mechanism leading to the dissolution. This may be a typical situation for many young star clusters. We propose a classification scheme which sheds light on the dissolution mechanism.     

Limits on initial mass segregation in young clusters

Mass segregation is observed in many star clusters, including several that are less than a few Myr old. Time-scale arguments are frequently used to argue that these clusters must be displaying primordial segregation, because they are too young to be dynamically relaxed. Looking at this argument from the other side, the youth of these clusters and the limited time available to mix spatially distinct populations of stars can provide constraints on the amount of initial segregation that is consistent with current observations. We present n -body experiments testing this idea, and discuss the implications of our results for theories of star formation. For system ages less than a few crossing times, we show that star formation scenarios predicting general primordial mass segregation are inconsistent with observed segregation levels.