Dancing with black holes

We describe efforts over the last six years to implement regularization methods suitable for studying one or more interacting black holes by direct N-body simulations. Three different methods have been adapted to large-N systems: (i) Time-Transformed Leapfrog, (ii) Wheel-Spoke, and (iii) Algorithmic Regularization. These methods have been tried out with some success on GRAPE-type computers. Special emphasis has also been devoted to including post-Newtonian terms, with application to moderately massive black holes in stellar clusters. Some examples of simulations leading to coalescence by gravitational radiation will be presented to illustrate the practical usefulness of such methods.Comment: 8 figures, 10 pages, to appear in "Dynamical Evolution of Dense Stellar Systems", ed. E. Vesperin

The Formation of a Bound Star Cluster: From the Orion Nebula Cluster to the Pleiades

(shortened) 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 10^4 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 (DIVA and GAIA). These missions should also detect the original Pleiades members as an associated expanding young Galactic-field sub-population. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations.Comment: MNRAS, in press, 36 pages, 15 figures; repl.vers. contains adjustments for consistency with published versio

Are Supernova Kicks Responsible for X-ray Binary Ejection from Young Clusters?

Recent Chandra observations of interacting and starburst galaxies have led us to investigate the apparent correlation between the positions of young star clusters and Chandra point sources. Assumed to be X-ray binaries (XRBs), these point sources do not seem to coincide with the massive (~1e5 Msun), young (1-50 Myr) stellar clusters that can easily form systems capable of such emission. We use a sophisticated binary evolution and population synthesis code (StarTrack) and a simplified cluster model to track both the X-ray luminosity and position of XRBs as a function of time. These binaries are born within the cluster potential with self-consistent positions and velocities and we show that a large fraction (~70%) can be ejected from the parent due to supernova explosions and associated systemic velocities. For brighter sources and cluster masses below ~1e6 Msun, we find that the average number of bright XRBs per cluster remains near or below unity, consistent with current observations.Comment: 5 pages, 1 figure. Accepted for publication in Astrophysical Journal Letter

Collisional dynamics around binary black holes in galactic centers

We follow the sinking of two massive black holes in a spherical stellar system where the black holes become bound under the influence of dynamical friction. Once bound, the binary hardens by three-body encounters with surrounding stars. We find that the binary wanders inside the core, providing an enhanced supply of reaction partners for the hardening. The binary evolves into a highly eccentric orbit leading to coalescence well beyond a Hubble time. These are the first results from a hybrid ``self consistent field'' (SCF) and direct Aarseth N-body integrator (NBODY6), which combines the advantages of the direct force calculation with the efficiency of the field method. The code is designed for use on parallel architectures and is therefore applicable to collisional N-body integrations with extraordinarily large particle numbers (> 10^5). This creates the possibility of simulating the dynamics of both globular clusters with realistic collisional relaxation and stellar systems surrounding supermassive black holes in galactic nuclei.Comment: 38 pages, 13 figures, submitted to ApJ, accepted, revised text and added figure

The Formation and Evolution of Multiple Star Systems

Multiple systems play an important role in the evolution of star clusters. First we discuss several formation mechanisms which depend on the presence of binaries, either primordial or of dynamical origin. Hierarchical configurations are often stable over long times and yet may experience evolution of the internal orbital parameters. We describe an attempt to model the eccentricity change induced by the outer component using an averaging method, together with the effects due to tidal dissipation and apsidal motion acting on the inner binary. This treatment is adopted for systems with high induced eccentricity which gives rise to some interesting outcomes of significant period shrinkage

Simulated Versus Observed Cluster Eccentricity Evolution

The rate of galaxy cluster eccentricity evolution is useful in understanding large scale structure. Rapid evolution for $z <$ 0.13 has been found in two different observed cluster samples. We present an analysis of projections of 41 clusters produced in hydrodynamic simulations augmented with radiative cooling and 43 clusters from adiabatic simulations. This new, larger set of simulated clusters strengthens the claims of previous eccentricity studies. We find very slow evolution in simulated clusters, significantly different from the reported rates of observational eccentricity evolution. We estimate the rate of change of eccentricity with redshift and compare the rates between simulated and observed clusters. We also use a variable aperture radius to compute the eccentricity, r$_{200}$. This method is much more robust than the fixed aperture radius used in previous studies. Apparently radiative cooling does not change cluster morphology on scales large enough to alter eccentricity. The discrepancy between simulated and observed cluster eccentricity remains. Observational bias or incomplete physics in simulations must be present to produce halos that evolve so differently.Comment: ApJ, in press, minor revision

Basic N-Body Modelling of the Evolution of Globular Clusters. I. Time Scaling

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, and 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 which are in good agreement with N-body models of those clusters which are relaxation dominated, at least for N-body models with several thousand particles, but that the Fokker-Planck models evolve too fast for clusters which dissipate promptly.Comment: 24 pages, 3 figures, MNRAS, in pres