We review recent progress in computational methods for studying the dynamical evolution of large star clusters. After describing some highlights of a new comparison of different models, including N-body models, we mention in detail recent developments in three codes which allow models with anisotropic distributions of velocity to be studied: (i) a Fokker-Planck code using finite differences, (ii) a Monte Carlo code and (iii) a gaseous model code.

D. C. Heggie M. Giersz R. Spurzem K. Takahashi

We have developed a new parallel supercomputer code based on Henon's Monte Carlo method for simulating the dynamical evolution of globular clusters. This new code allows us to calculate the evolution of a cluster containing a realistic number of stars (N ~ 10^5 - 10^6) in about a day of computing time. The discrete, star-by-star representation of the cluster in the simulation allows us to treat naturally a number of important processes, including single and binary star evolution, all dynamical interactions of single stars and primordial binaries, and tidal interactions with the Galaxy.

F. A. Rasio

We study the survival of substructures (clumps) within larger self-gravitating dark matter halos. Building on scaling relations obtained from N-body calculations of violent relaxation, we argue that the tidal field of galaxies and halos can only destroy substructures if spherical symmetry is imposed at formation. We explore other mechanisms that may tailor the number of halo substructures during the course of virialization. Unless the larger halo is built up from a few large clumps, we find that clump-clump encounters are unlikely to homogenize the halo on a dynamical timescale. Phase mixing would proceed faster in the inner parts and allow for the secular evolution of a stellar disk.

C. M. Boily N. Nakastao R. Spurzem T. Tsuchiya

We present some preliminary results from recent numerical simulations that model the evolution of super-massive black hole (SMBH) binaries in galactic nuclei. Including the post-Newtonian terms for the binary system and adopting appropriate models for the galaxies allows us, for the first time, to follow the evolution of SMBH binaries from kpc scales down to the coalescence phase. We use our results to make predictions of the detectability of such events with the gravitational wave detector LISA.

I. Berentzen M. Preto P. Berczik D. Merritt R. Spurzem

The chemodynamical evolution of spherical multi-component self-gravitating models for isolated dwarf galaxies is studied. We compare their evolution with and without feedback effects from star formation processes. We find that initially cuspy dark matter profiles flatten with time as a result of star formation, without any special tuning conditions. Thus the seemingly flattened profiles found in many dwarfs do not contradict the cuspy profiles predicted by cosmological models. We also calculate the chemical evolution of stars and gas, to permit comparisons with observational data.

S. Pasetto E. K. Grebel P. Berczik R. Spurzem W. Dehnen

Observations of internal motions in globular clusters offer unique insights into the dynamics of the clusters. We have recently developed methods of high-precision astrometry with HST's WFPC2 camera, which allow us to measure internal proper motions of individual stars. These new data open up many new avenues for study of the clusters. Comparison of the dispersion of proper motion with that of radial velocity offers what is potentially the best method of measuring cluster distances, but reliable results will require dynamical modeling of each cluster. Proper motions are much better able to measure anisotropy of stellar motions than are radial velocities. In 47 Tucanae we have measured thousands of proper motions near the center; their velocity distribution is remarkably Gaussian. In two outer fields we have begun to study anisotropy, which appears in the high velocities but not in the lower ones, contrary to the spheroidal velocity distributions that have commonly been assumed.

Ivan R. King Jay Anderson

The Milky Way's satellites provide unique information about the density of the Galactic halo at large radii. The inclusion of even a few rather inaccurate proper motions resolves an ambiguity in older mass estimates in favour of higher values. Many of the satellites are concentrated into streams. The dynamics of the Magellanic Stream provided an early indication that the halo reaches out to beyond 100 kpc. Tidal forces between the Clouds are currently disturbing the Clouds' internal dynamics. One would expect this damage to worsen rapidly as the tidal field of the MW excites the eccentricity of the Clouds' mutual orbit. This process, which has yet to be completely modelled, is important for understanding the degree of self-lensing in searches for gravitational lensing events. The Sagittarius Dwarf galaxy very likely contributes significantly to the Galactic warp. The direction of the warp's line of nodes is incorrectly predicted by the simplest models of the Dwarf's orbit. More sophisticated models, in which a complex distribution of stripped dark matter is predicted, may be more successful.

James Binney

We present Superbox, a particle-mesh code with high resolution sub-grids and an NGP (nearest grid point) force-calculation scheme based on the second derivatives of the potential. Superbox implements a fast low-storage FFT-algorithm, giving the possibility to work with millions of particles on desk-top computers. Test calculations show energy and angular momentum conservation to one part in 10^5 per crossing-time. The effects of grid and numerical relaxation remain negligible, even when these calculations cover a Hubble-time of evolution. As the sub-grids follow the trajectories of individual galaxies, the code allows a highly resolved treatment of interactions in clusters of galaxies, such as high-velocity encounters between elliptical galaxies and the tidal disruption of dwarf galaxies. Excellent agreement is obtained in a comparison with a direct-summation N-body code running on special-purpose Grape3 hardware. The orbital decay of satellite galaxies due to dynamical friction obtained with Superbox agrees with Chandrasekhar's treatment when the Coulomb logarithm is approximately 1.5.

M. Fellhauer P. Kroupa H. Baumgart R. Bien C. M. Boily R. Spurzem N. Wassmer

We consider both observational and theoretical issues related to dynamical mass loss from the old globular star clusters of the Galaxy. On the observational side the evidence includes tidal tails and extratidal extensions, kinematic effects, effects on the mass function, and influences on the statistical properties of surviving objects. Even for isolated clusters, the theoretical issues are not fully understood. The effects of a steady tide (i.e. for a cluster in a circular orbit) include the imposition of a tidal boundary, and lowering of the escape energy. Less familiar, however, are the effects of induced mass loss. Even the definition of an ``escaper'' is not straightforward. When mass loss is driven by relaxation, as in N-body models, the rate of loss of mass does not scale in a simple way with the relaxation time. Reasons for this include the very long time scales on which stars escape even with energies above the escape threshold. For the realistic case of unsteady tides it is still unclear under what circumstances mass loss is dominated by relaxation or tidal heating.

Douglas C. Heggie

Milli-arcsecond astrometry provided by Hipparcos and by radio observations makes it possible to retrace the orbits of nearby runaway stars and pulsars with sufficient accuracy to identify their parent stellar cluster or association. For two cases it is even possible to deduce the specific formation scenario. The runaway star zeta Oph and PSR J1932+1059 are the result of a supernova explosion which took place 1 Myr ago in a massive binary in the Upper Scorpius association. The pulsar received a kick velocity of about 350 km/s in this event. The runaway stars mu Col and AE Aur and the isolated eccentric massive binary iota Ori result from a binary-binary encounter, most likely inside the Trapezium cluster, 2.5 Myr ago. Future astrometric missions such as DIVA, FAME and in particular GAIA will allow extension of these studies to a significant fraction of the Galactic disk, and will provide new constraints on the formation and evolution of massive stars.

Tim de Zeeuw Ronnie Hoogerwerf Jos de Bruijne