Supermassive black holes are a ubiquitous feature of galaxy centers. Understanding the problems posed by their formation and co-evolution with their host galaxies is fertile ground for an astrophysicist with a computer.

I present N-body simulations of isolated and interacting galaxies, made on GRAPE machines. In particular I discuss the formation and evolution of N-body bars and compare their properties to those of bars in early-type and late-type galactic discs. I argue that the halo can help the bar grow, contrary to previous beliefs, by taking positive angular momentum from it via its resonant stars. I then focus on the interaction and subsequent merging of a barred disc galaxy with a spheroidal satellite. The evolution depends strongly on the mass (density) of the satellite and may lead to its destruction or to the destruction of the bar.

Cosmological simulations of magnetic fields in galaxy clusters show that remarkable agreement between simulations and observations of Faraday rotation and radio haloes can be achieved assuming that seed fields of ∼ 10−9 G were present at redshifts ∼ 15−20. The structure of the seed field is irrelevant for the final intracluster field. On average, the field grows exponentially with decreasing cluster redshift, but merger events cause steep transient increases in the field strength. Typical field-reversal scales are of order 50h−1kpc. In most cases, the intracluster fields are dynamically unimportant. Assuming secondary electron models, the average structure of cluster radio haloes can naturally be reproduced.

In this paper I show recent results of our studies on the evolution of an isolated cluster of galaxies using N-body simulations. In Sensui, Funato & Makino (1999) only one initial cluster model are investigated. In the present study, we varied the initial model of galaxies and clusters, and studied the dependence of evolution on initial conditions. We found that the mass of galactic halos are stripped and a common halo develops for any cluster models. Using result of scattering experiments of two halo-halo encounters, we show that the growth rate of the common halo (and complimentarily decrease rate of average mass of galactic halos) can be explained as a result of stripping due to cumulative encounters between two galactic halos.

We also found that the galaxies evolved so as to satisfy the relation between the masses of galaxies mgx and their velocity dispersion σgx expressed as mgx ∝ σ3∼4gx for all galaxy models as a consequence of their dynamical evolution through galaxy-galaxy interactions. We discuss the relation between our result and the observed Faber-Jackson relation.

Dwarf galaxies that fall into the Milky Way's potential are tidally disrupted. Their tidal tails are one of the most powerful probes of the mass distribution in the Galaxy. If the distribution of dark matter in the Galaxy is lumpy, then these lumps will scatter stars in the stream and alter its shape. We describe our approach to using the tidal debris to constrain substructure in the Galaxy halo.

I review the arguments for the importance of halo structure in driving galaxy evolution and coupling a galaxy to its environment. We begin with a general discussion of the key dynamics and examples of structure dominated by modes. We find that simulations with large numbers of particles (N ≳ 106) are required to resolve the dynamics. Finally, I will describe some new results which demonstrates that a disk bar can produce cores in a cuspy CDM dark-matter profile within a gigayear. An inner Lindblad-like resonance couples the rotating bar to halo orbits at all radii through the cusp, rapidly flattening it. This resonance disappears for profiles with cores and is responsible for a qualitative difference in bar-driven halo evolution with and without a cusp. Although the bar gives up the angular momentum in its pattern to make the core, the formation epoch is rich in accretion events to recreate or trigger a classic stellar bar. The evolution of the cuspy inner halo by the first-generation bar paves the way for a long-lived subsequent bar with low torque and a stable pattern speed.

We show, by adopting a plausible model for star formation and energetic feedback in cosmological simulations of galaxy formation, that we are able to alleviate the angular momentum problem which has bedeviled many previous attempts to generate realistic disc galaxies in Cold Dark Matter cosmogonies. This paper highlights the “cooling catastrophe” as manifest in numerical cosmology and describes a simple prescription for modelling the sub-resolution physics of star formation and feedback in Smoothed Particle Hydrodynamic simulations. We show results for angular momentum and disc scale length for simulations with and without feedback.

We report on recent numerical investigations of the dynamical evolution of galaxies in clusters. Simulations of spiral galaxies falling into forming clusters show the development of the morphology-density relationship and the formation of regular and giant elliptical galaxies. The regular elliptical merger remnants end up in a fundamental plane very similar to the observed relation. The giant ellipticals have much in common with their real counterparts but their central velocity dispersions are too high. We also quantify the amount and distribution of diffuse light in clusters.

A timely combination of new theoretical ideas and observational discoveries has brought about significant advances in our understanding of cosmic evolution. Computer simulations have played a key role in these developments by providing the means to interpret astronomical data in the context of physical and cosmological theory. In the current paradigm, our Universe has a flat geometry, is undergoing accelerated expansion and is gravitationaly dominated by elementary particles that make up cold dark matter. Within this framework, it is possible to simulate in a computer the emergence of galaxies and other structures from small quantum fluctuations imprinted during an epoch of inflationary expansion shortly after the Big Bang. The simulations must take into account the evolution of the dark matter as well as the gaseous processes involved in the formation of stars and other visible components. Although many unresolved questions remain, a coherent picture for the formation of cosmic structure in now beginning to emerge.

I report on recent progress in our understanding of the structure of CDM halos, and in particular of the inner mass profile of galaxy-sized systems. Numerical simulations have consistently shown that the density profiles of CDM halos steepen monotonically from the center outwards, with slopes shallower than isothermal near the center and steeper than isothermal near the virial radius. Ongoing debate centers on the precise radial dependence of the logarithmic slope, as well as on whether it approaches a well defined asymptotic central value. The latest high-resolution simulations suggest that the circular velocity profile is well approximated by the model proposed by Navarro, Frenk & White (NFW). On the other hand, the radial dependence of the slope of the density profile differs modestly, but significantly, from the model proposed by NFW. As a result, NFW fits tend to underestimate the density at radii just inside the scale radius. Rather than implying a very steep (ρ ∝ r-1.5) inner divergent slope, I argue that the data is actually best represented by a model where the density profile becomes increasingly shallow with radius, with little sign of approach to a well-defined asymptotic value. A model where the phase-space density profile is a power law accounts well for these results and suggests that the innermost slope may be as shallow as ρ ∝ r-0.75. These conclusions are supported by a thorough numerical convergence study that elucidates the effect of numerical parameters such as the timestep, gravitational softening, and particle number, on the mass profile of simulated dark matter halos.

We discuss SPH simulations of galaxy formation which use a hybrid method to describe a two-phase structure of the star forming ISM on unresolved scales. Our modeling includes radiative cooling, heating due to a UV background, growth of cold clouds embedded in an ambient hot gas, star formation out of cloud material, feedback due to supernovae in the form of thermal heating and cloud evaporation, starbursts that can lead to galactic outflows, and metal enrichment. Our particular model for the treatment of the two-phase structure is based on a modified and extended version of the grid-based approach of Yepes et al. (1997). We discuss the properties of the feedback model and show how it stabilizes star forming disk galaxies and reduces the cosmic star formation rate to a level consistent with current observational constraints.

I review recent progress in numerically simulating the formation and evolution of galaxies in hierarchically clustering universes. Special emphasis is given to results based on high-resolution gas dynamical simulations using the N-body hardware integrator GRAPE. Applications address the origin of the spin of disk galaxies, the structure and kinematics of damped Ly-α systems, and the origin of galaxy morphology and of galaxy scaling laws.

We first discuss two-body and chain regularization methods for direct N-body simulations on HARP-2 and GRAPE-6. The former is used for accurate integration of perturbed binaries and hierarchies, whereas the latter deals with strong interactions involving binaries. Combined with a powerful stability criterion for hierarchical systems, this versatile treatment provides an efficient way of studying all dynamical processes in globular clusters containing a realistic population of primordial binaries. These algorithms are also ideal for modelling a variety of astrophysical effects, such as averaging over Kozai cycles, tidal circularization, spin-orbit coupling and stellar collisions, where well-defined elements are used to describe near-singular solutions. We also describe a new time-transformed leapfrog scheme which has been developed to deal with black-hole binaries in galactic centres. This formulation is valid for large mass ratios and dominant two-body motions in a compact subsystem can be treated accurately in the post-Newtonian approximation. This method has been combined with the existing regularization algorithms into a new simulation code NBODY7. Some preliminary results of a test problem illustrating possible applications are presented.

We invented the pseudoparticle multipole method (P2M2), a method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the Barnes-Hut treecode and FMM. The primary advantage of P2M2 is that it works on GRAPE. Although the treecode has been implemented on GRAPE, we could handle terms only up to dipole, since GRAPE can calculate forces from point-mass particles only. Thus the calculation cost grows quickly when high accuracy is required. With P2M2, the multipole expansion is expressed by particles, and thus GRAPE can calculate high order terms. Using P2M2, we realized arbitrary-order treecode on MDGRAPE-2. Timing result shows MDGRAPE-2 accelerates the calculation by a factor between 20 (for low accuracy) to 150 (for high accuracy). We parallelized the code so that it runs on MDGRAPE-2 cluster. The calculation speed of the code shows close-to-linear scaling up to 16 processors for N ≳ 106.

We summarize the ideas that led to the Adaptive Smoothed Particle Hydrodynamics (ASPH) algorithm, with anisotropic smoothing and shock-tracking. We then identify a serious new problem for SPH simulations with shocks and radiative cooling — false cooling — and discuss a possible solution based on the shock-tracking ability of ASPH.

We investigate galaxy formation with Radiation-SPH simulations in order to find the effects of ultraviolet background radiation field on the star formation in the forming galaxies. We find the ultraviolet background radiation field can delay the star formation in protogalactic clouds, especially at low redshift (z < 2). This result suggests that galaxies formed at lower redshift tend to be late type galaxies, and early type galaxies tend to be formed at higher redshift.

Traditionally, a simulation of a dense stellar system required choosing an initial model, running an integrator, and analyzing the output. Almost all of the effort went into writing a clever integrator that could handle binaries, triples and encounters between various multiple systems efficiently. Recently, the scope and complexity of these simulations has increased dramatically, for three reasons: 1) the sheer size of the data sets, measured in Terabytes, make traditional ‘awking and grepping’ of a single output file impractical; 2) the addition of stellar evolution data brings qualitatively new challenges to the data reduction; 3) increased realism of the simulations invites realistic forms of ‘SOS’: Simulations of Observations of Simulations, to be compared directly with observations. We are now witnessing a shift toward the construction of archives as well as tailored forms of visualization including the use of virtual reality simulators and planetarium domes, and a coupling of both with budding efforts in constructing virtual observatories. This review describes these new trends, presenting Starlab as the first example of a full software environment for realistic large-scale simulations of dense stellar systems.

This paper describes partiview, a free software tool for interactive graphical display of collections of particles in 3-space, and its application in studying the results of N-body collisional stellar dynamics calculations from Starlab.

We developed a special-purpose computer for molecular dynamics simulations, which we call Molecular Dynamics Machine (MDM). MDM accelerates the Coulomb and van der Waals force calculation with the Ewald method. It is composed of three parts: MDGRAPE-2, WINE-2 and a host computer. MDGRAPE-2 accelerates the real-space part of the Coulomb and van der Waals forces. WINE-2 accelerates wavenumber-space part of the Coulomb force. The host computer performs other calculations. The peak performance is 78 Tflop/s. It can also be used for cosmological, Smoothed Particle Hydrodynamics, and vortex dynamics simulations.

Like hardware, evolution of software has had a major impact on the field of particle simulations. This paper illustrates how simulation software has evolved, and where it can go. In addition, with the various ongoing Virtual Observatory efforts, producers of data should think more about sharing their data! Some examples are given of what we can do with our data and how to share it with our colleagues and observers. In the Appendix we summarize the findings of an informal data and software usage survey that we took during this conference.