Direct-summation N -body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O(N 2 ). Performance can be greatly enhanced via the use of special-purpose accelerator boards like the GRAPE-6A. However the memory of the GRAPE boards is limited. Here, we present a performance analysis of direct N -body codes on two parallel supercomputers that incorporate special-purpose boards, allowing as many as four million particles to be integrated. Both computers employ high-speed, Infiniband interconnects to minimize communication overhead, which can otherwise become significant due to the small number of "active" particles at each time step. We find that the computation time scales well with processor number; for 2×10 6 particles, efficiencies greater than 50% and speeds in excess of 2 TFlops are reached.

We present Sapporo, a library for performing high-precision gravitational N -body simulations on NVIDIA Graphical Processing Units (GPUs). Our library mimics the GRAPE-6 library, and N -body codes currently running on GRAPE-6 can switch to Sapporo by a simple relinking of the library. The precision of our library is comparable to that of GRAPE-6, even though internally the GPU hardware is limited to single precision arithmetics. This limitation is effectively overcome by emulating double precision for calculating the distance between particles. The performance loss of this operation is small ( < ∼ 20%) compared to the advantage of being able to run at high precision. We tested the library using several GRAPE-6-enabled N-body codes, in particular with Starlab and phiGRAPE. We measured peak performance of 800 Gflop/s for running with 10 6 particles on a PC with four commercial G92 architecture GPUs (two GeForce 9800GX2). As a production test, we simulated a 32k Plummer model with equal mass stars well beyond core collapse. The simulation took 41 days, during which the mean performance was 113 Gflop/s. The GPU did not show any problems from running in a production environment for such an extended period of time. IntroductionGraphical processing units (GPUs) are quickly becoming main stream in computational science. The introduction of Compute Unified Device Architecture (CUDA, Fernando, 2004), in which GPUs can be programmed effectively, has generated a paradigm shift in scientific computing (Hoekstra et al., 2007). Modern GPUs are greener in terms of CO 2 production, have a smaller footprint, are cheaper, and as easy to program as traditional parallel computers. In addition, you will not have a waiting queue when running large simulations on your local GPU-equipped workstation.Newtonian stellar dynamics is traditionally on the forefront of high-performance computing. The first dedicated Newtonian solver (Applegate et al., 1986) was used to study the stability of the solar system (Sussman and Wisdom, 1992). And soon even faster specialized hardware was introduced by the inauguration of the GRAPE family of computers, which have an impressive history of breaking computing speed records (Makino and Taiji, 1998).Nowadays, the GPUs are being used in various scientific areas, such as molecular dynamics (Anderson et al., 2008;van Meel et al., 2008), solving Kepler's equations (Ford, 2009) and Newtonian N -body simulations. Solving the Newtonian N -body problem with GPUs started in the early 2000s by adopting a shared time step algorithm with a 2nd order integrator (Nyland et al., 2004). A few years later this algorithm was improved to include individual time steps and a higher order integrator , in a code that was written in the device specific language Cg (Fernando and Kilgard, 2003). The performance was still relatively low compared to later implementations in CUDA via the Cunbody package (Hamada and Iitaka, 2007), Kirin library , and the Yebisu N -body code (Nitadori and Makino, 2008;Nitadori, 2009). The main p...

We present the results of the "Cosmogrid" cosmological N-body simulation suites based on the concordance LCDM model. The Cosmogrid simulation was performed in a 30 Mpc box with 2048 3 particles. The mass of each particle is 1.28 × 10 5 M , which is sufficient to resolve ultra-faint dwarfs. We found that the halo mass function shows good agreement with the Sheth & Tormen fitting function down to ∼10 7 M . We have analyzed the spherically averaged density profiles of the three most massive halos which are of galaxy group size and contain at least 170 million particles. The slopes of these density profiles become shallower than −1 at the innermost radius. We also find a clear correlation of halo concentration with mass. The mass dependence of the concentration parameter cannot be expressed by a single power law, however a simple model based on the Press-Schechter theory proposed by Navarro et al. gives reasonable agreement with this dependence. The spin parameter does not show a correlation with the halo mass. The probability distribution functions for both concentration and spin are well fitted by the log-normal distribution for halos with the masses larger than ∼10 8 M . The subhalo abundance depends on the halo mass. Galaxy-sized halos have 50% more subhalos than ∼10 11 M halos have.

We have performed a series of N‐body simulations to model the Arches cluster. Our aim is to find the best‐fitting model for the Arches cluster by comparing our simulations with observational data and to constrain the parameters for the initial conditions of the cluster. By neglecting the Galactic potential and stellar evolution, we are able to efficiently search through a large parameter space to determine, for example, the initial mass function (IMF), size and mass of the cluster. We find that the cluster's observed present‐day mass function can be well explained with an initial Salpeter IMF. The lower mass limit of the IMF cannot be constrained well from our models. In our best models, the initial total mass down to a mass limit of 0.5 M⊙ is (4.9 ± 0.8) × 104 M⊙. The initial virial radius of the cluster is 0.77 ± 0.12 pc. A concentration parameter of the initial King model W0= 3 gives the best results.

We show that the presence of a ρ ∼ r −3/2 dark matter overdensity can be robustly predicted at the center of any galaxy old enough to have grown a power-law density cusp in the stars via the Bahcall-Wolf mechanism. Using both Fokker-Planck and direct N -body integrations, we demonstrate collisional generation of these dark matter "crests" (Collisionally REgenerated STtructures) even in the extreme case that the density of both stars and dark matter were previously lowered by slingshot ejection from a binary supermassive black hole. The time scale for collisional growth of the crest is approximately the two-body relaxation time as defined by the stars, which is 10 Gyr at the centers of stellar spheroids with luminosities L 10 9.5 L⊙, including the bulge of the Milky Way. The presence of crests can robustly be predicted in such galaxies, unlike the steeper enhancements, called "spikes", produced by the adiabatic growth of black holes. We discuss special cases where the prospects for detecting dark matter annihilations from the centers of galaxy haloes are significantly affected by the formation of crests.

Recently, more than 100 Wolf-Rayet and OB stars were identified in the Galactic center. About a third of these sources are not spatially associated with any of the known star clusters in this region. We probe the distribution of drifted sources in numerical models of the massive clusters in the Galactic center and compare it to the observed distribution of isolated massive sources in this region. We find that stars as massive as 100 M drift away from the center of each cluster by up to ∼60 pc using the cluster models. Our best model reproduces ∼60% of the known isolated massive stars out to 80 pc from the center of the Arches cluster. This number increases to 70-80% when we only consider the region that is ∼20 pc from the Arches cluster.

We present a new particle code for modelling the evolution of galaxies. The code is based on a multi-phase description for the interstellar medium (ISM). We include star formation (SF), stellar feedback by massive stars and planetary nebulae, phase transitions, and interactions between gas clouds and ambient diffuse gas, namely condensation, evaporation, drag, and energy dissipation. The last is realised by radiative cooling and inelastic cloud-cloud collisions. We present new schemes for SF and stellar feedback that include a consistent calculation of the star-formation efficiency (SFE) based on ISM properties, as well as a detailed redistribution of the feedback energy into the different ISM phases. As a first test we show a model of the evolution of a present day Milky-Way-type galaxy. Though the model exhibits a quasi-stationary behaviour in global properties like mass fractions or surface densities, the evolution of the ISM is strongly variable locally depending on the local SF and stellar feedback. We start only with two distinct phases, but a three-phase ISM is formed soon and consists of cold molecular clouds, a warm gas disk, and a hot gaseous halo. Hot gas is also found in bubbles in the disk accompanied by type II supernovae explosions. The volume-filling factor of the hot gas in the disk is ∼35%. The mass spectrum of the clouds follows a power-law with an index of α ≈ −2. The star-formation rate (SFR) is ∼1.6 M yr −1 on average, decreasing slowly with time due to gas consumption. In order to maintain a constant SFR, gas replenishment, e.g. by infall, of the order 1 M yr −1 is required. Our model is in fair agreement with Kennicutt's (1998, ApJ, 498, 541) SF law including the cut-off at ∼10 M pc −2 . Models with a constant SFE, i.e. no feedback on the SF, fail to reproduce Kennicutt's law. We performed a parameter study varying the particle resolution, feedback energy, cloud radius, SF time scale, and metallicity. In most these cases the evolution of the model galaxy was not significantly different to our reference model. Increasing the feedback energy by a factor of 4−5 lowers the SF rate by ∼0.5 M yr −1 , while decreasing the metallicity by a factor of ∼100 increases the mass fraction of the hot gas from about 10% to 30%.

Most stars form in a cluster environment. These stars are initially surrounded by discs from which potentially planetary systems form. Of all cluster environments starburst clusters are probably the most hostile for planetary systems in our Galaxy. The intense stellar radiation and extreme density favour rapid destruction of circumstellar discs via photoevaporation and stellar encounters. Evolving a virialized model of the Arches cluster in the Galactic tidal field we investigate the effect of stellar encounters on circumstellar discs in a prototypical starburst cluster. Despite its proximity to the deep gravitational potential of the Galactic centre only a moderate fraction of members escapes to form an extended pair of tidal tails. Our simulations show that encounters destroy one third of the circumstellar discs in the cluster core within the first 2.5 Myr of evolution, preferentially affecting the least and most massive stars. A small fraction of these events causes rapid ejection and the formation of a weaker second pair of tidal tails that is overpopulated by disc-poor stars. Two predictions arise from our study: (i) If not destroyed by photoevaporation protoplanetary discs of massive late B-and early O-type stars represent the most likely hosts of planet formation in starburst clusters. (ii) Multiepoch Kand L-band photometry of the Arches cluster would provide the kinematically selected membership sample required to detect the additional pair of disc-poor tidal tails.