by Anders, P. and Baumgardt, H. and Gaburov, E. and Zwart, S. Portegies
14 pages incl. 3 pages with figures and 4 pages of tables (analysis results), MNRAS in press

Most recent progress in understanding the dynamical evolution of star clusters relies on direct N-body simulations. Owing to the computational demands, and the desire to model more complex and more massive star clusters, hardware calculational accelerators, such as GRAPE special-purpose hardware or, more recently, GPUs (i.e. graphics cards), are generally utilised. In addition, simulations can be accelerated by adjusting parameters determining the calculation accuracy (i.e. changing the internal simulation time step used for each star).

We extend our previous thorough comparison (Anders et al. 2009) of basic quantities as derived from simulations performed either with STARLAB/KIRA or NBODY6. Here we focus on differences arising from using different hardware accelerations (including the increasingly popular graphic card accelerations/GPUs) and different calculation accuracy settings.

We use the large number of star cluster models (for a fixed stellar mass function, without stellar/binary evolution, primordial binaries, external tidal fields etc) already used in the previous paper, evolve them with STARLAB/KIRA (and NBODY6, where required), analyse them in a consistent way and compare the averaged results quantitatively. For this quantitative comparison, we apply the bootstrap algorithm for functional dependencies developed in our previous study.

In general we find very high comparability of the simulation results, independent of the used computer hardware (including the hardware accelerators) and the used N-body code. For the tested accuracy settings we find that for reduced accuracy (i.e. time step at least a factor 2.5 larger than the standard setting) most simulation results deviate significantly from the results using standard settings. The remaining deviations are comprehensible and explicable.

by Li, Shuo and Liu, F. K. and Berczik, Peter and Chen, Xian and Spurzem, Rainer
38 pages, 10 figues; accepted for publication in ApJ

Supermassive black hole binaries (SMBHBs) are the products of frequent galaxy mergers. The coalescence of the SMBHBs is a distinct source of gravitational wave (GW) radiation. The detections of the strong GW radiation and their possible electromagnetic counterparts are essential. Numerical relativity suggests that the post-merger supermassive black hole (SMBH) gets a kick velocity up to 4000 km/s due to the anisotropic GW radiations. Here we investigate the dynamical co-evolution and interaction of the recoiling SMBHs and their galactic stellar environments with one million direct N-body simulations including the stellar tidal disruption by the recoiling SMBHs. Our results show that the accretion of disrupted stars does not significantly affect the SMBH dynamical evolution. We investigate the stellar tidal disruption rates as a function of the dynamical evolution of oscillating SMBHs in the galactic nuclei. Our simulations show that most of stellar tidal disruptions are contributed by the unbound stars and occur when the oscillating SMBHs pass through the galactic center. The averaged disruption rate is ~10^{-6} M_\odot yr^{-1}, which is about an order of magnitude lower than that by a stationary SMBH at similar galactic nuclei. Our results also show that a bound star cluster is around the oscillating SMBH of about ~ 0.7% the black hole mass. In addition, we discover a massive cloud of unbound stars following the oscillating SMBH. We also investigate the dependence of the results on the SMBH masses and density slopes of the galactic nuclei.

by Farr, Will M. and Ames, Jeff and Hut, Piet and Makino, Junichiro and McMillan, Steve and Muranushi, Takayuki and Nakamura, Koichi and Nitadori, Keigo and Zwart, Simon Portegies
5 pages; submitted to New Astronomy

We present a data format for the output of general N-body simulations, allowing the presence of individual time steps. By specifying a standard, different N-body integrators and different visualization and analysis programs can all share the simulation data, independent of the type of programs used to produce the data. Our Particle Stream Data Format, PSDF, is specified in YAML, based on the same approach as XML but with a simpler syntax. Together with a specification of PSDF, we provide background and motivation, as well as specific examples in a variety of computer languages. We also offer a web site from which these examples can be retrieved, in order to make it easy to augment existing codes in order to give them the option to produce PSDF output.

by Nakasato, Naohito
Journal of Computational Science, 2011; See our recent update at http://galaxy.u-aizu.ac.jp/trac/note/wiki/Octree_On_GPU

The kd-tree is a fundamental tool in computer science. Among other applications, the application of kd-tree search (by the tree method) to the fast evaluation of particle interactions and neighbor search is highly important, since the computational complexity of these problems is reduced from O(N^2) for a brute force method to O(N log N) for the tree method, where N is the number of particles. In this paper, we present a parallel implementation of the tree method running on a graphics processing unit (GPU). We present a detailed description of how we have implemented the tree method on a Cypress GPU. An optimization that we found important is localized particle ordering to effectively utilize cache memory. We present a number of test results and performance measurements. Our results show that the execution of the tree traversal in a force calculation on a GPU is practical and efficient.

by Jalali, B. and Baumgardt, H. and Kissler-Patig, M. and Gebhardt, K. and Noyola, E. and Lützgendorf, N. and de Zeeuw, P. T.
Accepted for publication in A&A

Supermassive black holes (SMBHs) are fundamental keys to understand the formation and evolution of their host galaxies. However, the formation and growth of SMBHs are not yet well understood. One of the proposed formation scenarios is the growth of SMBHs from seed intermediate-mass black holes (IMBHs, 10^2 to 10^5 M_{\odot}) formed in star clusters. In this context, and also with respect to the low mass end of the M-sigma relation for galaxies, globular clusters are in a mass range that make them ideal systems to look for IMBHs. Among Galactic star clusters, the massive cluster $latex \omega$ Centauri is a special target due to its central high velocity dispersion and also its multiple stellar populations. We study the central structure and dynamics of the star cluster $latex \omega$ Centauri to examine whether an IMBH is necessary to explain the observed velocity dispersion and surface brightness profiles. We perform direct N-body simulations to follow the dynamical evolution of $latex \omega$ Centauri. The simulations are compared to the most recent data-sets in order to explain the present-day conditions of the cluster and to constrain the initial conditions leading to the observed profiles. We find that starting from isotropic spherical multi-mass King models and within our canonical assumptions, a model with a central IMBH mass of 2% of the cluster stellar mass, i.e. a 5×10^4 M_{\odot} IMBH, provides a satisfactory fit to both the observed shallow cusp in surface brightness and the continuous rise towards the center of the radial velocity dispersion profile. In our isotropic spherical models, the predicted proper motion dispersion for the best-fit model is the same as the radial velocity dispersion one. (abridged)

by Noyola, Eva and Baumgardt, Holger
Accepted for publication in ApJ

Surface photometry is a necessary tool to establish the dynamical state of stars clusters. We produce realistic HST-like images from N-body models of star clusters with and without central intermediate-mass black holes (IMBHs) in order to measure their surface brightness profiles. The models contain ~600,000 individual stars, black holes of various masses between 0% to 2% of the total mass, and are evolved for a Hubble time. We measure surface brightness and star count profiles for every constructed image in order to test the effect of intermediate mass black holes on the central logarithmic slope, the core radius, and the half-light radius. We use these quantities to test diagnostic tools for the presence of central black holes using photometry. We find that the the only models that show central shallow cusps with logarithmic slopes between -0.1 and -0.4 are those containing central black holes. Thus, the central logarithmic slope seems to be a good way to choose clusters suspect of containing intermediate-mass black holes. Clusters with steep central cusps can definitely be ruled out to host an IMBH. The measured r_c/r_h ratio has similar values for clusters that have not undergone core-collapse, and those containing a central black hole. We notice that observed Galactic globular clusters have a larger span of values for central slope and r_c/r_h than our modeled clusters, and suggest possible reasons that could account for this and contribute to improve future models.

by Fiestas, Jose and Porth, Oliver and Berczik, Peter and Spurzem, Rainer
15 pages, 7 figures,accepted by MNRAS

NBody realizations of axisymmetric collisional galaxy cores (e.g. M32, M33, NGC205, Milky Way) with embedded growing black holes are presented. Stars which approach the disruption sphere are disrupted and accreted to the black hole. We measure the zone of influence of the black hole and disruption rates in relaxation time scales. We show that secular gravitational instabilities dominate the initial core dynamics, while the black hole is small and growing due to consumption of stars. Later, the black hole potential dominates the core, and loss cone theory can be applied. Our simulations show that central rotation in galaxies can not be neglected for relaxed systems, and compare and discuss our results with the standard theory of spherically symmetric systems.

by Brockamp, M. and Baumgardt, H. and Kroupa, P.
19 pages, 11 figures, accepted for publication in MNRAS

The disruption rate of stars by supermassive black holes (SMBHs) is calculated numerically with a modified version of Aarseth’s NBODY6 code. The initial stellar distribution around the SMBH follows a S\’{e}rsic n=4 profile representing bulges and early type galaxies. In order to infer relaxation driven effects and to increase the statistical significance, a very large set of N-body integrations with different particle numbers N, ranging from 10^{3} to 0.5 \cdot 10^{6} particles, is performed. Three different black hole capture radii are taken into account, enabling us to scale these results to a broad range of astrophysical systems with relaxation times shorter than one Hubble time, i.e. for SMBHs up to M_bh \approx 10^{7} M_sun. The computed number of disrupted stars are driven by diffusion in angular momentum space into the loss cone of the black hole and the rate scales with the total number of particles as dN/dt \propto N^{b}, where b is as large as 0.83. This is significantly steeper than the expected scaling dN/dt \propto ln(N) derived from simplest energy relaxation arguments. Only a relatively modest dependence of the tidal disruption rate on the mass of the SMBH is found and we discuss our results in the context of the M_bh/sigma relation. The number of disrupted stars contribute a significant part to the mass growth of black holes in the lower mass range as long as a significant part of the stellar mass becomes swallowed by the SMBH. This also bears direct consequences for the search and existence of IMBHs in globular clusters. For SMBHs similar to the galactic center black hole SgrA*, a tidal disruption rate of 55 \pm 27 events per Myr is deduced. Finally relaxation driven stellar feeding can not account for the masses of massive black holes M_bh \geq 10^{7} M_sun. (abridged)

by Bédorf, Jeroen and Gaburov, Evghenii and Zwart, Simon Portegies
Submitted to Journal of Computational Physics. 34 pages, 13 figures, single column

We present parallel algorithms for constructing and traversing sparse octrees on graphics processing units (GPUs). The algorithms are based on parallel-scan and sort methods. To test the performance and feasibility, we implemented them in CUDA in the form of a gravitational tree-code which completely runs on the GPU.(The code is publicly available at: http://castle.strw.leidenuniv.nl/software.html) The tree construction and traverse algorithms are portable to many-core devices which have support for CUDA or OpenCL programming languages. The gravitational tree-code outperforms tuned CPU code during the tree-construction and shows a performance improvement of more than a factor 20 overall, resulting in a processing rate of more than 2.8 million particles per second.

by Moeckel, Nickolas and Clarke, Cathie J.
8 pages, submitted to MNRAS. Includes revisions per referee’s comments

We investigate the contraction of accreting protoclusters using an extension of n-body techniques that incorporates the accretional growth of stars from the gaseous reservoir in which they are embedded. Following on from Monte Carlo studies by Davis et al., we target our experiments toward populous clusters likely to experience collisions as a result of accretion-driven contraction. We verify that in less extreme star forming environments, similar to Orion, the stellar density is low enough that collisions are unimportant, but that conditions suitable for stellar collisions are much more easily satisfied in large-n clusters, i.e. n ~ 30,000 (we argue, however, that the density of the Arches cluster is insufficient for us to expect stellar collisions to have occurred in the cluster’s prior evolution). We find that the character of the collision process is not such that it is a route toward smoothly filling the top end of the mass spectrum. Instead, runaway growth of one or two extreme objects can occur within less than 1 Myr after accretion is shut off, resulting in a few objects with masses several times the maximum reached by accretion. The rapid formation of these objects is due to not just the post-formation dynamical evolution of the clusters, but an interplay of dynamics and the accretional growth of the stars. We find that accretion-driven cluster shrinkage results in a distribution of gas and stars that offsets the disruptive effect of gas expulsion, and we propose that the process can lead to massive binaries and early mass segregation in star clusters.

by Konstantinidis, Simos and Kokkotas, Kostas D.
24 pages, 28 figures

We present a new C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed using the GRAPE-6 board. Special treatment is used for close encounters, binary and multiple sub-systems that either form dynamically or exist in the initial configuration. The structure of the code is modular and allows the appropriate treatment of more physical phenomena, such as stellar and binary evolution, stellar collisions and evolution of close black-hole binaries. Moreover, it can be easily modified so that the part of the code that uses GRAPE-6, could be replaced by another module that uses other accelerating-hardware like the Graphics Processing Units (GPUs). Appropriate choice of the free parameters give a good accuracy and speed for simulations of star clusters up to and beyond core collapse. Simulations of Plummer models consisting of equal-mass stars reached core collapse at t~17 half-mass relaxation times, which compares very well with existing results, while the cumulative relative error in the energy remained below 0.001. Also, comparisons with published results of other codes for the time of core collapse for different initial conditions, show excellent agreement. Simulations of King models with an initial mass-function, similar to those found in the literature, reached core collapse at t~0.17, which is slightly smaller than the expected result from previous works. Finally, the code accuracy becomes comparable and even better than the accuracy of existing codes, when a number of close binary systems is dynamically created in a simulation. This is due to the high accuracy of the method that is used for close binary and multiple sub-systems.

by Galley, Chad R. and Herrmann, Frank and Silberholz, John and Tiglio, Manuel and Guerberoff, Gustavo

We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal component analysis of spin and orbital angular momentum variables we systematically look for uncorrelated quantities and find three of them which are highly conserved in a statistical sense, both as functions of time and with respect to variations in initial spin orientations. We also look for and find the variables that account for the largest variations in the problem. We present binary black hole simulations of the full Einstein equations analyzing to what extent these results might carry over to the full theory in the inspiral and merger regimes. Among other applications these results should be useful both in semi-analytical and numerical building of templates of gravitational waves for gravitational wave detectors.

by Zwart, Simon Portegies and McMillan, Steve and Gieles, Mark
Only 88 pages. To be published in ARAA. Final version to be submitted on Friday 12 February

Young massive clusters are dense aggregates of young stars that form the fundamental building blocks of galaxies. Several examples exist in the Milky Way Galaxy and the Local Group, but they are particularly abundant in starburst and interacting galaxies. The few young massive clusters that are close enough to resolve are of prime interest for studying the stellar mass function and the ecological interplay between stellar evolution and stellar dynamics. The distant unresolved clusters may be effectively used to study the star-cluster mass function, and they provide excellent constraints on the formation mechanisms of young cluster populations. Young massive clusters are expected to be the nurseries for many unusual objects, including a wide range of exotic stars and binaries. So far only a few such objects have been found in young massive clusters, although their older cousins, the globular clusters, are unusually rich in stellar exotica. In this review we focus on star clusters younger than $latex \sim100$ Myr, more than a few current crossing times old, and more massive than $latex \sim10^4$ \Msun, irrespective of cluster size or environment. We describe the global properties of the currently known young massive star clusters in the Local Group and beyond, and discuss the state of the art in observations and dynamical modeling of these systems. In order to make this review readable by observers, theorists, and computational astrophysicists, we also review the cross-disciplinary terminology.

by Khanna, Gaurav and McKennon, Justin
14 pages, 4 figures

In this work, we make use of the OpenCL framework to accelerate an EMRI modeling application using the hardware accelerators — Cell BE and Tesla CUDA GPU. We describe these compute technologies and our parallelization approach in detail, present our performance results, and then compare them with those from our previous implementations based on the native CUDA and Cell SDKs. The OpenCL framework allows us to execute identical source-code on both architectures and yet obtain strong performance gains that are comparable to what can be derived from the native SDKs.

by Khanna, Gaurav and McKennon, Justin
8 pages, 4 figures, Accepted for publication in Parallel and Distributed Computing and Systems (PDCS 2009)

In this paper, we accelerate a gravitational physics numerical modelling application using hardware accelerators — Cell processor and Tesla CUDA GPU. We describe these new technologies and our approach in detail, and then present our final performance results. We obtain well over an order-of-magnitude performance gain in our application by making use of these many-core architectures.

by Capuzzo-Dolcetta, R.
Invited talk to the 2009 general Conference of the Societa’ Astronomica Italiana. 6 pages including 1 figure

In this paper I will outline some of the aspects and problems of modern celestial mechanics and stellar dynamics, in the context of the quickly growing computing facilities. I will point the attention on the great advantages in using, for astrophysical simulations, the modern, fast and cheap Graphic Processing Units (GPUs) acting as true supercomputers. Finally, I present and discuss some characteristics and performances of a new double-parallel code exploiting the joint power of multicore CPUs and GPUs.

by Nakasato, N.
Poster paper to be appeared in SC09

The kd-tree is a fundamental tool in computer science. Among others, an application of the kd-tree search (oct-tree method) to fast evaluation of particle interactions and neighbor search is highly important since computational complexity of these problems are reduced from O(N^2) with a brute force method to O(N log N) with the tree method where N is a number of particles. In this paper, we present a parallel implementation of the tree method running on a graphic processor unit (GPU). We successfully run a simulation of structure formation in the universe very efficiently. On our system, which costs roughly $900, the run with N ~ 2.87×10^6 particles took 5.79 hours and executed 1.2×10^13 force evaluations in total. We obtained the sustained computing speed of 21.8 Gflops and the cost per Gflops of 41.6/Gflops that is two and half times better than the previous record in 2006.