Dynamical evolution of rotating dense stellar systems with embedded black holes

Evolution of self-gravitating rotating dense stellar systems (e.g. globular clusters, galactic nuclei) with embedded black holes is investigated. The interaction between the black hole and stellar component in differential rotating flattened systems is followed. The interplay between velocity diffusion due to relaxation and black hole star accretion is investigated together with cluster rotation using 2D+1 Fokker-Planck numerical methods. The models can reproduce the Bahcall-Wolf solution $f \propto E^{1/4}$ ($n \propto r^{-7/4}$) inside the zone of influence of the black hole. Gravo-gyro and gravothermal instabilities conduce the system to a faster evolution leading to shorter collapse times with respect to the non-rotating systems. Angular momentum transport and star accretion support the development of central rotation in relaxation time scales. We explore system dissolution due to mass-loss in the presence of an external tidal field (e.g. globular clusters in galaxies).Comment: 16 pages, 23 figures, 6 table

Compact Binaries in Star Clusters II - Escapers and Detection Rates

We use a self-consistent Monte Carlo treatment of stellar dynamics to investigate black hole binaries that are dynamically ejected from globular clusters to determine if they will be gravitational wave sources. We find that many of the ejected binaries have initially short periods and will merge within a Hubble time due to gravitational wave radiation. Thus they are potential sources for ground-based gravitational wave detectors. We estimate the yearly detection rate for current and advanced ground-based detectors and find a modest enhancement over the rate predicted for binaries produced by pure stellar evolution in galactic fields. We also find that many of the ejected binaries will pass through the longer wavelength Laser Interferometer Space Antenna (LISA) band and may be individually resolvable. We find a low probability that the Galaxy will contain a binary in the LISA band during its three-year mission. Some such binaries may, however, be detectable at Mpc distances implying that there may be resolvable stellar-mass LISA sources beyond our Galaxy. We conclude that globular clusters have a significant effect on the detection rate of ground-based detectors and may produce interesting LISA sources in local group galaxies.Comment: 19 pages, 16 figures, 2 tables, submitted to MNRA

2D Fokker-Planck models of rotating clusters

Globular clusters rotate significantly, and with the increasing amount of detailed morphologicaland kinematical data obtained in recent years on galactic globular clusters many interesting features show up. We show how our theoretical evolutionary models of rotating clusters can be used to obtain fits, which at least properly model the overall rotation and its implied kinematics in full 2D detail (dispersions, rotation velocities). Our simplified equal mass axisymmetric rotatingmodel provides detailed two-dimensional kinematical and morphological data for star clusters. The degree of rotation is not dominant in energy, but also non-negligible for the phase space distribution function, shape and kinematics of clusters. Therefore the models are well applicable for galactic globular clusters. Since previously published papers on that matter by us made it difficult to do detailed comparisons with observations we provide a much more comprehensive and easy-to-use set of data here, which uses as entries dynamical age and flattening of observed cluster andthen offers a limited range of applicable models in full detail. The method, data structure and some exemplary comparison with observations are presented. Future work will improve modelling anddata base to take a central black hole, a mass spectrum and stellar evolution into account

Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies

We use direct-summation N-body integrations to follow the evolution of binary black holes at the centers of galaxy models with large, constant-density cores. Particle numbers as large as 400K are considered. The results are compared with the predictions of loss-cone theory, under the assumption that the supply of stars to the binary is limited by the rate at which they can be scattered into the binary's influence sphere by gravitational encounters. The agreement between theory and simulation is quite good; in particular, we are able to quantitatively explain the observed dependence of binary hardening rate on N. We do not verify the recent claim of Chatterjee, Hernquist & Loeb (2003) that the hardening rate of the binary stabilizes when N exceeds a particular value, or that Brownian wandering of the binary has a significant effect on its evolution. When scaled to real galaxies, our results suggest that massive black hole binaries in gas-poor nuclei would be unlikely to reach gravitational-wave coalescence in a Hubble time.Comment: 13 pages, 8 figure

A pilgrimage to gravity on GPUs

In this short review we present the developments over the last 5 decades that have led to the use of Graphics Processing Units (GPUs) for astrophysical simulations. Since the introduction of NVIDIA's Compute Unified Device Architecture (CUDA) in 2007 the GPU has become a valuable tool for N-body simulations and is so popular these days that almost all papers about high precision N-body simulations use methods that are accelerated by GPUs. With the GPU hardware becoming more advanced and being used for more advanced algorithms like gravitational tree-codes we see a bright future for GPU like hardware in computational astrophysics.Comment: To appear in: European Physical Journal "Special Topics" : "Computer Simulations on Graphics Processing Units" . 18 pages, 8 figure

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

Particle-Particle, Particle-Scaling function (P3S) algorithm for electrostatic problems in free boundary conditions

An algorithm for fast calculation of the Coulombic forces and energies of point particles with free boundary conditions is proposed. Its calculation time scales as N log N for N particles. This novel method has lower crossover point with the full O(N^2) direct summation than the Fast Multipole Method. The forces obtained by our algorithm are analytical derivatives of the energy which guarantees energy conservation during a molecular dynamics simulation. Our algorithm is very simple. An MPI parallelised version of the code can be downloaded under the GNU General Public License from the website of our group.Comment: 19 pages, 11 figures, submitted to: Journal of Chemical Physic

Accelerating NBODY6 with Graphics Processing Units

We describe the use of Graphics Processing Units (GPUs) for speeding up the code NBODY6 which is widely used for direct $N$-body simulations. Over the years, the $N^2$ nature of the direct force calculation has proved a barrier for extending the particle number. Following an early introduction of force polynomials and individual time-steps, the calculation cost was first reduced by the introduction of a neighbour scheme. After a decade of GRAPE computers which speeded up the force calculation further, we are now in the era of GPUs where relatively small hardware systems are highly cost-effective. A significant gain in efficiency is achieved by employing the GPU to obtain the so-called regular force which typically involves some 99 percent of the particles, while the remaining local forces are evaluated on the host. However, the latter operation is performed up to 20 times more frequently and may still account for a significant cost. This effort is reduced by parallel SSE/AVX procedures where each interaction term is calculated using mainly single precision. We also discuss further strategies connected with coordinate and velocity prediction required by the integration scheme. This leaves hard binaries and multiple close encounters which are treated by several regularization methods. The present nbody6-GPU code is well balanced for simulations in the particle range $10^4-2 \times 10^5$ for a dual GPU system attached to a standard PC.Comment: 8 pages, 3 figures, 2 tables, MNRAS accepte

Linking the formation and fate of exo-Kuiper belts within solar system analogues

Abstract Escalating observations of exo-minor planets and their destroyed remnants both passing through the solar system and within white dwarf planetary systems motivate an understanding of the orbital history and fate of exo-Kuiper belts and planetesimal discs. Here we explore how the structure of a 40 − 1000 au annulus of planetesimals orbiting inside of a solar system analogue that is itself initially embedded within a stellar cluster environment varies as the star evolves through all of its stellar phases. We attempt this computationally challenging link in four parts: (1) by performing stellar cluster simulations lasting 100 Myr, (2) by making assumptions about the subsequent quiescent 11 Gyr main-sequence evolution, (3) by performing simulations throughout the giant branch phases of evolution, and (4) by making assumptions about the belt’s evolution during the white dwarf phase. Throughout these stages, we estimate the planetesimals’ gravitational responses to analogues of the four solar system giant planets, as well as to collisional grinding, Galactic tides, stellar flybys, and stellar radiation. We find that the imprint of stellar cluster dynamics on the architecture of ≳ 100 km-sized exo-Kuiper belt planetesimals is retained throughout all phases of stellar evolution unless violent gravitational instabilities are triggered either (1) amongst the giant planets, or (2) due to a close (≪103 au) stellar flyby. In the absence of these instabilities, these minor planets simply double their semimajor axis while retaining their primordial post-cluster eccentricity and inclination distributions, with implications for the free-floating planetesimal population and metal-polluted white dwarfs