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 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 Zocchi, A. and Bertin, G. and Varri, A. L.
18 pages, 7 figures. Accepted for publication in Astronomy & Astrophysics

We perform a systematic combined photometric and kinematic analysis of a sample of globular clusters under different relaxation conditions, based on their core relaxation time (as listed in available catalogs), by means of two well-known families of spherical stellar dynamical models. Systems characterized by shorter relaxation time scales are expected to be better described by isotropic King models, while less relaxed systems might be interpreted by means of non-truncated, radially-biased anisotropic f^(\nu) models, originally designed to represent stellar systems produced by a violent relaxation formation process and applied here for the first time to the study of globular clusters. The comparison between dynamical models and observations is performed by fitting simultaneously surface brightness and velocity dispersion profiles. For each globular cluster, the best-fit model in each family is identified, along with a full error analysis on the relevant parameters. Detailed structural properties and mass-to-light ratios are also explicitly derived. We find that King models usually offer a good representation of the observed photometric profiles, but often lead to less satisfactory fits to the kinematic profiles, independently of the relaxation condition of the systems. For some less relaxed clusters, f^(\nu) models provide a good description of both observed profiles. Some derived structural characteristics, such as the total mass or the half-mass radius, turn out to be significantly model-dependent. The analysis confirms that, to answer some important dynamical questions that bear on the formation and evolution of globular clusters, it would be highly desirable to acquire larger numbers of accurate kinematic data-points, well distributed over the cluster field.

by Taylor, Paul A. and Miller, John C.
14 pages, 9 figures, submitted to MNRAS

A commonly cited drawback of SPH is the introduction of spurious shear viscosity by the artificial viscosity term in situations involving rotation. Existing approaches for understanding its effect include approximative analytic formulae and disc-averaged behaviour in specific ring-spreading simulations, based on the kinematic contribution of the artificial viscosity. In this work, we have developed a simple, general technique for evaluating the local effect of artificial viscosity directly from the entropic function of each SPH particle. This is simple and quick to implement, and it allows a detailed characterization of its effects as a function of position. Several advantages of this local method are discussed, including its ease in evaluation, its greater accuracy and its broad applicability to arbitary flow geometries and equations of state. Here, we apply this approach to various disc flows, including simulations which implement the commonly-used Balsara switch. Comparisons with existing analytic estimates are made, and examples of quantifying explicit dependencies of the effective viscosity in terms of SPH and flow parameters are given. Additionally, a method for the initial placement of SPH particles which reduces numerical fluctuations is discussed and utilised.

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 Garcia-Senz, Domingo and Cabezon, Ruben M. and Escartin, Jose Antonio
15 pages, 12 figures, accepted for publication in Astronomy & Astrophysics

In this paper we develop and check a fully conservative SPH scheme based on a tensor formulation which can be applied to simulate astrophysical systems. In the proposed scheme derivatives are calculated from an integral expression which leads to a tensor, rather than vectorial, estimation of gradients and reduces to the standard formulation in the continuum limit. The new formulation improves the interpolation of physical magnitudes, leading to a set of conservative equations which looks similar to those of standard SPH. The resulting scheme was checked using a variety of well known tests, all of them simulated in two dimensions. An application of the proposed tensor method to astrophysics was also discussed by simulating the stability of a sun-like polytrope calculated in three dimensions.

by Rice, W. K. M. and Forgan, D. H. and Armitage, P. J.
9 pages, 11 figures, MNRAS in press

Recent simulations of self-gravitating accretion discs, carried out using a three-dimensional Smoothed Particle Hydrodynamics (SPH) code by Meru and Bate, have been interpreted as implying that three-dimensional global discs fragment much more easily than would be expected from a two-dimensional local model. Subsequently, global and local two-dimensional models have been shown to display similar fragmentation properties, leaving it unclear whether the three-dimensional results reflect a physical effect or a numerical problem associated with the treatment of cooling or artificial viscosity in SPH. Here, we study how fragmentation of self-gravitating disc flows in SPH depends upon the implementation of cooling. We run disc simulations that compare a simple cooling scheme, in which each particle loses energy based upon its internal energy per unit mass, with a method in which the cooling is derived from a smoothed internal energy density field. For the simple per particle cooling scheme, we find a significant increase in the minimum cooling time scale for fragmentation with increasing resolution, matching previous results. Switching to smoothed cooling, however, results in lower critical cooling time scales, and tentative evidence for convergence at the highest spatial resolution tested. We conclude that precision studies of fragmentation using SPH require careful consideration of how cooling (and, probably, artificial viscosity) is implemented, and that the apparent non-convergence of the fragmentation boundary seen in prior simulations is likely a numerical effect. In real discs, where cooling is physically smoothed by radiative transfer effects, the fragmentation boundary is probably displaced from the two-dimensional value by a factor that is only of the order of unity.

by Laibe, Guillaume and Price, Daniel J.
Accepted for publication in MNRAS

In a companion paper (Laibe & Price 2011b), we have presented an algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH). In this paper, we develop an implicit timestepping method that preserves the exact conservation of the both linear and angular momentum in the underlying SPH algorithm, but unlike previous schemes, allows the iterations to converge to arbitrary accuracy and is suited to the treatment of non- linear drag regimes. The algorithm presented in Paper I is also extended to deal with realistic astrophysical drag regimes, including both linear and non-linear Epstein and Stokes drag. The scheme is benchmarked against the test suite presented in Paper I, including i) the analytic solutions of the dustybox problem and ii) solutions of the dustywave, dustyshock, dustysedov and dustydisc obtained with explicit timestepping. We find that the implicit method is 1- 10 times faster than the explicit temporal integration when the ratio r between the the timestep and the drag stopping time is 1 < r < 1000.

by Laibe, Guillaume and Price, Daniel J.
Accepted for publication in MNRAS

We present a new algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH), systematically addressing a number of key issues including the generalised SPH density estimate in multi-fluid systems, the consistent treatment of variable smoothing length terms, finite particle size, time step stability, thermal coupling terms and the choice of kernel and smoothing length used in the drag operator. We find that using double-hump shaped kernels improves the accuracy of the drag interpolation by a factor of several hundred compared to the use of standard SPH bell-shaped kernels, at no additional computational expense. In order to benchmark our algorithm, we have developed a comprehensive suite of standardised, simple test problems for gas and dust mixtures: dustybox, dustywave, dustyshock, dustysedov and dustydisc, the first three of which have known analytic solutions. We present the validation of our algorithm against all of these tests. In doing so, we show that the spatial resolution criterion \Delta < cs ts is a necessary condition in all gas+dust codes that becomes critical at high drag (i.e. small stopping time ts) in order to correctly predict the dynamics. Implicit timestepping and the implementation of realistic astrophysical drag regimes are addressed in a companion paper.

by Aranha, R. F. and Soares, I. Damião and Tonini, E. V.
18 pages, 12 Figures

We examine numerically the post-merger regime of two Schwarzschild black holes in non head-on collision. Our treatment is made in the realm of non-axisymmetric Robinson-Trautman spacetimes which are appropriate for the description of the system. Characteristic initial data for the system are constructed and the Robinson-Trautman equation is integrated using a numerical code based on the Galerkin spectral method. The collision is planar, restricted to the plane determined by the directions of the two initial colliding black holes, with the net momentum fluxes of gravitational waves confined to this plane. We evaluate the efficiency of mass-energy extraction, the total energy and momentum carried out by gravitational waves and the momentum distribution of the remnant black hole. Our analysis is based on the Bondi-Sachs four momentum conservation laws. Head-on collisions and orthogonal collisions constitute, respectively, upper and lower bounds to the power emission and to the efficiency of mass-energy extraction by gravitational waves. The momentum extraction and the pattern of the momentum fluxes, as a function of the incidence angle, are examined. The momentum extraction characterizes a regime of strong deceleration of the system. The angular pattern of gravitational wave signals is also examined. They are typically bremsstrahlung for early times emission. Gravitational waves are also emitted outside the plane of collision but this component has a zero net momentum flux. The relation between the incidence angle of collision and the exit angle of the remnant closely approximates a relation for inelastic collisions of classical particles in Newtonian dynamics.

by Springel, Volker
35 pages, 10 figures; invited review for the volume “Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings”, eds. R. van de Weijgaert, G. Vegter, J. Ritzerveld and V. Icke, Springer (accepted)

At the heart of any method for computational fluid dynamics lies the question of how the simulated fluid should be discretized. Traditionally, a fixed Eulerian mesh is often employed for this purpose, which in modern schemes may also be adaptively refined during a calculation. Particle-based methods on the other hand discretize the mass instead of the volume, yielding an approximately Lagrangian approach. It is also possible to achieve Lagrangian behavior in mesh-based methods if the mesh is allowed to move with the flow. However, such approaches have often been fraught with substantial problems related to the development of irregularity in the mesh topology. Here we describe a novel scheme that eliminates these weaknesses. It is based on a moving unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite volume approach, based on a second-order Godunov scheme with an exact Riemann solver. A particularly powerful feature of the approach is that the mesh-generating points can in principle be moved arbitrarily. If they are given the velocity of the local flow, a highly accurate Lagrangian formulation of continuum hydrodynamics is obtained that is free of mesh distortion problems, while it is at the same time fully Galilean-invariant, unlike ordinary Eulerian codes. We describe the formulation and implementation of our new Voronoi-based hydrodynamics, and we discuss a number of illustrative test problems that highlight its performance in practical applications.

by Springel, Volker
43 pages, 11 figures, invited review that appeared in ARA&A

This review discusses Smoothed Particle Hydrodynamics (SPH) in the astrophysical context, with a focus on inviscid gas dynamics. The particle-based SPH technique allows an intuitive and simple formulation of hydrodynamics that has excellent conservation properties and can be coupled to self-gravity easily and highly accurately. The Lagrangian character of SPH allows it to automatically adjust its resolution to the clumping of matter, a property that makes the scheme ideal for many applications in astrophysics, where often a large dynamic range in density is encountered. We discuss the derivation of the basic SPH equations in their modern formulation, and give an overview about extensions of SPH developed to treat physics such as radiative transfer, thermal conduction, relativistic dynamics or magnetic fields. We also briefly describe some of the most important applications areas of SPH in astrophysical research. Finally, we provide a critical discussion of the accuracy of SPH for different hydrodynamical problems, including measurements of its convergence rate for important classes of problems.

by Nakano, Hiroyuki and Zlochower, Yosef and Lousto, Carlos O. and Campanelli, Manuela
23 pages, 35 figures, revtex4

We revisit the scenario of small-mass-ratio (q) black-hole binaries; performing new, more accurate, simulations of mass ratios 10:1 and 100:1 for initially nonspinning black holes. We propose fitting functions for the trajectories of the two black holes as a function of time and mass ratio (in the range 1/100 < q < 1/10$) that combine aspects of post-Newtonian trajectories at smaller orbital frequencies and plunging geodesics at larger frequencies. We then use these trajectories to compute waveforms via black hole perturbation theory. Using the advanced LIGO noise curve, we see a match of ~99.5% for the leading (l,m)=(2,2) mode between the numerical relativity and perturbative waveforms. Nonleading modes have similarly high matches. We thus prove the feasibility of efficiently generating a bank of gravitational waveforms in the intermediate-mass-ratio regime using only a sparse set of full numerical simulations.

by Cordero-Carrión, Isabel and Cerdá-Durán, Pablo and Ibáñez, José María
18 pages, 9 figures, 2 tables

The Fully Constrained Formulation (FCF) of General Relativity is a novel framework introduced as an alternative to the hyperbolic formulations traditionally used in numerical relativity. The FCF equations form a hybrid elliptic-hyperbolic system of equations including explicitly the constraints. We present an implicit-explicit numerical algorithm to solve the hyperbolic part, whereas the elliptic sector shares the form and properties with the well known Conformally Flat Condition (CFC) approximation. We show the stability andconvergence properties of the numerical scheme with numerical simulations of vacuum solutions. We have performed the first numerical evolutions of the coupled system of hydrodynamics and Einstein equations within FCF. As a proof of principle of the viability of the formalism, we present 2D axisymmetric simulations of an oscillating neutron star. In order to simplify the analysis we have neglected the back-reaction of the gravitational waves into the dynamics, which is small (<2 %) for the system considered in this work. We use spherical coordinates grids which are well adapted for simulations of starsand allow for extended grids that marginally reach the wave zone. We have extracted the gravitational wave signature and compared to the Newtonian quadrupole and hexadecapole formulae. Both extraction methods show agreement within the numerical errors and the approximations used (~5 %).

by Tonita, Aaryn
Code available at https://github.com/SwampWalker/LeapingMonkey

Black hole initial data is usually produced using Bowen-York type puncture initial data or by applying an excision boundary condition. The benefits of the Bowen-York initial data are the ability to specify the spin and momentum of the system as parameters of the initial data. In an attempt to extend these benefits to other formulations of the Einstein constraints, the puncture method is reformulated using distributions as source terms. It is shown how the Bowen-York puncture black hole initial data and the trumpet variation is generated by distributional sources. A heuristic argument is presented to argue that these sources are the general sources of spin and momentum. In order to clarify the meaning of other distributional sources, an exact family of initial data with generalized sources to the Hamiltonian constraint are studied; spinning trumpet black hole initial data and black hole initial data with higher order momentum sources are also studied.

by Kiuchi, Kenta and Shibata, Masaru and Montero, Pedro J. and Font, José A.
4 pages, 4 figure, to be published in PRL

Black hole (BH)–torus systems are promising candidates for the central engine of gamma-ray bursts (GRBs), and also possible outcomes of the collapse of supermassive stars to supermassive black holes (SMBHs). By three-dimensional general relativistic numerical simulations, we show that an $latex m=1$ nonaxisymmetric instability grows for a wide range of self-gravitating tori orbiting BHs. The resulting nonaxisymmetric structure persists for a timescale much longer than the dynamical one, becoming a strong emitter of large amplitude, quasiperiodic gravitational waves. Our results indicate that both, the central engine of GRBs and newly formed SMBHs, can be strong gravitational wave sources observable by forthcoming ground-based and spacecraft detectors.

by Canizares, Priscilla and Sopuerta, Carlos F.
4 pages, 2 figures, JPCS latex style. Submitted to JPCS (special issue for the proceedings of the Spanish Relativity Meeting (ERE2010))

When a stellar-mass compact object is captured by a supermassive black hole located in a galactic centre, the system losses energy and angular momentum by the emission of gravitational waves. Subsequently, the stellar compact object evolves inspiraling until plunging onto the massive black hole. These EMRI systems are expected to be one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna (LISA). However, the detection of EMRI signals will require of very accurate theoretical templates taking into account the gravitational self-force, which is the responsible of the stellar-compact object inspiral. Due to its potential applicability on EMRIs, the obtention of an efficient method to compute the scalar self-force acting on a point-like particle orbiting around a massive black hole is being object of increasing interest. We present here a review of our time-domain numerical technique to compute the self-force acting on a point-like particle and we show its suitability to deal with both circular and eccentric orbits.

by Oshino, Shoichi and Funato, Yoko and Makino, Junichiro
22 pages, 15 figures

In this paper, we present a new hybrid algorithm for the time integration of collisional N-body systems. In this algorithm, gravitational force between two particles is divided into short-range and long-range terms, using a distance-dependent cutoff function. The long-range interaction is calculated using the tree algorithm and integrated with the constant-timestep leapfrog integrator. The short-range term is calculated directly and integrated with the high-order Hermite scheme. We can reduce the calculation cost per orbital period from O(N^2) to O(N log N), without significantly increasing the long-term integration error. The results of our test simulations show that close encounters are integrated accurately. Long-term errors of the total energy shows random-walk behaviour, because it is dominated by the error caused by tree approximation.

by Canizares, Priscilla and Sopuerta, Carlos F.
IOP LaTeX style. 11 pages, 4 pages. Contribution to the NRDA/CAPRA 2010 Conference

The computation of the self-force constitutes one of the main challenges for the construction of precise theoretical waveform templates in order to detect and analyze extreme-mass-ratio inspirals with the future space-based gravitational-wave observatory LISA. Since the number of templates required is quite high, it is important to develop fast algorithms both for the computation of the self-force and the production of waveforms. In this article we show how to tune a recent time-domain technique for the computation of the self-force, what we call the Particle without Particle scheme, in order to make it very precise and at the same time very efficient. We also extend this technique in order to allow for highly eccentric orbits.

by Lodato, Giuseppe and Clarke, Cathie C.
7 pages, 2 figures. Accepted by MNRAS

Stimulated by recent results by Meru and Bate (2010a,b), we revisit the issue of resolution requirements for simulating self-gravitating accretion discs with Smoothed Particle Hydrodynamics (SPH). We show that the results by Meru and Bate (2010a) are consistent with those of Meru and Bate (2010b) if they are both interpreted as driven by resolution effects, therefore implying that the resolution criterion for cooling gaseous discs is a function of the imposed cooling rate. We discuss two possible numerical origins of such dependence, which are both consistent with the limited number of available data. Our results tentatively indicate that convergence for current simulations is being reached for a number of SPH particles approaching 10 millions (for a disc mass of order 10 per cent of the central object mass), which would set the critical cooling time for fragmentation at about $latex 15\Omega^{-1}$, roughly a factor two larger than previously thought. More in general, we discuss the extent to which the large number of recent numerical results are reliable or not. We argue that those results that pertain to the dynamics associated with gravitational instabilities (such as the locality of angular momentum transport, and the relationship between density perturbation and induced stress) are robust, while those pertaining to the thermodynamics of the system (such as the determination of the critical cooling time for fragmentation) can be affected by poor resolution.

by Sperhake, Ulrich and Bruegmann, Bernd and Mueller, Doreen and Sopuerta, Carlos F.
Submitted to CQG, Special Edition for NRDA/CAPRA 2010, 13 pages, 7 figures

We analyse an eleven-orbit inspiral of a non-spinning black-hole binary with mass ratio q=M1/M2=4. The numerically obtained gravitational waveforms are compared with post-Newtonian (PN) predictions including several sub-dominant multipoles up to multipolar indices (l=5,m=5). We find that (i) numerical and post-Newtonian predictions of the phase of the (2,2) mode accumulate a phase difference of about 0.35 rad at the PN cut off frequency 0.1 for the Taylor T1 approximant; (ii) in contrast to previous studies of equal-mass and specific spinning binaries, we find the Taylor T4 approximant to agree less well with numerical results, provided the latter are extrapolated to infinite extraction radius; (iii) extrapolation of gravitational waveforms to infinite extraction radius is particularly important for subdominant multipoles with l unequal m; (iv) 3PN terms in post-Newtonian multipole expansions significantly improve the agreement with numerical predictions for sub-dominant multipoles.

by McWilliams, Sean T.
Invited review for NRDA/CAPRA 2010, CQG special issue – 7 pages, 1 figure, 1 table

The advent of long-term stability in numerical relativity has yielded a windfall of answers to long-standing questions regarding the dynamics of space-time, matter, and electromagnetic fields in the strong-field regime of black-hole binary mergers. In this review, we will briefly summarize the methodology currently applied to these problems, emphasizing the most recent advancements. We will discuss recent results of astrophysical relevance, and present some novel interpretation. Though we primarily present a review, we also present a simple analytical model for the time-dependent Poynting flux from two orbiting black holes immersed in a magnetic field, which compares favorably with recent numerical results. Finally, we will discuss recent advancements in our theoretical understanding of merger dynamics and gravitational waveforms that have resulted from interpreting the ever-growing body of numerical relativity results.

by Bernuzzi, Sebastiano and Nagar, Alessandro and Zenginoglu, Anil

We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses $latex \mu$ and $latex M$ in the extreme-mass-ratio limit, $latex \mu/M=\nu\ll 1$. We focus on the transition from quasicircular inspiral to plunge, merger and ringdown.We compare the EOB waveform to a Regge-Wheeler-Zerilli (RWZ) waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by leading-order $latex {\cal O}(\nu)$ analytically–resummed radiation reaction. The EOB and the RWZ waveforms have an initial dephasing of about $latex 5\times 10^{-4}$ rad and maintain then a remarkably accurate phase coherence during the long inspiral ($latex \sim 33$ orbits), accumulating only about $latex -2\times 10^{-3}$ rad until the last stable orbit, i.e. $latex \Delta\phi/\phi\sim -5.95\times 10^{-6}$. We obtain such accuracy without calibrating the analytically-resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for LISA-oriented studies. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasi-circular corrections both in the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasi-circular parameters by requiring compatibility between EOB and RWZ waveforms at the light-ring. The resulting phase difference around merger time is as small as $latex \pm 0.015$ rad, with a fractional amplitude agreement of $latex 2.5%$. This suggest that next-to-quasi-circular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical relativity waveforms.

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 Lubich, Christian and Walther, Benny and Bruegmann, Bernd
9 pages, 6 figures

We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In the context of the splitting, it is possible to integrate the individual terms of the spin-orbit and spin-spin Hamiltonians analytically, exploiting the special structure of the underlying equations of motion. The outcome is a symplectic, time-reversible integrator, which can be raised to arbitrary order by composition. A fourth-order version is shown to give excellent behavior concerning error growth and conservation of energy and angular momentum in long-term simulations. Favorable properties of the integrator are retained in the presence of weak dissipative forces due to radiation damping in the full post-Newtonian equations.

by Manca, Gian Mario and Vallisneri, Michele
RevTeX4, 21 pages, 9 PDF figures

The efficient placement of signal templates in source-parameter space is a crucial requisite for exhaustive matched-filtering searches of modeled gravitational-wave sources. Unfortunately, the current placement algorithms based on regular parameter-space meshes are difficult to generalize beyond simple signal models with few parameters. Various authors have suggested that a general, flexible, yet efficient alternative can be found in randomized placement strategies such as random placement and stochastic placement, which enhances random placement by selectively rejecting templates that are too close to others. In this article we explore several theoretical and practical issues in randomized placement: the size and performance of the resulting template banks; the effects of parameter-space boundaries; the use of quasi-random (self avoiding) number sequences; most important, the implementation of these algorithms in curved signal manifolds with and without the use of a Riemannian signal metric, which may be difficult to obtain. Specifically, we show how the metric can be replaced with a discrete triangulation-based representation of local geometry. We argue that the broad class of randomized placement algorithms offers a promising answer to many search problems, but that the specific choice of a scheme and its implementation details will still need to be fine-tuned separately for each problem.

by Barack, Leor and Sago, Norichika
42 pages

We present a numerical code for calculating the local gravitational self-force acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenz-gauge metric perturbation equations (sourced by the delta-function particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical self-force along the orbit is then obtained via mode-sum regularization. The total self-force contains a dissipative piece as well as a conservative piece, and we describe a simple method for disentangling these two pieces in a time-domain framework. The dissipative component is responsible for the loss of orbital energy and angular momentum through gravitational radiation; as a test of our code we demonstrate that the work done by the dissipative component of the computed force is precisely balanced by the asymptotic fluxes of energy and angular momentum, which we extract independently from the wave-zone numerical solutions. The conservative piece of the self force does not affect the time-averaged rate of energy and angular-momentum loss, but it influences the evolution of the orbital phases; this piece is calculated here for the first time in eccentric strong-field orbits. As a first concrete application of our code we recently reported the value of the shift in the location and frequency of the innermost stable circular orbit due to the conservative self-force [Phys. Rev. Lett.\ {\bf 102}, 191101 (2009)]. Here we provide full details of this analysis, and discuss future applications.

by Lousto, Carlos O. and Nakano, Hiroyuki and Zlochower, Yosef and Campanelli, Manuela
4 pages, 5 figures, revtex4

We study black-hole binaries in the intermediate-mass-ratio regime 0.01 < q < 0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO/VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully-nonlinear numerical simulations.

by Mueller, Doreen and Bruegmann, Bernd
15 pages, submitted to CQG for NRDA 2009 conference proceedings

Moving puncture simulations of black hole binaries rely on a specific gauge choice that leads to approximately stationary coordinates near each black hole. Part of the shift condition is a damping parameter, which has to be properly chosen for stable evolutions. However, a constant damping parameter does not account for the difference in mass in unequal mass binaries. We introduce a position dependent shift damping that addresses this problem. Although the coordinates change, the changes in the extracted gravitational waves are small.

by Zenginoglu, Anil
9 pages, 8 figures

We study linear gravitational perturbations of Schwarzschild spacetime by solving numerically Regge-Wheeler-Zerilli equations in time domain using hyperboloidal surfaces and a compactifying radial coordinate. We stress the importance of including the asymptotic region in the computational domain in studies of gravitational radiation. The hyperboloidal approach should be helpful in a wide range of applications employing black hole perturbation theory.

by Pollney, Denis and Reisswig, Christian and Schnetter, Erik and Dorband, Nils and Diener, Peter

We present results from a new code for binary black hole evolutions using the moving-puncture approach, implementing finite differences in generalised coordinates, and allowing the spacetime to be covered with multiple communicating non-singular coordinate patches. Here we consider a regular Cartesian near zone, with adapted spherical grids covering the wave zone. The efficiencies resulting from the use of adapted coordinates allow us to maintain sufficient grid resolution to an artificial outer boundary location which is causally disconnected from the measurement. For the well-studied test-case of the inspiral of an equal-mass non-spinning binary (evolved for more than 8 orbits before merger), we determine the phase and amplitude to numerical accuracies better than 0.010% and 0.090% during inspiral, respectively, and 0.003% and 0.153% during merger. The waveforms, including the resolved higher harmonics, are convergent and can be consistently extrapolated to $latex r\to\infty$ throughout the simulation, including the merger and ringdown. Ringdown frequencies for these modes (to $latex (\ell,m)=(6,6)$) match perturbative calculations to within 0.01%, providing a strong confirmation that the remnant settles to a Kerr black hole with irreducible mass $latex M_{\rm irr} = 0.884355\pm20\times10^{-6}$ and spin $latex S_f/M_f^2 = 0.686923 \pm 10\times10^{-6}$

by Chung, Shin Kee and Wen, Linqing and Blair, David and Cannon, Kipp and Datta, Amitava
12 pages, 4 figures, submitted to CQG

We report a novel application of graphics processing units (GPUs) for the purpose of accelerating the search pipelines for gravitational waves from coalescing binaries of compact objects. A speed-up of 16 fold has been achieved compared with a single central processing unit (CPU). We show that substantial improvements are possible and discuss the reduction in CPU count required for the detection of inspiral sources afforded by the use of GPUs.

by Preto, Miguel and Saha, Prasenjit
21 pages, 5 figures, submitted to Astrophysical Journal

Stars near the Galactic center reach a few percent of light speed during pericenter passage, which makes post-Newtonian effects potentially detectable. We formulate the orbit equations in Hamiltonian form such that the $latex O(v^2/c^2)$ and $latex O(v^3/c^3)$ post-Newtonian effects of the Kerr metric appear as a simple generalization of the Kepler problem. A related perturbative Hamiltonian applies to photon paths. We then derive a symplectic integrator with adaptive time-steps, for fast and accurate numerical calculation of post-Newtonian effects. Using this integrator, we explore relativistic effects. Taking the star S2 as an example, we find that general relativity would contribute tenths of mas in astrometry and tens of $latex \rm km s^{-1}$ in kinematics. (For eventual comparison with observations, redshift and time-delay contributions from the gravitational field on light paths will need to be calculated, but we do attempt these in the present paper.) The contribution from stars, gas, and dark matter in the Galactic center region is still poorly constrained observationally, but current models suggest that the resulting Newtonian perturbation on the orbits could plausibly be of the same order as the relativistic effects for stars with semi-major axes $latex \gtrsim 0.01$ pc (or 250 mas). Nevertheless, the known and distinctive {\it time dependence} of the relativistic perturbations may make it possible to disentangle and extract both effects from observations.

by Lodato, G. and Nayakshin, S. and King, A. R. and Pringle, J. E.
11 pages, 10 figures, MNRAS accepted

We compute the effect of an orbiting gas disc in promoting the coalescence of a central supermassive black hole binary. Unlike earlier studies, we consider a finite mass of gas with explicit time dependence: we do not assume that the gas necessarily adopts a steady state or a spatially constant accretion rate, i.e. that the merging black hole was somehow inserted into a pre–existing accretion disc. We consider the tidal torque of the binary on the disc, and the binary’s gravitational radiation. We study the effects of star formation in the gas disc in a simple energy feedback framework. The disc spectrum differs in detail from that found before. In particular, tidal torques from the secondary black hole heat the edges of the gap, creating bright rims around the secondary. These rims do not in practice have uniform brightness either in azimuth or time, but can on average account for as much as 50 per cent of the integrated light from the disc. This may lead to detectable high–photon–energy variability on the relatively long orbital timescale of the secondary black hole, and thus offer a prospective signature of a coalescing black hole binary. We also find that the disc can drive the binary to merger on a reasonable timescale only if its mass is at least comparable with that of the secondary black hole, and if the initial binary separation is relatively small, i.e. $latex a_0 \lesssim 0.05$ pc. Star formation complicates the merger further by removing mass from the disc. In the feedback model we consider, this sets an effective limit to the disc mass. As a result, binary merging is unlikely unless the black hole mass ratio is $latex \la 0.001$. Gas discs thus appear not to be an effective solution to the `last parsec’ problem for a significant class of mergers.

by Megevand, Miguel and Anderson, Matthew and Frank, Juhan and Hirschmann, Eric W. and Lehner, Luis and Liebling, Steven L. and Motl, Patrick M. and Neilsen, David
10 pages, 13 figures

The merger process of a binary black hole system can have a strong impact on a circumbinary disk. In the present work we study the effect of both central mass reduction (due to the energy loss through gravitational waves) and a possible black hole recoil (due to asymmetric emission of gravitational radiation). For the mass reduction case and recoil directed along the disk’s angular momentum, oscillations are induced in the disk which then modulate the internal energy and bremsstrahlung luminosities. On the other hand, when the recoil direction has a component orthogonal to the disk’s angular momentum, the disk’s dynamics are strongly impacted, giving rise to relativistic shocks. The shock heating leaves its signature in our proxies for radiation, the total internal energy and bremsstrahlung luminosity. Interestingly, for cases where the kick velocity is below the smallest orbital velocity in the disk (a likely scenario in real AGN), we observe a common, characteristic pattern in the internal energy of the disk. Variations in kick velocity simply provide a phase offset in the characteristic pattern implying that observations of such a signature could yield a measure of the kick velocity through electromagnetic signals alone.

by Palenzuela, Carlos and Anderson, Matthew and Lehner, Luis and Liebling, Steven L. and Neilsen, David
4 pages, 4 figures

In addition to producing gravitational waves (GW), the dynamics of a binary black hole system could induce emission of electromagnetic (EM) radiation by affecting the behavior of plasmas and electromagnetic fields in their vicinity. We here study how the electromagnetic fields are affected by a pair of orbiting black holes through the merger. In particular, we show how the binary’s dynamics induce a variability in possible electromagnetically induced emissions as well as a possible enhancement of electromagnetic fields during the late-merge and merger epochs. These time dependent features will likely leave their imprint in processes generating detectable emissions and can be exploited in the detection of electromagnetic counterparts of gravitational waves.