Sapporo2: a versatile direct N-body library

Bédorf, Jeroen; Gaburov, Evghenii; Zwart, Simon Portegies

doi:10.1186/s40668-015-0012-z

Cited by 10 publications

(7 citation statements)

References 28 publications

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“…With these choices, energy conservation was typically of order 0.1% over the entire length of the integration. The calculations were carried out in serial mode using graphics processing units combined with the sapporo library (Gaburov et al 2009;Bédorf et al 2015). Figure 4 shows the evolution of the semi-major axis and eccentricity of the massive binary in N -body models with γ = (0.6, 1.5, 2), two values of binary mass ratio q = (2×10 −4 , 5×10 −5 ), and two different values for the mass of the field particles m ⋆ = (5 × 10 −6 , 1 × 10 −5 ).…”

Section: Initial Setup and Numerical Methodsmentioning

confidence: 99%

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Dynamical Friction and the Evolution of Supermassive Black Hole Binaries: The Final Hundred-parsec Problem

Dosopoulou

Antonini

2017

ApJ

105

108

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The supermassive black holes originally in the nuclei of two merging galaxies will form a binary in the remnant core. The early evolution of the massive binary is driven by dynamical friction before the binary becomes "hard" and eventually reaches coalescence through gravitational wave emission. We consider the dynamical friction evolution of massive binaries consisting of a secondary hole orbiting inside a stellar cusp dominated by a more massive central black hole. In our treatment we include the frictional force from stars moving faster than the inspiralling object which is neglected in the standard Chandrasekhar's treatment. We show that the binary eccentricity increases if the stellar cusp density profile rises less steeply than ρ ∝ r −2 . In cusps shallower than ρ ∝ r −1 the frictional timescale can become very long due to the deficit of stars moving slower than the massive body. Although including the fast stars increases the decay rate, low mass-ratio binaries (q 10 −3 ) in sufficiently massive galaxies have decay timescales longer than one Hubble time. During such minor mergers the secondary hole stalls on an eccentric orbit at a distance of order one tenth the influence radius of the primary hole (i.e., ≈ 10 − 100pc for massive ellipticals). We calculate the expected number of stalled satellites as a function of the host galaxy mass, and show that the brightest cluster galaxies should have 1 of such satellites orbiting within their cores. Our results could provide an explanation to a number of observations, which include multiple nuclei in core ellipticals, off-center AGNs and eccentric nuclear disks.

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Section: Initial Setup and Numerical Methodsmentioning

confidence: 99%

Section: Initial Setup and Numerical Methodsmentioning

confidence: 99%

Dynamical Friction and the Evolution of Supermassive Black Hole Binaries: The Final Hundred-parsec Problem

Dosopoulou

Antonini

2017

ApJ

105

108

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“…When combined with the Sapporo GPU/GRAPE library (Gaburov et al, 2009), Kira can be run on modern, distributed GPU systems with comparable performance to the NBODY series of codes (Anders et al, 2012). Hardware acceleration was not implemented the current RAPID version, since we have not considered systems with sufficiently large numbers of BHs for efficient GPU useage; however, the development of the Sapporo2 library (Bédorf et al, 2015) provides efficient GPU saturation for small-N systems. We will explore the advantages of a RAPID integration with Sapporo2 in a future paper.…”

Section: Discussionmentioning

confidence: 99%

A new hybrid technique for modeling dense star clusters

et al. 2018

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The "gravitational million-body problem," to model the dynamical evolution of a self-gravitating, collisional N -body system with ∼ 10 6 particles over many relaxation times, remains a major challenge in computational astrophysics. Unfortunately, current techniques to model such systems suffer from severe limitations. A direct N -body simulation with more than 10 5 particles can require months or even years to complete, while an orbit-sampling Monte Carlo approach cannot adequately model the dynamics in a dense cluster core, particularly in the presence of many black holes. We have developed a new technique combining the precision of a direct N -body integration with the speed of a Monte Carlo approach. Our Rapid And Precisely Integrated Dynamics code, the RAPID code, statistically models interactions between neighboring stars and stellar binaries while integrating directly the orbits of stars or black holes in the cluster core. This allows us to accurately simulate the dynamics of the black holes in a realistic globular cluster environment without the burdensome N 2 scaling of a full N -body integration. We compare RAPID models of idealized globular clusters to identical models from the direct N -body and Monte Carlo methods. Our tests show that RAPID can reproduce the half-mass radii, core radii, black hole ejection rates, and binary properties of the direct N -body models far more accurately than a standard Monte Carlo integration while remaining significantly faster than a full N -body integration. With this technique, it will be possible to create more realistic models of Milky Way globular clusters with sufficient rapidity to explore the full parameter space of dense stellar clusters.

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“…Additionally, higher-order Hermite schemes can be unstable unless used with multiple predictor-corrector iterations (Nitadori 2015). High-order Hermite N-body algorithms have been preferred because their larger time step sizes outweigh their cost in floating point operations, and because of their improved treatment of interactions between particles with large mass ratios (Bédorf et al 2015). The present work extends these benefits to simulations of planetary and protoplanetary systems along the lines of the methods presented in Kokubo & Makino (2004).…”

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confidence: 94%

Modified Hermite Integrators of Arbitrary Order

Dittmann

2020

Preprint

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We present a family of modified Hermite integrators of arbitrary order possessing superior behaviour for the integration of Keplerian and near-Keplerian orbits. After recounting the derivation of Hermite N-body integrators of arbitrary order, we derive a corrector expression that minimises integrated errors in the argument of periapsis for any such integrator. In addition to providing an alternate derivation of the modified corrector for the 4th-order Hermite integrator, we focus on improved correctors for the 6th-and 8th-order integrators previously featured in the literature. We present a set of numerical examples and find that the higher-order schemes improve performance, even when considering their slightly higher cost in floating point operations. The algorithms presented herein hold promise for systems dominated by central potentials, such as planetary systems and the centres of galaxies. Existing Hermite integrators of any order can be modified to use the expressions presented here with minimal effort. Accordingly the schemes presented herein can be easily implemented on massively parallel architectures.

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Sapporo2: a versatile direct N-body library

Cited by 10 publications

References 28 publications

Dynamical Friction and the Evolution of Supermassive Black Hole Binaries: The Final Hundred-parsec Problem

Dynamical Friction and the Evolution of Supermassive Black Hole Binaries: The Final Hundred-parsec Problem

A new hybrid technique for modeling dense star clusters

Modified Hermite Integrators of Arbitrary Order

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