GraviDy, a GPU modular, parallel direct-summation N-body integrator: Dynamics with softening

A wide variety of outstanding problems in astrophysics involve the motion of a large number of particles ($N\gtrsim 10^{6}$) under the force of gravity. These include the global evolution of globular clusters, tidal disruptions of stars by a massive black hole, the formation of protoplanets and the detection of sources of gravitational radiation. The direct-summation of $N$ gravitational forces is a complex problem with no analytical solution and can only be tackled with approximations and numerical methods. To this end, the Hermite scheme is a widely used integration method. With different numerical techniques and special-purpose hardware, it can be used to speed up the calculations. But these methods tend to be computationally slow and cumbersome to work with. Here we present a new GPU, direct-summation $N-$body integrator written from scratch and based on this scheme. This code has high modularity, allowing users to readily introduce new physics, it exploits available high-performance computing resources and will be maintained by public, regular updates. The code can be used in parallel on multiple CPUs and GPUs, with a considerable speed-up benefit. The single GPU version runs about 200 times faster compared to the single CPU version. A test run using 4 GPUs in parallel shows a speed up factor of about 3 as compared to the single GPU version. The conception and design of this first release is aimed at users with access to traditional parallel CPU clusters or computational nodes with one or a few GPU cards

GraviDy: a modular, GPU-based, direct-summation N-body code

The direct-summation of N gravitational forces is a complex problem for which there is no analytical solution. Dense stellar systems such as galactic nuclei and stellar clusters are the loci of different interesting problems. In this work we present a new GPU, direct-summation N-body integrator written from scratch and based on the Hermite scheme. The first release of the code consists of the Hermite integrator for a system of N bodies with softening. We find an acceleration factor of about ≈ 90 of the GPU version in a single node as compared to the Serial-Single-CPU one. We additionally investigate the impact of using softening in the dynamics of a dense cluster. We study how it affects the two body relaxation, as compared with another code, NBODY6, which uses KS regularization, so as to understand the role of softening in the evolution of the system. This initial release is the first step towards more and more realistic scenarios, starting for a proper treatment for binary evolution, close encounters and the role of a massive black hole

Retrograde binaries of massive black holes in circum-binary accretion discs

We explore the hardening of a massive black hole binary embedded in a circum-binary gas disc when the binary and the gas are coplanar and the gas is counter-rotating. The secondary black hole, revolving in the direction opposite to the gas, experiences a drag from gas-dynamical friction and from direct accretion of part of it. Using two-dimensional (2D) hydrodynamical grid simulations we investigate the effect of changing the accretion prescriptions on the dynamics of the secondary black hole which in turn affect the binary hardening and eccentricity evolution. We find that realistic accretion prescriptions lead to results that differ from those inferred assuming accretion of all the gas within the Roche Lobe of the secondary black hole. Different accretion prescriptions result in different disc's surface densities which alter the black hole's dynamics back. Full 3D SPH realizations of a number of representative cases, run over a shorter interval of time, validate the general trends observed in the less computationally demanding 2D simulations. Initially circular black hole binaries increase only slightly their eccentricity which then oscillates around small values (<0.1) while they harden. By contrast, initially eccentric binaries become more and more eccentric. A semi-analytical model describing the black hole's dynamics under accretion only explores the late evolution stages of the binary in an otherwise unperturbed retrograde disc to illustrate how eccentricity evolves with time in relation to the shape of the underlying surface density distribution