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

Accretion of clumpy cold gas onto massive black holes binaries: the challenging formation of extended circumbinary structures

Massive black hole binaries (MBHBs) represent an unavoidable outcome of hierarchical galaxy formation, but their dynamical evolution at sub-parsec scales is poorly understood, due to a combination of uncertainties in theoretical models and lack of firm observational evidence. In gas rich environments, it has been shown that a putative extended, steady circumbinary gaseous disc plays an important role in the MBHB evolution, facilitating its coalescence. How gas on galactic scales is transported to the nuclear region to form and maintain such a stable structure is, however, unclear. If, following a galaxy merger, turbulent gas is condenses in cold clumps and filaments that are randomly scattered, gas is naturally transported on parsec scales and interacts with the MBHB in discrete incoherent pockets. The aim of this work is to investigate the gaseous structures arising from this interaction. We employ a suite of smoothed-particle-hydrodynamic simulations to study the formation and evolution of gaseous structures around a MBHB constantly perturbed by the incoherent infall of molecular clouds. We investigate the influence of the infall rate and angular momentum distribution of the clouds on the geometry and stability of the arising structures. We find that the continuous supply of incoherent clouds is a double-edge sword, resulting in the intermittent formation and disruption of circumbinary structures. Anisotropic cloud distributions featuring an excess of co-rotating events generate more prominent co-rotating circumbinary discs. Similar structures are seen when mostly counter-rotating clouds are fed to the binary, even though they are more compact and less stable. In general, our simulations do not show the formation of extended smooth and stable circumbinary discs, typically assumed in analytical and numerical investigations of the the long term evolution of MBHBs. (Abridged)Comment: 22 Pages, 17 Figures. To be submitted to MNRA

Accretion of clumpy cold gas onto massive black hole binaries: a possible fast route to binary coalescence

In currently favoured hierarchical cosmologies, the formation of massive black hole binaries (MBHBs) following galaxy mergers is unavoidable. Still, due the complex physics governing the (hydro)dynamics of the post-merger dense environment of stars and gas in galactic nuclei, the final fate of those MBHBs is still unclear. In gas-rich environments, it is plausible that turbulence and gravitational instabilities feed gas to the nucleus in the form of a series of cold incoherent clumps, thus providing a way to exchange energy and angular momentum between the MBHB and its surroundings. Within this context, we present a suite of smoothed-particle-hydrodynamical models to study the evolution of a sequence of near-radial turbulent gas clouds as they infall towards equal-mass, circular MBHBs. We focus on the dynamical response of the binary orbit to different levels of anisotropy of the incoherent accretion events. Compared to a model extrapolated from a set of individual cloud-MBHB interactions, we find that accretion increases considerably and the binary evolution is faster. This occurs because the continuous infall of clouds drags inwards circumbinary gas left behind by previous accretion events, thus promoting a more effective exchange of angular momentum between the MBHB and the gas. These results suggest that sub-parsec MBHBs efficiently evolve towards coalescence during the interaction with a sequence of individual gas pockets.Comment: 18 pages, 17 figures. Accepted for publication by MNRAS. Find companion paper at arXiv:1801.06179 Animations available at http://multipleclouds.xyz/movies

Black hole binary systems : from dynamics to accretion

The problem of the evolution of a large number of particles due to gravity is crucial to many astrophysical phenomena. An important problem is the dynamical evolution of a dense stellar system, such as a globular cluster (GC), a galactic nucleus (GN) or nuclear star cluster (NSC). Such loci are the breeding grounds of sources of tidal disruptions and gravitational waves. Right in the middle of these regions a massive black hole (MBH) might be lurking, which makes the problem even more interesting, because such massive objects can form a pair and later a binary, which could be powerful source of gravitational radiation for space-borne observatories. The detailed tracking of the dynamical evolution of a set of $N$ stars is a complex problem. Since we lack an analytical solution, it needs to be studied by approximations and numerical methods close to what we might expect from Nature. The close interactions between stars define the core mechanism that determines the global evolution of dense stellar systems. These interactions are responsible for defining the timescale in which catastrophic phenomena happen, such as the core collapse of the system; particularly relevant for the formation of a gravitational capture, that eventually will evolve mostly due to the emission of gravitational radiation. Moreover, depending on the problem we are addressing we might need to add further layers of complexity. For instance, in the case of a GN the presence of gas can play an crucial role, so it needs to be considered, particularly in the massive black hole binary (MBHB) formation process. It has been put forward in the literature that this gas will distribute itself around each MBH in the shape of a disc. The formation of the disc structure around the MBHB is in particular a very important problem which has received very little numerical investigation until the presentation of this work. It is usually assumed that the gas is supplied via the accumulated infall of gaseous clouds on to the binary, and hence this gas is distributed in a disc-like structure around it. Hence, it is relevant to address the formation of binaries taking into account such a gaseous disc around the system in different orbits, and the interaction of the gas with the black holes, not just dynamically, but also via the accretion on to them. Motivated by the complexity and many open question of these fundamental problems, this thesis is (i) a detailed study of the non-linear dynamics that occur in dense stellar systems with state-of-the-art numerical techniques, (ii) a detailed study of the impact of gas on to the binary, in particular to address the role of circumbinary discs on the evolution of a MBHB, and (iii) how repeated infall events of gaseous clouds distribute and shape around such massive binaries, as well as the impact on the dynamical evolution of the binary itself. All of these topics are intertwined and I have worked in them in a parallel way during my PhD. The most remarkable findings of my work are that (i) the use of a softening parameter is critical to analyse the long-term evolution of a dense stellar system, with an important impact on the timescale in which crucial events happen, including the formation of binaries, (ii) the way binaries of MBHs accrete gas in counter-rotating circumbinary discs, will determine the evolution of the massive binary, and (iii) the formation of disc-like structures around these binaries in a GN is, to say the least, challenging. Also, episodic circumbinary structures will modify the orbital evolution of MBHBs, altering their associated gravitational merger timescale

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