arXiv subjects

Peter Berczik

Publications and source records attributed to Peter Berczik.

At least 73 records · Page 4Linked to original sources

arXiv2017

Galaxy Rotation and Supermassive Black Hole Binary Evolution

Supermassive black hole (SMBH) binaries residing at the core of merging galaxies are recently found to be strongly affected by the rotation of their host galaxies. The highly eccentric orbits that form when the host is counterrotating emit strong bursts of gravitational waves that propel rapid SMBH binary coalescence. Most prior work, however, focused on planar orbits and a uniform rotation profile, an unlikely interaction configuration. However, the coupling between rotation and SMBH binary evolution appears to be such a strong dynamical process that it warrants further investigation. This study uses direct N-body simulations to isolate the effect of galaxy rotation in more realistic interactions. In particular, we systematically vary the SMBH orbital plane with respect to the galaxy rotation axis, the radial extent of the rotating component, and the initial eccentricity of the SMBH binary orbit. We find that the initial orbital plane orientation and eccentricity alone can change the inspiral time by an order of magnitude. Because SMBH binary inspiral and merger is such a loud gravitational wave source, these studies are critical for the future gravitational wave detector, LISA, an ESA/NASA mission currently set to launch by 2034.

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arXiv2016

Boosted Tidal Disruption by Massive Black Hole Binaries During Galaxy Mergers FROM The View of N-Body Simulation

Supermassive black hole binaries (SMBHBs) are productions of the hierarchical galaxy formation model. There are many close connections between central SMBH and its host galaxy because the former plays very important roles on the formation and evolution of a galaxy. For this reason, the evolution of SMBHBs in merging galaxies is an essential problem. Since there are many discussions about SMBHB evolution in gas rich environment, we focus on the quiescent galaxy, using tidal disruption as a diagnostic tool. Our study is based on a series of numerical large particle number direct N-body simulations for dry major mergers. According to the simulation results, the evolution can be divided into three phases. In phase I, the tidal disruption rate for two well separated SMBHs in merging system has similar level to single SMBH in isolate galaxy. After two SMBHs getting close enough to form a bound binary in phase II, the disruption rate can be enhanced for ~ 2 order of magnitudes within a short time. This "boosted" disruption stage finishes after the SMBHB evolving to compact binary system in phase III, corresponding to a drop back of disruption rate to a level of a few times higher than that in Phase I. How to correctly extrapolate our N-body simulation results to reality, and implications of our results to observations, are discussed too.

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arXiv2016

Swift coalescence of supermassive black holes in cosmological mergers of massive galaxies

Supermassive black holes (SMBHs) are ubiquitous in galaxies with a sizable mass. It is expected that a pair of SMBHs originally in the nuclei of two merging galaxies would form a binary and eventually coalesce via a burst of gravitational waves. So far theoretical models and simulations have been unable to predict directly the SMBH merger timescale from ab-initio galaxy formation theory, focusing only on limited phases of the orbital decay of SMBHs under idealized conditions of the galaxy hosts. The predicted SMBH merger timescales are long, of order Gyrs, which could be problematic for future gravitational wave searches. Here we present the first multi-scale $Λ$CDM cosmological simulation that follows the orbital decay of a pair of SMBHs in a merger of two typical massive galaxies at $z\sim3$, all the way to the final coalescence driven by gravitational wave emission. The two SMBHs, with masses $\sim10^{8}$ M$_{\odot}$, settle quickly in the nucleus of the merger remnant. The remnant is triaxial and extremely dense due to the dissipative nature of the merger and the intrinsic compactness of galaxies at high redshift. Such properties naturally allow a very efficient hardening of the SMBH binary. The SMBH merger occurs in only $\sim10$ Myr after the galactic cores have merged, which is two orders of magnitude smaller than the Hubble time.

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arXiv2016

On the bar formation mechanism in galaxies with cuspy bulges

We show by numerical simulations that a purely stellar dynamical model composed of an exponential disc, a cuspy bulge, and an NFW halo with parameters relevant to the Milky Way Galaxy is subject to bar formation. Taking into account the finite disc thickness, the bar formation can be explained by the usual bar instability, in spite of the presence of an inner Lindblad resonance, that is believed to damp any global modes. The effect of replacing the live halo and bulge by a fixed external axisymmetric potential (rigid models) is studied. It is shown that while the e-folding time of bar instability increases significantly (from 250 to 500 Myr), the bar pattern speed remains almost the same. For the latter, our average value of 55 km/s/kpc agrees with the assumption that the Hercules stream in the solar neighbourhood is an imprint of the bar--disc interaction at the outer Lindblad resonance of the bar. Vertical averaging of the radial force in the central disc region comparable to the characteristic scale length allows us to reproduce the bar pattern speed and the growth rate of the rigid models, using normal mode analysis of linear perturbation theory in a razor thin disc. The strong increase of the e-folding time with decreasing disc mass predicted by the mode analysis suggests that bars in galaxies similar to the Milky Way have formed only recently.

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arXiv2016

Star-disc interaction in galactic nuclei: orbits and rates of accreted stars

We examine the effect of an accretion disc on the orbits of stars in the central star cluster surrounding a central massive black hole by performing a suite of 39 high-accuracy direct N-body simulations using state-of-the art software and accelerator hardware, with particle numbers up to 128k. The primary focus is on the accretion rate of stars by the black hole (equivalent to their tidal disruption rate for black holes in the small to medium mass range) and the eccentricity distribution of these stars. Our simulations vary not only the particle number, but disc model (two models examined), spatial resolution at the centre (characterised by the numerical accretion radius) and softening length. The large parameter range and physically realistic modelling allow us for the first time to confidently extrapolate these results to real galactic centres. While in a real galactic centre both particle number and accretion radius differ by a few orders of magnitude from our models, which are constrained by numerical capability, we find that the stellar accretion rate converges for models with N > 32k. The eccentricity distribution of accreted stars, however, does not converge. We find that there are two competing effects at work when improving the resolution: larger particle number leads to a smaller fraction of stars accreted on nearly-circular orbits, while higher spatial resolution increases this fraction. We scale our simulations to some nearby galaxies and find that the expected boost in stellar accretion (or tidal disruption, which could be observed as X-ray flares) in the presence of a gas disc is about a factor of 10. Even with this boost, the accretion of mass from stars is still a factor of ~ 100 slower than the accretion of gas from the disc. Thus, it seems accretion of stars is not a major contributor to black hole mass growth.

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arXiv2016

The DRAGON simulations: globular cluster evolution with a million stars

Introducing the DRAGON simulation project, we present direct $N$-body simulations of four massive globular clusters (GCs) with $10^6$ stars and 5$\%$ primordial binaries at a high level of accuracy and realism. The GC evolution is computed with NBODY6++GPU and follows the dynamical and stellar evolution of individual stars and binaries, kicks of neutron stars and black holes, and the effect of a tidal field. We investigate the evolution of the luminous (stellar) and dark (faint stars and stellar remnants) GC components and create mock observations of the simulations (i.e. photometry, color-magnitude diagrams, surface brightness and velocity dispersion profiles). By connecting internal processes to observable features we highlight the formation of a long-lived 'dark' nuclear subsystem made of black holes (BHs), which results in a two-component structure. The inner core is dominated by the BH subsystem and experiences a core collapse phase within the first Gyr. It can be detected in the stellar (luminous) line-of-sight velocity dispersion profiles. The outer extended core - commonly observed in the (luminous) surface brightness profiles - shows no collapse features and is continuously expanding. We demonstrate how a King (1966) model fit to observed clusters might help identify the presence of post core-collapse BH subsystems. For global observables like core and half-mass radii the direct simulations agree well with Monte-Carlo models. Variations in the initial mass function can result in significantly different GC properties (e.g. density distributions) driven by varying amounts of early mass loss and the number of forming BHs.

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arXiv2015

Supermassive Black Holes in Galactic Nuclei with Tidal Disruption of Stars: Paper II - Axisymmetric Nuclei

Tidal Disruption of stars by supermassive central black holes from dense rotating star clusters is modelled by high-accuracy direct N-body simulation. As in a previous paper on spherical star clusters we study the time evolution of the stellar tidal disruption rate and the origin of tidally disrupted stars, now according to several classes of orbits which only occur in axisymmetric systems (short axis tube and saucer). Compared with that in spherical systems, we found a higher TD rate in axisymmetric systems. The enhancement can be explained by an enlarged loss-cone in phase space which is raised from the fact that total angular momentum $\bf J$ is not conserved. As in the case of spherical systems, the distribution of the last apocenter distance of tidally accreted stars peaks at the classical critical radius. However, the angular distribution of the origin of the accreted stars reveals interesting features. Inside the influence radius of the supermassive black hole the angular distribution of disrupted stars has a conspicuous bimodal structure with a local minimum near the equatorial plane. Outside the influence radius this dependence is weak. We show that the bimodal structure of orbital parameters can be explained by the presence of two families of regular orbits, namely short axis tube and saucer orbits. Also the consequences of our results for the loss cone in axisymmetric galactic nuclei are presented.

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arXiv2015

Performance analysis of parallel gravitational $N$-body codes on large GPU cluster

We compare the performance of two very different parallel gravitational $N$-body codes for astrophysical simulations on large GPU clusters, both pioneer in their own fields as well as in certain mutual scales - NBODY6++ and Bonsai. We carry out the benchmark of the two codes by analyzing their performance, accuracy and efficiency through the modeling of structure decomposition and timing measurements. We find that both codes are heavily optimized to leverage the computational potential of GPUs as their performance has approached half of the maximum single precision performance of the underlying GPU cards. With such performance we predict that a speed-up of $200-300$ can be achieved when up to 1k processors and GPUs are employed simultaneously. We discuss the quantitative information about comparisons of two codes, finding that in the same cases Bonsai adopts larger time steps as well as relative energy errors than NBODY6++, typically ranging from $10-50$ times larger, depending on the chosen parameters of the codes. While the two codes are built for different astrophysical applications, in specified conditions they may overlap in performance at certain physical scale, and thus allowing the user to choose from either one with finetuned parameters accordingly.

astro-ph.IM↗

arXiv2015

NBODY6++GPU: Ready for the gravitational million-body problem

Accurate direct $N$-body simulations help to obtain detailed information about the dynamical evolution of star clusters. They also enable comparisons with analytical models and Fokker-Planck or Monte-Carlo methods. NBODY6 is a well-known direct $N$-body code for star clusters, and NBODY6++ is the extended version designed for large particle number simulations by supercomputers. We present NBODY6++GPU, an optimized version of NBODY6++ with hybrid parallelization methods (MPI, GPU, OpenMP, and AVX/SSE) to accelerate large direct $N$-body simulations, and in particular to solve the million-body problem. We discuss the new features of the NBODY6++GPU code, benchmarks, as well as the first results from a simulation of a realistic globular cluster initially containing a million particles. For million-body simulations, NBODY6++GPU is $400-2000$ times faster than NBODY6 with 320 CPU cores and 32 NVIDIA K20X GPUs. With this computing cluster specification, the simulations of million-body globular clusters including $5\%$ primordial binaries require about an hour per half-mass crossing time.

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arXiv2015

On the Influence of Minor Mergers on the Radial Abundance Gradient in Disks of Milky Way-like Galaxies

We investigate the influence of stellar migration caused by minor mergers (mass ratio from 1:70 to 1:8) on the radial distribution of chemical abundances in the disks of Milky Way-like galaxies during the last four Gyr. A GPU-based pure N-body tree-code model without hydrodynamics and star formation was used. We computed a large set of mergers with different initial satellite masses, positions, and orbital velocities. We find that there is no significant metallicity change at any radius of the primary galaxy in the case of accretion of a low-mass satellite of 10$^9$ M$_{\odot}$ (mass ratio 1:70) except for the special case of prograde satellite motion in the disk plane of the host galaxy. The accretion of a satellite of a mass $\gtrsim3\times10^9$ M$_{\odot}$ (mass ratio 1:23) results in an appreciable increase of the chemical abundances at galactocentric distances larger than $\sim10$ kpc. The radial abundance gradient flattens in the range of galactocentric distances from 5 to 15 kpc in the case of a merger with a satellite with a mass $\gtrsim3\times10^9$ M$_{\odot}$. There is no significant change in the abundance gradient slope in the outer disk (from $\sim15$ kpc up to 25 kpc) in any merger while the scatter in metallicities at a given radius significantly increases for most of the satellite's initial masses/positions compared to the case of an isolated galaxy. This argues against attributing the break (flattening) of the abundance gradient near the optical radius observed in the extended disks of Milky Way-like galaxies only to merger-induced stellar migration.

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arXiv2014

SMBH in Galactic Nuclei with Tidal Disruption of Stars

Tidal Disruption of stars by super massive central black holes from dense star clusters is modeled by high-accuracy direct $N$-body simulation. The time evolution of the stellar tidal disruption rate, the effect of tidal disruption on the stellar density profile and for the first time the detailed origin of tidally disrupted stars are carefully examined and compared with classic papers in the field. Up to 128k particles are used in simulation to model the star cluster around the super massive black hole, we use the particle number and the tidal radius of black hole as free parameters for a scaling analysis. The transition from full to empty loss-cone is analyzed in our data, the tidal disruption rate scales with the particle number $N$ in the expected way for both cases. For the first time in numerical simulations (under certain conditions) we can support the concept of a critical radius of Frank & Rees (1976), which claims that most stars are tidally accreted on highly eccentric orbits originating from regions far outside the tidal radius. Due to the consumption of stars moving on radial orbits, a velocity anisotropy is founded inside the cluster. Finally we make an estimation for the real galactic center based on our simulation results and the scaling analysis.

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arXiv2014

Ultramassive Black Hole Coalescence

Although supermassive black holes (SMBHs) correlate well with their host galaxies, there is an emerging view that outliers exist. Henize 2-10, NGC 4889, and NGC1277 are examples of SMBHs at least an order of magnitude more massive than their host galaxy suggests. The dynamical effects of such ultramassive central black holes is unclear. Here, we perform direct N-body simulations of mergers of galactic nuclei where one black hole is ultramassive to study the evolution of the remnant and the black hole dynamics in this extreme regime. We find that the merger remnant is axisymmetric near the center, while near the large SMBH influence radius, the galaxy is triaxial. The SMBH separation shrinks rapidly due to dynamical friction, and quickly forms a binary black hole; if we scale our model to the most massive estimate for the NGC1277 black hole, for example, the timescale for the SMBH separation to shrink from nearly a kiloparsec to less than a parsec is roughly 10 Myr. By the time the SMBHs form a hard binary, gravitational wave emission dominates, and the black holes coalesce in a mere few Myr. Curiously, these extremely massive binaries appear to nearly bypass the 3-body scattering evolutionary phase. Our study suggests that in this extreme case, SMBH coalescence is governed by dynamical friction followed nearly directly by gravitational wave emission, resulting in an rapid and efficient SMBH coalescence timescale. We discuss the implications for gravitational wave event rates and hypervelocity star production.

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arXiv2013

The Link Between Ejected Stars, Hardening and Eccentricity Growth of Super Massive Black Holes in Galactic Nuclei

The hierarchical galaxy formation picture suggests that super massive black holes (MBHs) observed in galactic nuclei today have grown from coalescence of massive black hole binaries (MBHB) after galaxy merging. Once the components of a MBHB become gravitationally bound, strong three-body encounters between the MBHB and stars dominate its evolution in a "dry" gas free environment, and change the MBHB's energy and angular momentum (semi-major axis, eccentricity and orientation). Here we present high accuracy direct N-body simulations of spherical and axisymmetric (rotating) galactic nuclei with order a million stars and two massive black holes that are initially unbound. We analyze the properties of the ejected stars due to slingshot effects from three-body encounters with the MBHB in detail. Previous studies have investigated the eccentricity and energy changes of MBHs using approximate models or Monte-Carlo three body scatterings. We find general agreement with the average results of previous semi-analytic models for spherical galactic nuclei, but our results show a large statistical variation. Our new results show many more phase space details of how the process works, and also show the influence of stellar system rotation on the process. We detect that the angle between the orbital plane of the MBHBs and that of the stellar system (when it rotates) influences the phase-space properties of the ejected stars. We also find that massive MBHB tend to switch stars with counter-rotating orbits into co-rotating orbits during their interactions.

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arXiv2012

Enhanced accretion rates of stars on Super-massive Black Holes by star-disk interactions in galactic nuclei

We investigate the dynamical interaction of a central star cluster surrounding a super-massive black hole and a central accretion disk. The dissipative force acting on stars in the disk leads to an enhanced mass flow towards the super-massive black hole and to an asymmetry in the phase space distribution due to the rotating accretion disk. The accretion disk is considered as a stationary Keplerian rotating disk, which is vertically extended in order to employ a fully self-consistent treatment of stellar dynamics including the dissipative force originating from star-gas ram pressure effects. The stellar system is treated with a direct high-accuracy N-body integration code. A star-by-star representation, desirable in N-body simulations, cannot be extended to real particle numbers yet. Hence, we carefully discuss the scaling behavior of our model with regard to particle number and tidal accretion radius. The main idea is to find a family of models for which the ratio of two-body relaxation time and dissipation time (for kinetic energy of stellar orbits) is constant, which then allows us to extrapolate our results to real parameters of galactic nuclei. Our model is derived from basic physical principles and as such it provides insight into the role of physical processes in galactic nuclei, but it should be regarded as a first step towards more realistic and more comprehensive simulations. Nevertheless, the following conclusions appear to be robust: the star accretion rate onto the accretion disk and subsequently onto the super-massive black hole is enhanced by a significant factor compared to purely stellar dynamical systems neglecting the disk. This process leads to enhanced fueling of central disks in active galactic nuclei and to an enhanced rate of tidal stellar disruptions. [Abridged]

astro-ph.CO↗

arXiv2012

Formation and Hardening of Supermassive Black Hole Binaries in Minor Mergers of Disk Galaxies

We model for the first time the complete orbital evolution of a pair of Supermassive Black Holes (SMBHs) in a 1:10 galaxy merger of two disk dominated gas-rich galaxies, from the stage prior to the formation of the binary up to the onset of gravitational wave emission when the binary separation has shrunk to 1 milli parsec. The high-resolution smoothed particle hydrodynamics (SPH) simulations used for the first phase of the evolution include star formation, accretion onto the SMBHs as well as feedback from supernovae explosions and radiative heating from the SMBHs themselves. Using the direct N-body code ϕ-GPU we evolve the system further without including the effect of gas, which has been mostly consumed by star formation in the meantime. We start at the time when the separation between two SMBHs is ~ 700 pc and the two black holes are still embedded in their galaxy cusps. We use 3 million particles to study the formation and evolution of the SMBH binary till it becomes hard. After a hard binary is formed, we reduce (reselect) the particles to 1.15 million and follow the subsequent shrinking of the SMBH binary due to 3-body encounters with the stars. We find approximately constant hardening rates and that the SMBH binary rapidly develops a high eccentricity. Similar hardening rates and eccentricity values are reported in earlier studies of SMBH binary evolution in the merging of dissipation-less spherical galaxy models. The estimated coalescence time is ~ 2.9 Gyr, significantly smaller than a Hubble time. We discuss why this timescale should be regarded as an upper limit. Since 1:10 mergers are among the most common interaction events for galaxies at all cosmic epochs, we argue that several SMBH binaries should be detected with currently planned space-borne gravitational wave interferometers, whose sensitivity will be especially high for SMBHs in the mass range considered here.

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arXiv2012

Mergers of Unequal Mass Galaxies: Supermassive Black Hole Binary Evolution and Structure of Merger Remnants

Galaxy centers are residing places for Super Massive Black Holes (SMBHs). Galaxy mergers bring SMBHs close together to form gravitationally bound binary systems which, if able to coalesce in less than a Hubble time, would be one of the most promising sources of gravitational waves for the Laser Interferometer Space Antenna (LISA). In spherical galaxy models, SMBH binaries stall at a separation of approximately one parsec, leading to the "final parsec problem" (FPP). On the other hand, it has been shown that merger-induced triaxiality of the remnant in equal-mass mergers is capable of supporting a constant supply of stars on so-called centrophilic orbits that interact with the binary and thus avoid the FPP. In this paper, using a set of direct N-body simulations of mergers of initially spherically symmetric galaxies with different mass ratios, we show that the merger-induced triaxiality is able to drive unequal-mass SMBH binaries to coalescence. The binary hardening rates are high and depend only weakly on the mass ratios of SMBHs for a wide range of mass ratios q. The hardening rates are significantly higher for galaxies having steep cusps in comparison with those having shallow cups at centers. The evolution of the binary SMBH leads to relatively shallower inner slopes at the centers of the merger remnants. The stellar mass displaced by the SMBH binary on its way to coalescence is ~ 1-5 times the combined mass of binary SMBHs. The coalescence times for SMBH binary with mass ~ million solar masses are less than 1 Gyr and for those at the upper end of SMBH masses (~ billion solar masses) are 1-2 Gyr for less eccentric binaries whereas less than 1 Gyr for highly eccentric binaries. SMBH binaries are thus expected to be promising sources of gravitational waves at low and high redshifts.

astro-ph.CO↗

arXiv2012

Interaction of Recoiling Supermassive Black Holes with Stars in Galactic Nuclei

Supermassive black hole binaries (SMBHBs) are the products of frequent galaxy mergers. The coalescence of the SMBHBs is a distinct source of gravitational wave (GW) radiation. The detections of the strong GW radiation and their possible electromagnetic counterparts are essential. Numerical relativity suggests that the post-merger supermassive black hole (SMBH) gets a kick velocity up to 4000 km/s due to the anisotropic GW radiations. Here we investigate the dynamical co-evolution and interaction of the recoiling SMBHs and their galactic stellar environments with one million direct N-body simulations including the stellar tidal disruption by the recoiling SMBHs. Our results show that the accretion of disrupted stars does not significantly affect the SMBH dynamical evolution. We investigate the stellar tidal disruption rates as a function of the dynamical evolution of oscillating SMBHs in the galactic nuclei. Our simulations show that most of stellar tidal disruptions are contributed by the unbound stars and occur when the oscillating SMBHs pass through the galactic center. The averaged disruption rate is ~10^{-6} M_\odot yr^{-1}, which is about an order of magnitude lower than that by a stationary SMBH at similar galactic nuclei. Our results also show that a bound star cluster is around the oscillating SMBH of about ~ 0.7% the black hole mass. In addition, we discover a massive cloud of unbound stars following the oscillating SMBH. We also investigate the dependence of the results on the SMBH masses and density slopes of the galactic nuclei.

astro-ph.GA↗

arXiv2011

Evolution of growing black holes in axisymmetric galaxy cores

NBody realizations of axisymmetric collisional galaxy cores (e.g. M32, M33, NGC205, Milky Way) with embedded growing black holes are presented. Stars which approach the disruption sphere are disrupted and accreted to the black hole. We measure the zone of influence of the black hole and disruption rates in relaxation time scales. We show that secular gravitational instabilities dominate the initial core dynamics, while the black hole is small and growing due to consumption of stars. Later, the black hole potential dominates the core, and loss cone theory can be applied. Our simulations show that central rotation in galaxies can not be neglected for relaxed systems, and compare and discuss our results with the standard theory of spherically symmetric systems.

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