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Peter Berczik

Publications and source records attributed to Peter Berczik.

At least 37 records · Page 2Linked to original sources
arXiv2023

Exploring the origin of stars on bound and unbound orbits causing tidal disruption events

Tidal disruption events (TDEs) provide a clue to the properties of a central supermassive black hole (SMBH) and an accretion disk around it, and to the stellar density and velocity distributions in the nuclear star cluster surrounding the SMBH. Deviations of TDE light curves from the standard occurring at a parabolic encounter with the SMBH depends on whether the stellar orbit is hyperbolic or eccentric (Hayasaki et al. 2018) and the penetration factor ($β$, tidal disruption radius to orbital pericenter ratio). We study the orbital parameters of bound and unbound stars being tidally disrupted by comparison of direct $N$-body simulation data with an analytical model. Starting from the classical steady-state Fokker-Planck model of Cohn & Kulsrud (1978), we develop an analytical model of the number density distribution of those stars as a function of orbital eccentricity ($e$) and $β$. To do so fittings of the density and velocity distribution of the nuclear star cluster and of the energy distribution of tidally disrupted stars are required and obtained from $N$-body data. We confirm that most of the stars causing TDEs in a spherical nuclear star cluster originate from the full loss-cone region of phase space, derive analytical boundaries in eccentricity-$β$ space, and find them confirmed by $N$-body data. Since our limiting eccentricities are much smaller than critical eccentricities for full accretion or full escape of stellar debris, we conclude that those stars are only very marginally eccentric or hyperbolic, close to parabolic.

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arXiv2023

Milky Way globular clusters on cosmological timescales. III. Interaction rates

Aims. We carry out the self-consistent dynamic evolution of the orbital structure of Milky Way globular clusters. This allows us to estimate possible and probable close passages and even collisions of the clusters with each other. Methods. We reproduced the orbits of 147 globular clusters in 10 Gyr lookback time using our own high-order N-body parallel dynamic phi-GPU code. The initial conditions (three coordinates and three velocities for the present time) were derived from the Gaia DR3 catalogue. The galaxy is represented by five external potentials from the IllustrisTNG-100, whose masses and sizes of the disk and halo components are similar to the physical values of the Milky Way at present. Results. We present a statistical analysis of the cumulative close passages rate: About ten close passages with relative distances shorter than 50 pc for every billion years for each of the five external potentials. We present the 22 most reliable collision pairs with a good probability. As an example: Terzan 4 versus Terzan 2 (49%), Terzan 4 versus NGC 6624 (44%), Terzan 4 versus Terzan 5 (40%), Terzan 4 versus NGC 6440 (40%), and Terzan 4 versus Liller 1 (42%). The most active globular cluster in the collision sense is Terzan 4, which has 5.65 collision events on average (averaged over all individual 1000 initial condition realisations). Most collisions are located inside the Galactic disk and form two ring-like structures. The first ring-like structure has the highest collision number density at 1 kpc, and the second sturcture has a maximum at 2 kpc. Conclusions. Based on our numerical simulations, we can conclude that the few dozen Milky Way globular clusters probably undergo some close encounters and even possible collisions during their lifetimes, which can significantly affect their individual dynamical evolution and possibly even their stellar content.

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arXiv2023

Dynamics of supermassive black hole triples in the ROMULUS25 cosmological simulation

For a pair of supermassive black holes (SMBHs) in the remnant of a dual galaxy merger, well-known models exist to describe their dynamical evolution until the final coalescence accompanied by the emission of a low-frequency gravitational wave (GW) signal. In this article, we investigate the dynamical evolution of three SMBH triple systems recovered from the ROMULUS25 cosmological simulation to explore common dynamical evolution patterns and assess typical coalescence times. For this purpose, we construct initial conditions from the ROMULUS25 data and perform high-resolution gravitodynamical \N-body simulations. We track the orbital evolution from the galactic inspiral to the formation of hard binaries at sub-parsec separation and use the observed hardening rates to project the time of coalescence. In all cases, the two heaviest black holes form an efficiently hardening binary that merges within fractions of the Hubble time. The lightest SMBH either gets ejected, forms a stable hierarchical triple system with the heavier binary, forms a hardening binary with the previously merged binary's remnant, or remains on a wide galactic orbit. The coalescence times of the lighter black holes are thus significantly longer than for the heavier binary, as they experience lower dynamical friction and stellar hardening rates. We observe the formation of hierarchical triples when the density profile of the galactic nucleus is sufficiently steep.

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arXiv2023

Growth of Seed Black Holes in Galactic Nuclei

The evolution of dense star clusters is followed by direct high-accuracy N-body simulation. The problem is to first order a gravitational N-body problem, but stars evolve due to astrophysics and the more massive ones form black holes or neutron stars as compact remnants at the end of their life. After including updates of stellar evolution of massive stars and for the relativistic treatment of black hole binaries we find the growth of intermediate mass black holes and we show that in star clusters binary black hole mergers in the so-called pair creation supernova (PSN) gap occur easily. Such black hole mergers have been recently observed by the LIGO-Virgo-KAGRA (LVK) collaboration, a network of ground based gravitational wave detectors.

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arXiv2023

The Dragon-II simulations -- I. Evolution of single and binary compact objects in star clusters with up to 1 million stars

We present the first results of the \textsc{Dragon-II} simulations, a suite of 19 $N$-body simulations of star clusters with up to $10^6$ stars, with up to $33\%$ of them initially paired in binaries. In this work, we describe the main evolution of the clusters and their compact objects (COs). All \textsc{Dragon-II} clusters form in their centre a black hole (BH) subsystem with a density $10-100$ times larger than the stellar density, with the cluster core containing $50-80\%$ of the whole BH population. In all models, the BH average mass steeply decreases as a consequence of BH burning, reaching values $\langle m_{\rm BH}\rangle < 15$ M$_\odot$ within $10-30$ relaxation times. Generally, our clusters retain only BHs lighter than $30$ M$_\odot$ over $30$ relaxation times. Looser clusters retain a higher binary fraction, because in such environments binaries are less likely disrupted by dynamical encounters. We find that BH-main sequence star binaries have properties similar to recently observed systems. Double CO binaries (DCOBs) ejected from the cluster exhibit larger mass ratios and heavier primary masses than ejected binaries hosting a single CO (SCOBs). Ejected SCOBs have BH masses $m_{\rm BH} = 3-20$ M$_\odot$, definitely lower than those in DCOBs ($m_{\rm BH} = 10-100$ M$_\odot$).

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arXiv2023

The Dragon-II simulations -- II. Formation mechanisms, mass, and spin of intermediate-mass black holes in star clusters with up to 1 million stars

The processes that govern the formation of intermediate-mass black holes (IMBHs) in dense stellar clusters are still unclear. Here, we discuss the role of stellar mergers, star-BH interactions and accretion, as well as BH binary (BBH) mergers in seeding and growing IMBHs in the \textsc{Dragon-II} simulation database, a suite of 19 direct $N$-body models representing dense clusters with up to $10^6$ stars. \textsc{Dragon-II} IMBHs have typical masses of $m_{\rm IMBH} = (100-380)$ M$_\odot$ and relatively large spins $χ_{\rm IMBH} > 0.6$. We find a link between the IMBH formation mechanism and the cluster structure. In clusters denser than $3\times 10^5$ M$_\odot$ pc$^{-3}$, the collapse of massive star collision products represents the dominant IMBH formation process, leading to the formation of heavy IMBHs ($m_{\rm IMBH} > 200$ M$_\odot$), possibly slowly rotating, that form over times $<5$ Myr and grow further via stellar accretion and mergers in just $<30$ Myr. BBH mergers are the dominant IMBH formation channel in less dense clusters, for which we find that the looser the cluster, the longer the formation time ($10-300$ Myr) and the larger the IMBH mass, although remaining within $200$ M$_\odot$. Strong dynamical scatterings and relativistic recoil efficiently eject all IMBHs in \textsc{Dragon-II} clusters, suggesting that IMBHs in this type of cluster are unlikely to grow beyond a few $10^2$ M$_\odot$.

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arXiv2023

The Dragon-II simulations -- III. Compact binary mergers in clusters with up to 1 million stars: mass, spin, eccentricity, merger rate and pair instability supernovae rate

Compact binary mergers forming in star clusters may exhibit distinctive features that can be used to identify them among observed gravitational-wave (GW) sources. Such features likely depend on the host cluster structure and the physics of massive star evolution. Here, we dissect the population of compact binary mergers in the \textsc{Dragon-II} simulation database, a suite of 19 direct $N$-body models representing dense star clusters with up to $10^6$ stars and $<33\%$ of stars in primordial binaries. We find a substantial population of black hole binary (BBH) mergers, some of them involving an intermediate-mass BH (IMBH), and a handful mergers involving a stellar BH and either a neutron star (NS) or a white dwarf (WD). Primordial binary mergers, $\sim 30\%$ of the whole population, dominate ejected mergers. Dynamical mergers, instead, dominate the population of in-cluster mergers and are systematically heavier than primordial ones. Around $20\%$ of \textsc{Dragon-II} mergers are eccentric in the LISA band and $5\%$ in the LIGO band. We infer a mean cosmic merger rate of $\mathcal{R}\sim 12(4.4)(1.2)$ yr$^{-1}$ Gpc$^3$ for BBHs, NS-BH, and WD-BH binary mergers, respectively, and discuss the prospects for multimessenger detection of WD-BH binaries with LISA. We model the rate of pair-instability supernovae (PISNe) in star clusters and find that surveys with a limiting magnitude $m_{\rm bol}=25$ can detect $\sim 1-15$ yr$^{-1}$ PISNe. Comparing these estimates with future observations could help to pin down the impact of massive star evolution on the mass spectrum of compact stellar objects in star clusters.

astro-ph.HE↗
arXiv2023

Milky Way globular clusters on cosmological timescales. II. Interaction with the Galactic centre

Aims. We estimate the dynamical evolution of the Globular Clusters interaction with the Galactic centre that dynamically changed in the past. Methods. We simulated the orbits of 147 globular clusters over 10 Gyr lookback time using the parallel N-body code phi-GPU. For each globular cluster, we generated 1000 sets of initial data with random proper motions and radial velocities based on the observed values. To distinguish globular clusters interacting with the galactic centre, we used the criterion of a relative distance of less than 100 pc. We used four external potentials from the IllustrisTNG-100 database, which were selected for their similarity to the present-day Milky Way, to simulate the structure of the Galaxy at different times. Results. We obtained 3-4 globular cluster interactions per Gyr at distances of less than 50 pc and 5-6 interactions per Gyr at distances of less than 80 pc among the studied 147 globular clusters that had close passages near the Galactic centre. We selected 10 of them for detailed study and found almost 100% probability of interaction with the Galactic centre for six of them. Conclusions. According to our results, the maximum interaction frequency of globular clusters with the Galactic centre in the Milky Way is likely to be a few dozens of passages per Gyr within a central zone of 100 pc. This low frequency may not be sufficient to fully explain the relatively high mass (of order 10^7 Msol) of the nuclear star cluster in the Milky Way, if we consider only the periodic capture of stars from globular clusters during close encounters. Therefore, we must also consider the possibility that some early globular clusters were completely tidally disrupted during interactions with the forming nuclear star cluster and the Galactic centre.

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arXiv2023

Dynamical evolution modeling of the Collinder 135 & UBC 7 binary star cluster

The purpose of the present work is a detailed investigation of the dynamical evolutionof Collinder 135 and UBC 7 star clusters. We present a set of dynamical numerical simulationsusing realistic star clusterN-body modeling technique with the forward integration of thestar-by-star cluster models to the present day, based on best-available 3D coordinates and velocitiesobtained from the latest Gaia EDR3 data release. We have established that Collinder 135 and UBC 7 are probably a binary star cluster and have common origin. We carried out a full star-by-star N-body simulation of the stellar population of both clusters using the new algorithm of Single Stellar Evolution and performed a comparison of the results obtained in the observational data (like cumulative number counts), which showed a fairly good agreement.

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arXiv2023

Tracing the Evolution of SMBHs and Stellar Objects in Galaxy Mergers: An Multi-mass Direct N-body Model

By using direct N-body numerical simulations, we model the dynamical co-evolution of two supermassive black holes (SMBHs) and the surrounding stars in merging galaxies. In order to investigate how different stellar components evolve during the merger, we generate evolved stellar distributions with an initial mass function. Special schemes have also been developed to deal with some rare but interesting events, such as tidal disruption of main sequence stars, the plunge of low mass stars, white dwarfs, neutron stars and stellar mass black holes, and the partial tidal disruption of red giants or asymptotic giant branch stars. Our results indicate that the formation of a bound supermassive black hole binary (SMBHB) will enhance the capture rates of stellar objects by the SMBHs. Compared to the equal stellar mass model, the multi-mass model tends to result in a higher average mass of disrupted stars. Instead of being tidally disrupted by the SMBH, roughly half of the captured main sequence stars will directly plunge into the SMBH because of their small stellar radius. Giant stars, on the other hand, can be stripped of their envelopes if they are close enough to the SMBH. Though most remnants of the giant stars can survive after the disruption, a small fraction still could plunge into the SMBH quickly or after many orbital periods. Our results also indicate significant mass segregation of compact stars at the beginning of the merger, and then this effect is destroyed as the two SMBHs form a bound binary.

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arXiv2023

Statistical Analysis of the Probability of Interaction of Globular Clusters with Each Other and with the Galactic Center on the Cosmological Time Scale According to Gaia DR2 Data

This study is aimed at investigating the dynamic evolution of the orbits of stellar globular clusters (GCs). To integrate the orbits backward in time, the authors use models of the time-varying potentials derived from cosmological simulations, which are closest to the potential of the Galaxy. This allows for estimating the probability of close passages (collisions) of GCs with respect to each other and the Galactic center (GalC) in the Galaxy undergoing dynamic changes in the past. To reproduce the dynamics of the Galaxy in time, five potentials selected from the IllustrisTNG-100 large-scale cosmological database, which are similar in their characteristics to the current physical parameters of the Milky Way, are used. With these time-varying potentials, we have reproduced the orbital trajectories of 143 GCs 10 Gyr back in time using our original phi-GPU N-body code. Each GC was treated as a single physical particle with the assigned position and velocity of the cluster center from the Gaia DR2 observations. For each of the potentials, 1000 initial conditions were generated with randomized initial velocities of GCs within the errors of the observational data. In this study, we consider close passages to be passages with a relative distance of less than 100 pc and a relative speed of less than 250 km/s. To select clusters that pass at close distances from the GalC, the following criterion is applied based only on the relative distance: it must be less than 100 pc. Applying the above criteria, the authors obtained statistically significant rates of close passages of GCs with respect to each other and to the GalC. It has been determined that GCs during their evolution have approximately 10 intersecting trajectories with each other on the average and approximately 3 to 4 close passages near the GalC in 1 Gyr at a distance of 50 pc for each of the chosen potentials.

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arXiv2022

Merging of unequal mass binary black holes in non-axisymmetric galactic nuclei

In this work, we study the stellar-dynamical hardening of unequal mass supermassive black hole (SMBH) binaries in the central regions of merging galactic nuclei. We present a comprehensive set of direct $N$-body simulations of the problem, varying both the total mass and the mass ratio of the SMBH binary (SMBHB). Simulations were carried out with the $φ-$GPU $N$-body code, which enabled us to fully exploit supercomputers equipped with graphic processing units (GPUs). As a model for the galactic nuclei, we adopted initial axisymmetric, rotating models, aimed at reproducing the properties of a galactic nucleus emerging from a galaxy merger event, containing two SMBHs which were unbound initially. We found no 'final-parsec problem', as our SMBHs tend to pair and shrink without showing significant signs of stalling. This confirms earlier results and extends them to large particle numbers and rotating systems. We find that the SMBHB hardening depends on the binary-reduced mass ratio via a single parameter function. Our results suggest that, at a fixed value for the SMBHB primary mass, the merger time of highly asymmetric binaries is up to four order of magnitudes smaller than the equal-mass binaries. This can significantly affect the population of SMBHs potentially detectable as gravitational wave sources.

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arXiv2022

Revisit the rate of tidal disruption events: the role of the partial tidal disruption event

Tidal disruption of stars in dense nuclear star clusters containing supermassive central black holes (SMBH) is modeled by high-accuracy direct N-body simulation. Stars getting too close to the SMBH are tidally disrupted and a tidal disruption event (TDE) happens. TDEs probe properties of SMBH, their accretion disks, and the surrounding nuclear stellar cluster. In this paper we compare rates of full tidal disruption events (FTDE) with partial tidal disruption events (PTDE). Since a PTDE does not destroy the star, a leftover object emerges; we use the term 'leftover star' for it; two novel effects occur in the simulation: (1) variation of the leftover star's mass and radius, (2) variation of the leftover star's orbital energy. After switching on these two effects in our simulation, the number of FTDEs is reduced by roughly 28%, and the reduction is mostly due to the ejection of the leftover stars from PTDEs coming originally from relatively large distance. The number of PTDEs is about 75% higher than the simple estimation given by Stone et al. (2020), and the enhancement is mainly due to the multiple PTDEs produced by the leftover stars residing in the diffusive regime. We compute the peak mass fallback rate for the PTDEs and FTDEs recorded in the simulation, and find 58% of the PTDEs have peak mass fallback rate exceeding the Eddington limit, and the number of super-Eddington PTDEs is 2.3 times the number of super-Eddington FTDEs.

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arXiv2022

Eccentricity evolution of massive black hole binaries from formation to coalescence

Coalescing supermassive black hole binaries (BHBs) are expected to be the loudest sources of gravitational waves (GWs) in the Universe. Detection rates for ground or space-based detectors based on cosmological simulations and semi-analytic models are highly uncertain. A major difficulty stems from the necessity to model the BHB from the scale of the merger to that of inspiral. Of particular relevance to the GW merger timescale is the binary eccentricity. Here we present a self-consistent numerical study of the eccentricity of BHBs formed in massive gas-free mergers from the early stages of the merger to the hardening phase, followed by a semi-analytical model down to coalescence. We find that the early eccentricity of the unbound black hole pair is largely determined by the initial orbit. It systematically decreases during the dynamical friction phase. The eccentricity at binary formation is affected by stochasticity and noise owing to encounters with stars, but preserves a strong correlation with the initial orbital eccentricity. Binding of the black holes is a phase characterised by strong perturbations, and we present a quantitative definition of the time of binary formation. During hardening the eccentricity increases in minor mergers, unless the binary is approximately circular, but remains largely unchanged in major mergers, in agreement with predictions from semi-analytical models based on isotropic scattering experiments. Coalescence times due to hardening and GW emission in gas-poor non-rotating ellipticals are <~0.5 Gyr for the large initial eccentricities (0.5 < e < 0.9) typical of galaxy mergers in cosmological simulations.

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arXiv2021

The impact of Post-Newtonian effects on massive black hole binary evolution at $\sim 1000\,R_{sch}$ separations

Aims: We study the impact of Post-Newtonian correction terms on the energetic interaction between a gravitational wave (GW)-emitting supermassive black hole (SMBH) binary system and incoming stars via three-body scattering experiments. Methods: We use the AR-chain code to simulate with high accuracy the interactions between stars and an SMBH binary at separations of$\sim 1000\,R_{sch}$. For all of the interactions, we investigate in detail the energy balance of the three-body systems, using both Newtonian and Post-Newtonian expressions for the SMBH binary orbital energy, taking into account the GW emission by the binary. Results: We find that at these separations, purely Newtonian treatment of the binary orbital energy is insufficient to properly account for the SMBH binary orbital evolution. Instead, along with GW emission, even terms in the PN-corrections must be included in order to describe the energy change of the binary during the stellar interaction.es, 2

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arXiv2021

Merging timescale for supermassive black hole binary in interacting galaxy NGC 6240

One of the main possible way of creating the supermassive black hole (SMBH) is a so call hierarchical merging scenario. Central SMBHs at the final phase of interacting and coalescing host-galaxies are observed as SMBH binary (SMBHB) candidates at different separations from hundreds of pc to mpc. Today one of the strongest SMBHB candidate is a ULIRG galaxy NGC 6240 which was X-ray spatially and spectroscopically resolved by Chandra. Dynamical calculation of central SMBHBs merging in a dense stellar environment allows us to retrace their evolution from kpc to mpc scales. The main goal of our dynamical modeling was to reach the final, gravitational wave (GW) emission regime for the model BHs. We present the direct N-body simulations with up to one million particles and relativistic post-Newtonian corrections for the SMBHs particles up to 3.5 post-Newtonian terms. Generally speaking, the set of initial physical conditions can strongly effect of our merging time estimations. But in a range of our parameters, we did not find any strong correlation between merging time and BHs mass or BH to bulge mass ratios. Varying the model numerical parameters (such as particle number - N) makes our results quite robust and physically more motivated. From our 20 models we found the upper limit of merging time for central SMBHB is less than $\sim$55 Myr. This concrete number are valid only for our set of combination of initial mass ratios. Further detailed research of rare dual/multiple BHs in dense stellar environment (based on observations data) can clarify the dynamical co-evolution of central BHs and their host-galaxies.

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arXiv2021

Mass loss from massive globular clusters in tidal fields

Massive globular clusters lose stars via internal and external processes. Internal processes include mainly two-body relaxation, while external processes include interactions with the Galactic tidal field. We perform a suite of N-body simulations of such massive clusters using three different direct-summation N-body codes, exploring different Galactic orbits and particle numbers. By inspecting the rate at which a star's energy changes as it becomes energetically unbound from the cluster, we can neatly identify two populations we call kicks and sweeps, that escape through two-body encounters internal to the cluster and the external tidal field, respectively. We find that for a typical halo globular cluster on a moderately eccentric orbit, sweeps are far more common than kicks but the total mass loss rate is so low that these clusters can survive for tens of Hubble times. The different N-body codes give largely consistent results, but we find that numerical artifacts may arise in relation to the time step parameter of the Hermite integration scheme, namely that the value required for convergent results is sensitive to the number of particles.

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arXiv2021

Properties of loss cone stars in a cosmological galaxy merger remnant

Aims: We investigate the orbital and phase space properties of loss cone stars that interact strongly with a hard, high-redshift binary supermassive black hole (SMBH) system formed in a cosmological scenario. Methods: We use a novel hybrid integration approach that combines the direct N-body code $φ$-GRAPE with ETICS, a collisionless code that employs the self-consistent field method for force calculation. The hybrid approach shows considerable speed-up over direct summation for particle numbers $> 10^6$, while retaining accuracy of direct N-body for a subset of particles. During the SMBH binary evolution we monitor individual stellar interactions with the binary in order to identify stars that noticeably contribute to the SMBH binary hardening. Results: We successfully identify and analyze in detail the properties of stars that extract energy from the binary. We find that the summed energy changes seen in these stars match very well with the overall binary energy change, demonstrating that stellar interactions are the primary drivers of SMBH binary hardening in triaxial, gas-poor systems. The slight triaxiality of our system results in efficient loss cone refilling, avoiding the final parsec problem. We distinguish three different populations of interactions based on their apocenter. We find a clear prevalence of interactions co-rotating with the binary. Nevertheless, retrograde interactions are the most energetic, contributing only slightly less than the prograde population to the overall energy exchange. The most energetic interactions are also likely to result in a change of sign in the angular momentum of the star. We estimate the merger timescale of the binary to be $\approx 20$ $\mathrm{Myr}$, a value larger by a factor of two than the timescale reported in a previous study.

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