Showing 1–50 of 137 results for author: Berczik, P

The effect of triaxial galaxy shapes on the dynamics of triple supermassive black holes in a cosmological context

Authors: Navonil Saha, Margarita Sobolenko, Peter Berczik, Andreas Just, Fazeel Mahmood Khan

Abstract: The hierarchical nature of galaxy formation in the Lambda cold dark matter ($Λ$CDM) cosmological framework model often leads to the presence of multiple supermassive black holes (SMBHs) in the galactic nuclei. The timescale over which galaxies merge plays a crucial role in shaping the dynamical evolution and the merger dynamics of their central SMBHs. While binary SMBH evolution has been extensive… ▽ More The hierarchical nature of galaxy formation in the Lambda cold dark matter ($Λ$CDM) cosmological framework model often leads to the presence of multiple supermassive black holes (SMBHs) in the galactic nuclei. The timescale over which galaxies merge plays a crucial role in shaping the dynamical evolution and the merger dynamics of their central SMBHs. While binary SMBH evolution has been extensively studied, the long-term dynamics of triple SMBH systems, especially in realistic, nonspherical galactic potentials, still remain less understood. In this work, we investigated the role of triaxiality in shaping the dynamical evolution of three SMBH triple systems taken from the ROMULUS25 cosmological simulation embedded in triaxial stellar backgrounds to find common dynamical evolution patterns and estimate typical coalescence times using high-resolution gravitodynamical $\textit{N}$-body simulations. We explored a range of orbital configurations and host galaxy shapes with initial conditions from the ROMULUS25 data and tracked the orbital evolution from the galactic inspiral to the formation of hard binaries at sub-parsec separations and used the observed hardening rates to estimate the time of coalescence. In all cases, the two heaviest black holes form an efficiently hardening binary, which merges within the Hubble time, while the third black hole (BH) either forms a stable hierarchical triple system with the heavier binary or remains on a wide galactic orbit. Finally, we analyzed the triaxiality of the galactic remnant from our simulations and conclude that the initial triaxial shape of the galaxies does not significantly change the final dynamical outcome of the triple systems. △ Less

Submitted 26 July, 2026; originally announced July 2026.

Comments: 13 pages, 5 figures, accepted for publication in A&A

Primordial Binary Stars, Mass segregation and Fractality Effects on the Early Evolution of Young Open Clusters

Authors: Vahid Amiri, Francesco Flammini Dotti, Xiaoying Pang, A. W. H. Kamlah, Peter Berczik, Bekdaulet Shukirgaliyev, Rainer Spurzem

Abstract: We want to understand how the combined effect of initial substructure, primordial mass segregation, and primordial binaries affects the dynamical evolution of the cluster, and which one of these features is the most important to agree with observations. Methods. We use Nbody6++GPU to simulate the dynamics of star clusters with initial substructure, primordial mass segregation, and primordial binar… ▽ More We want to understand how the combined effect of initial substructure, primordial mass segregation, and primordial binaries affects the dynamical evolution of the cluster, and which one of these features is the most important to agree with observations. Methods. We use Nbody6++GPU to simulate the dynamics of star clusters with initial substructure, primordial mass segregation, and primordial binaries, and we also study the relative importance of the processes. Initial models were generated by a modified version of McLuster, and we compared our results with observational data from Pang et al. 2022 database of open clusters. Our results show that primordial mass segregation and binaries do not change the result already obtained in previous works, as the time scale on which initial substructure disappears is of the order of few Myrs. However, we also find that in the presence of initial substructure, primordial mass segregation does not lead to an early expansion of the cluster. The processes in the core, discussed in previous works, lead to a loss of low mass stars and early expansion, are postponed in the presence of initial substructure. Finally, we find from comparison with observed clusters that primordial mass segregation is not a fundamental process to reproduce observational data. △ Less

Submitted 3 June, 2026; originally announced June 2026.

Comments: 12 Pages, 7 Images, 1 Table, Submitted to A&A, comments welcome

Formation of a nuclear star cluster through the inspiral of globular clusters: A case study of the dwarf elliptical galaxy UGC 7346

Authors: Ismael Khan, Fazeel Mahmood Khan, Andrea V. Macciò, Kelly Holley-Bockelmann, Peter Berczik

Abstract: Nuclear star clusters (NSCs) are dense stellar environments located in the center of most galaxies. NSCs are thought to form through two primary methods; through the inspiral of globular clusters (GCs) to the galactic center due to dynamical friction, and through in-situ star formation. Recent observations of dwarf elliptical galaxy UGC 7346 suggest that it might be undergoing NSC formation due to… ▽ More Nuclear star clusters (NSCs) are dense stellar environments located in the center of most galaxies. NSCs are thought to form through two primary methods; through the inspiral of globular clusters (GCs) to the galactic center due to dynamical friction, and through in-situ star formation. Recent observations of dwarf elliptical galaxy UGC 7346 suggest that it might be undergoing NSC formation due to the presence of multiple GCs near its photometric center. We perform direct N-body simulations of nine GCs belonging to UGC 7346's GC system to investigate whether their eventual infall to the galactic center would result in the formation of a NSC. Our simulations indicate that GC inspiral leads to the formation of a central stellar over-density relative to the background profile of the host galaxy within $\sim$1.5 Gyr, corresponding to a NSC with a typical mass of $(4.1\text{-}4.5)\times 10^5 M_{\odot}$. Several key structural parameters of the newly formed NSC, including the Sérsic index, effective radius, and central stellar density, lie well within the range observed for NSCs. We also test a hypothetical scenario in which some of the infalling GCs have larger masses ($M \sim 10^6 M_{\odot}$), resulting in the formation of a more massive NSC whose mass and size are more consistent with observations. Our results suggest that inspiral of GCs is a viable channel for assembling a significant mass in the shape of NSC in the center of dwarf galaxies and that UGC 7346 will host a NSC at its center in about 2-3 Gyr. △ Less

Submitted 19 May, 2026; originally announced May 2026.

Dynamical evolution of Milky Way globular clusters on the cosmological timescale II. Terzan 2, 4, and 5 mass loss and collision tracking

Authors: M. Ishchenko, P. Berczik, D. Kuvatova

Abstract: We investigate the long-term dynamical evolution of Ter2, Ter4, and Ter5, focusing on their mutual interactions, mass-loss behaviour, and survivability in the dense Galactic centre environment. We performed a suite of high-resolution direct N-body simulations over 8 Gyr, modelling three individual clusters that we also modelled as combined systems. We compared reference runs of isolated clusters w… ▽ More We investigate the long-term dynamical evolution of Ter2, Ter4, and Ter5, focusing on their mutual interactions, mass-loss behaviour, and survivability in the dense Galactic centre environment. We performed a suite of high-resolution direct N-body simulations over 8 Gyr, modelling three individual clusters that we also modelled as combined systems. We compared reference runs of isolated clusters with simulations of the full three-cluster system to quantify possible differences in mass loss, potential energy, and orbital behaviour. Our simulations reveal multiple close encounters between the Terzan clusters. The most significant encounters occur between Ter2-Ter4 and Ter4-Ter5, with their tidal radii exceeding the minimum separation. A notable case is the pair Ter2-Ter4, which approaches within 10 pc at a relative velocity of ~320 km/s. We found that the mass-loss rate is higher for the low-mass Ter2 and Ter4 systems in the combined three-cluster simulations than in our similar isolated runs, highlighting the importance of mutual cluster interactions. The common run clearly demonstrates that mutual gravitational interactions between clusters drive significant triaxial deformations, especially for Ter2 and Ter5, which evolve from nearly spherical to distinctly prolate shapes. In contrast, the isolated runs show clusters that remained almost perfectly spherical, confirming that the observed shape changes are correlated with the mutual interactions. The survivability and dynamical evolution of Galactic centre globular clusters cannot be fully understood without accounting for collective interactions among all systems within a few kiloparsecs. Our results emphasise the necessity of complex multi-cluster modelling in realistic Galactic potentials to capture the long-term fate of surviving and dissolved clusters △ Less

Submitted 8 May, 2026; originally announced May 2026.

Journal ref: Astronomy & Astrophysics, 710, A58 (2026)

Global m=1 slow mode in near-Keplerian self-gravitating torus: applications to stellar nuclear disks and AGN molecular tori

Authors: Elena Bannikova, Volodymyr Akhmetov, Peter Berczik, Serhii Skolota, Massimo Capaccioli, Maryna Ishchenko

Abstract: Global m=1 asymmetries are observed in many self-gravitating astrophysical systems and are often interpreted as large-scale slow modes in near-Keplerian potentials. Prominent examples include eccentric nuclear disks in galactic centres, such as the double nucleus of M31. However, the origin and long-term stability of such modes remain unclear. We investigate the evolution and stability of a collis… ▽ More Global m=1 asymmetries are observed in many self-gravitating astrophysical systems and are often interpreted as large-scale slow modes in near-Keplerian potentials. Prominent examples include eccentric nuclear disks in galactic centres, such as the double nucleus of M31. However, the origin and long-term stability of such modes remain unclear. We investigate the evolution and stability of a collisionless, self-gravitating torus orbiting a dominant central mass, aiming to determine whether a slow non-axisymmetric (m=1) mode can arise spontaneously. We perform direct N-body simulations exploring different torus-to-central mass ratios and initial conditions. The calculations use the high-order Hermite GPU integrator (φ-GPU), allowing us to follow long-term evolution with many particles. We find that a global slow m=1 mode forms spontaneously from initially axisymmetric configurations. The lopsided structure is sustained by coherent apsidal alignment and persists over secular timescales. Its maintenance requires nonlinear coupling of low-order modes, including the m=3 component, as well as a sufficient vertical thickness of the torus. As a result of the long-lived overdensity, the central mass is displaced from the system barycenter. These results provide a framework for understanding eccentric nuclear disks, such as those in M31 and NGC4486B, as well as molecular tori in AGNs, and suggest that such asymmetries may produce observable offsets of the central supermassive black hole. △ Less

Submitted 13 April, 2026; originally announced April 2026.

Comments: 15 pages, 24 figures

Formation and disruption of wide binaries in star clusters revealed by N-body simulations

Authors: Abylay Bissekenov, Xiaoying Pang, Rainer Spurzem, Bekdaulet Shukirgaliyev, Mukhagali Kalambay, Peter Berczik

Abstract: Wide (soft) binaries are expected to be rapidly disrupted in dense stellar environments, yet they are observed in both the Galactic field and open clusters (OCs). In this paper, we investigate the formation and disruption of wide binaries in star clusters using direct N-body simulations. We perform simulations containing 10,000 objects with varying binary fractions and initial bulk rotation to giv… ▽ More Wide (soft) binaries are expected to be rapidly disrupted in dense stellar environments, yet they are observed in both the Galactic field and open clusters (OCs). In this paper, we investigate the formation and disruption of wide binaries in star clusters using direct N-body simulations. We perform simulations containing 10,000 objects with varying binary fractions and initial bulk rotation to give an in-depth look into the dynamical evolution of wide binaries in star clusters. We find that wide binaries dominate early disruption and formation processes during the initial high-density phase of cluster evolution. We propose two semi-analytical models to reproduce the evolution of the wide-binary population in simulations. The exponential model consists of an early, rapid-disruption phase with a time less than 10 Myr, driven by frequent encounters at high density, and a longer, relaxation-driven phase between 200 and 300 Myr. The broken power-law model provides break timescales when the decrease of wide binaries slows down during the early and long-term disruption. All timescales from both models agree with each other and decrease with increasing stellar density induced by high primordial binary fraction and cluster rotation. Wide binary disruption is mostly responsible for the early decline in the total binary fraction of the cluster. Such disruption leads to the decrease of radial binary fraction toward the cluster center until 500 Myr. Our results suggest low-density OCs or stellar groups younger than 10 Myr as the optimal environments for detecting wide binaries and provide a physical framework for understanding their contribution to the Galactic field population. △ Less

Submitted 14 April, 2026; v1 submitted 30 March, 2026; originally announced March 2026.

Comments: Accepted to the Astrophysical Journal Letters

Report number: AAS73654

The contribution to Galactic Centre γ-ray excess from cluster-born millisecond pulsars. Constraints from direct N-body simulations

Authors: M. Kalambay, M. Ishchenko, D. Kuvatova, T. Panamarev, P. Berczik

Abstract: The Galactic Centre γ-ray excess (GCE), observed by Fermi-LAT around Sgr A*, exceeds expectations from standard cosmic-ray models and is commonly attributed either to dark matter annihilation or to unresolved millisecond pulsars (MSPs). We revisit the MSP scenario within a fully dynamical framework by tracking neutron stars (NSs) formed in globular clusters (GCs) and deposited into the central kil… ▽ More The Galactic Centre γ-ray excess (GCE), observed by Fermi-LAT around Sgr A*, exceeds expectations from standard cosmic-ray models and is commonly attributed either to dark matter annihilation or to unresolved millisecond pulsars (MSPs). We revisit the MSP scenario within a fully dynamical framework by tracking neutron stars (NSs) formed in globular clusters (GCs) and deposited into the central kiloparsec. Using high-resolution direct N-body simulations of GCs evolving in a time-dependent Milky Way potential, we model both present-day clusters and an early population of disrupted systems. From the simulated NS distributions, we infer the MSP population via an empirically calibrated MSP-to-NS ratio and construct mock γ-ray flux profiles assuming representative pulsar luminosities. MSPs associated with surviving clusters already produce a substantial γ-ray contribution, while disrupted clusters enhance both the amplitude and central concentration of the signal. Under reasonable assumptions, the combined MSP population reproduces the observed GCE properties, favouring an astrophysical origin over dark matter interpretations. △ Less

Submitted 6 March, 2026; originally announced March 2026.

Comments: 10 pages, 8 figures, accepted by A&A

Journal ref: Astronomy & Astrophysics, 708, A89 (2026)

Is the overconcentration of pristine populations in Galactic globular clusters real? An N-body approach to the problem

Authors: P. Berczik, O. Sobodar, F. Flammini Dotti, M. Sobolenko, M. Ishchenko, R. Spurzem, M. Giersz, A. Askar

Abstract: Recent observations indicate that in some Milky Way globular clusters (GCs) pristine red giant branch (RGB) stars appear more centrally concentrated than enriched ones. This contradicts most multiple stellar population (MSP) formation scenarios, which predict that the enriched (second) population (2P) should initially be more concentrated than the pristine (first) population (1P). Previous MOCCA M… ▽ More Recent observations indicate that in some Milky Way globular clusters (GCs) pristine red giant branch (RGB) stars appear more centrally concentrated than enriched ones. This contradicts most multiple stellar population (MSP) formation scenarios, which predict that the enriched (second) population (2P) should initially be more concentrated than the pristine (first) population (1P). Previous MOCCA Monte Carlo simulations suggested that this apparent overconcentration is a transient effect arising in clusters that have lost a large fraction of their initial mass and host an active black hole subsystem (BHS), and is visible only when RGB stars are used as tracers. In this letter, we test this interpretation using tailored NBODY6++GPU models evolved with direct N-body simulations, providing an independent validation that does not rely on a statistical treatment of relaxation. We performed direct N-body simulations with the NBODY6++GPU code, adopting initial conditions designed to reproduce the dynamical regime relevant to the proposed mechanism. The simulations include updated stellar and binary evolution, dynamical interactions, and the Galactic tidal field, enabling a direct comparison with MOCCA results. The simulations confirm that the spatial distributions and kinematics inferred from RGB stars can be strongly affected by stochastic fluctuations and interactions with the BHS. Preferential ejection of 2P RGB and their progenitors from the cluster center leads to a transient apparent overconcentration of 1P RGB stars, in agreement with earlier MOCCA predictions. △ Less

Submitted 18 May, 2026; v1 submitted 17 February, 2026; originally announced February 2026.

Comments: 6 pages, 5 figures, submitted to the A&A Letter

Report number: A&A, Volume 710, Article Number A106, Number of page(s) 6

How our proto-nuclear star cluster formed and grew due to early globular cluster disruption. I. Case of low masses

Authors: D. Kuvatova, M. Ishchenko, P. Berczik, O. Veles, O. Sobodar, T. Panamarev

Abstract: We investigate the accretion of globular cluster stars on early cosmological timescales through detailed N-body simulations of theoretical GC models to assess the role of this mechanism in Milky Way-like galaxies. For the dynamical modelling, we used the updated parallel N-body code phi-GPU, including stellar evolution. We prepared three sets of GC models with different half-mass radii (r_hm), eac… ▽ More We investigate the accretion of globular cluster stars on early cosmological timescales through detailed N-body simulations of theoretical GC models to assess the role of this mechanism in Milky Way-like galaxies. For the dynamical modelling, we used the updated parallel N-body code phi-GPU, including stellar evolution. We prepared three sets of GC models with different half-mass radii (r_hm), each consisting of 50 full N-body GC models, and integrated these models in an external, time-variable MW-like potential taken from the cosmological database IllustrisTNG-100. The simulations cover the time interval from -10 Gyr to -5 Gyr, enabling us to assess the rate of early stellar accretion onto the proto-NSC. We find that GC models with average orbital eccentricities of 0.4-0.5 and orbits oriented perpendicular to the galactic disc contribute most significantly to the mass of the proto-NSC formation. Accretion is especially efficient in the first billion years and in compact GC models with r_hm = 1 pc. In all sets, the dominant accreted stellar population consists of low-mass stars (~0.33 Msun). However, the accreted mass alone is insufficient to fully account for the current NSC mass. Based on our extended set of numerical simulations, we obtained an average lower limit of mass contribution (~6 percent) to the NSC from investigated GCs. The fraction of mass contribution from individual disrupted GCs can significantly vary from 0.1 percent up to 90 percent. Generally, we conclude that the GC stellar accretion channel alone might not be sufficient to ensure the present-day MW galaxy NSC mass budget. △ Less

Submitted 5 January, 2026; originally announced January 2026.

Journal ref: A&A 706, A220 (2026)

Dynamical evolution of massless particles in star clusters with NBODY6++GPU-MASSLESS: II. The long-term evolution of free-floating comets

Authors: Francesco Flammini Dotti, M. B. N. Kouwenhoven, Kai Wu, Abbas Askar, Peter Berczik, Mirek Giersz, Rainer Spurzem, Ian Dobbs-Dixon

Abstract: Context. Comets, asteroids, planetesimals, free-floating planets and brown dwarfs, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems or binary system. The dynamics of large populations of such free-floating comets (ffcs) in a star cluster environment is not yet fully understood. Aims. We investigate the dynamical evolution of comet popul… ▽ More Context. Comets, asteroids, planetesimals, free-floating planets and brown dwarfs, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems or binary system. The dynamics of large populations of such free-floating comets (ffcs) in a star cluster environment is not yet fully understood. Aims. We investigate the dynamical evolution of comet populations in star clusters, and characterize the kinematics and ejection rates of ffc in a star cluster. Moreover, we determine whether a different initial energy distribution affects the mass segregation of the less massive population. Methods. We carry out simulations using the N-body code NBODY6++GPU-MASSLESS (Flammini Dotti et al. 2025), which allows fast integration of star clusters that contain large numbers of massless particles, to characterize the dynamics of populations of low-mass particles with sub-virial and super-virial distributions. Results. Comets do not participate in the mass segregation process, similarly to planet-size objects, regardless of their initial energy distribution. The latter is slightly changing the whole dynamical evolution at the start of the simulation. We only observe an initial relaxation or collapse of the objects for super-virial and sub-virial ratios, respectively. The external regions of the ffcs population tend to be pulled back in the cluster core at the end of the simulation, suggesting the gravitational pull of the stars is pulling them back in the core. This phenomenon occurs at later times if the system in virial equilibrium. Compared to less massive bodies, brown dwarfs experiences more mass segregation the inner regions tend to be more mixed with the stellar population △ Less

Submitted 12 December, 2025; originally announced December 2025.

Comments: 15 pages, 31 figures, accepted for publication in A&A

Journal ref: A&A 706, A219 (2026)

Intermediate Mass Black Hole Binary Evolution in Nuclear Star Clusters: the effect of the stellar mass black hole population

Authors: Fazeel Mahmood Khan, Peter Berczik, Margarita Sobolenko, Andreas Just, Rainer Spurzem, Kelly Holley-Bockelmann, Andrea Valerio Macciò

Abstract: In this study, we investigate the dynamics of Intermediate-Mass Black Hole (IMBH) binaries within Nuclear Star Clusters (NSCs) that contain a population of stellar-mass black holes (BHs). We examine how these stellar and BH populations influence the dynamics of the IMBH binary and, in turn, how the evolving IMBH binary affects the surrounding stellar and BH populations. We conduct high-resolution… ▽ More In this study, we investigate the dynamics of Intermediate-Mass Black Hole (IMBH) binaries within Nuclear Star Clusters (NSCs) that contain a population of stellar-mass black holes (BHs). We examine how these stellar and BH populations influence the dynamics of the IMBH binary and, in turn, how the evolving IMBH binary affects the surrounding stellar and BH populations. We conduct high-resolution $N$-body simulations of NSCs constructed based on observational parameters from two local dwarf galaxies: NGC205 and NGC404. For the first time, we achieve a star particle mass resolution of $1\rm\;M_{\odot}$ and a BH mass resolution of $10\rm\;M_{\odot}$. This level of resolution is crucial for accurately modeling the collisional dynamics of these dense systems. Including stellar-mass BHs within the stellar population significantly influences the IMBH binary dynamics, nearly doubling the sinking rate and halving the merger time. During the initial phase of the inspiral, the IMBH binary disrupts both the stellar and BH cusps. However, the BH cusp quickly regains its steep slope due to its shorter relaxation time and continues to dominate the evolution of the IMBH binary, despite being much less massive compared to the stellar component. We uncover an interesting mechanism in which BHs first efficiently extract energy from the IMBH binary and then transfer this energy to the surrounding stars, allowing the BHs to spiral back toward the center of the system and restart the process. Our results imply that, although stellar mass BHs are a minor component of a stellar population, they can significantly facilitate IMBH growth within NSCs via mergers. We also notice that these dense systems can potentially boost Intermediate Mass Ratio Inspirals (IMRIs) predominantly on radial orbits. △ Less

Submitted 11 December, 2025; originally announced December 2025.

Comments: Accepted for publication in Astronomy & Astrophysics

Journal ref: A&A 706, A354 (2026)

Globular clusters of the Gaia Enceladus/Sausage -- I. Orbital and dynamical evolution on cosmological timescales

Authors: Mykyta Bilodid, Maryna Ishchenko, Peter Berczik

Abstract: We investigated Gaia-Enceladus/Sausage globular cluster samples and studied their orbital and dynamical evolution over cosmological timescales in external time-variable potential. We estimated the limits of distribution of the escaped stars from the globular clusters' orbital evolution in energy angular momentum space. To reconstruct the orbital evolution of the known globular clusters of the dwar… ▽ More We investigated Gaia-Enceladus/Sausage globular cluster samples and studied their orbital and dynamical evolution over cosmological timescales in external time-variable potential. We estimated the limits of distribution of the escaped stars from the globular clusters' orbital evolution in energy angular momentum space. To reconstruct the orbital evolution of the known globular clusters of the dwarf galaxy Gaia-Enceladus/Sausage, we used the parallel $N$-body code $\varphi$-GPU. We investigated the relationship between globular clusters and their progenitor by analysing their orbital parameters and phase-space distribution during 9 Gyr of evolution in the past. We created a $N$-body model of Gaia-Enceladus/Sausage globular clusters and analysed their dynamical evolution and distribution of the escaped stars today. We summarised the samples of the Gaia-Enceladus/Sausage globular clusters and created two main categories: `most probable' and `tentative', with 15 and 9 clusters, respectively. We analysed the evolution of their kinematic, orbital, and phase-space parameters in the external time-variable potential. We defined phase-space distribution limits of stars that escape from globular clusters during 9 Gyr of evolution: a specific energy from -18 to -12.2 $\times10^4$ km$^2$ s$^{-2}$, L$_{\rm z}$ from -0.98 to 0.72 $\times10^3$ kpc km s$^{-1}$, and L$_{\rm perp}$ from 0 to 1.8 $\times10^3$ kpc km s$^{-1}$. The limits of the GE/S debris in Galactic area based on orbital parameters of the GC's escaped stars are: for apocentre and pericetre distances of 10--28 and 1--4 kpc, < 18 kpc in Galactocentric radius and < |15| kpc in the Z direction. Generally we compared the phase-space distribution of escaped stars from the GCs GE/S debris energy-angular momentum limits with the observed very metal-poor stars, which belong to the GE/S itself and produce consistent results. △ Less

Submitted 24 December, 2025; v1 submitted 9 November, 2025; originally announced November 2025.

Journal ref: A&A, 704, A242 (2025)

The effect of triaxiality on the dynamics of triple supermassive black holes in a cosmological context

Authors: Navonil Saha, Peter Berczik, Andreas Just, Margarita Sobolenko

Abstract: The hierarchical nature of galaxy formation in the $Λ$CDM framework often leads to multiple supermassive black holes (SMBHs) in the galactic nuclei. The timescale over which galaxies merge, plays a crucial role in shaping the dynamical evolution and the merger dynamics of their central SMBHs. While binary SMBH evolution is well studied, the long-term dynamics of triple SMBH systems, particularly i… ▽ More The hierarchical nature of galaxy formation in the $Λ$CDM framework often leads to multiple supermassive black holes (SMBHs) in the galactic nuclei. The timescale over which galaxies merge, plays a crucial role in shaping the dynamical evolution and the merger dynamics of their central SMBHs. While binary SMBH evolution is well studied, the long-term dynamics of triple SMBH systems, particularly in non-spherical potentials, remain less understood. We investigate the role of triaxiality in the evolution and dynamics of triple SMBHs with initial conditions drawn from the ROMULUS25 cosmological simulation, using high-resolution gravitodynamical N-body simulations. We explore different orbital configurations and host shapes, tracking the evolution from galactic inspiral to hard binary formation at sub-parsec scales. In all cases, the two most massive SMBHs form a rapidly hardening binary that coalesces within a fraction of a Hubble time, while the third forms a stable hierarchical triple system with the heavier binary, or remains on a wide orbit. △ Less

Submitted 24 October, 2025; v1 submitted 23 October, 2025; originally announced October 2025.

Comments: 4 pages, 2 figures, accepted for publication in the International Astronomical Union Proceedings Series. Paper presented at the IAU Symposium 398 & MODEST-25 : Compact Objects and Binaries in Dense Stellar Systems

Dynamical evolution timescales for the supermassive black hole system in the galaxy NGC 7727 (Arp 222)

Authors: P. Berczik, M. Ishchenko, O. Veles, M. Sobolenko, K. Voggel, C. M. Boily, E. Polyachenko, R. State

Abstract: Context. A dual active galactic nucleus candidate with a separation of only 500 pc was recently found in NGC 7727. According to the hierarchical merging scenario, such objects would be expected to merge on a timescale of a few hundred Myr. However, estimating the accurate merging timescales for the two nuclei is still a complex challenge. Aims. Using our numerical N-body code, we can trace the ful… ▽ More Context. A dual active galactic nucleus candidate with a separation of only 500 pc was recently found in NGC 7727. According to the hierarchical merging scenario, such objects would be expected to merge on a timescale of a few hundred Myr. However, estimating the accurate merging timescales for the two nuclei is still a complex challenge. Aims. Using our numerical N-body code, we can trace the full evolution of central black holes during all phases: dynamical friction of unbound black holes, binary black hole formation, hardening of the system due to two-body scattering, and emission of gravitational waves leading to the final merger. Methods. Our model has next components: the bulge contains two dense stellar nuclei, each of which hosts a black hole. The most massive black hole in the center of the galaxy has a mass of 1.54x10^8 Msol and the least massive black hole in the offset second stripped nucleus has a mass of 6.33x10^6 Msol. We followed the dynamical evolution of the system up to a final separation of four Schwarzschild radii. The black holes were added as special relativistic particles and their equation of motion contains a full post-Newtonian approximation - 2.5 term. Results. Initially, the black holes are not gravitationally bound and, thus, the system spends more than 60 Myr in the phase of dynamical friction while tightening the orbit. The two-body scattering phase takes place from 60 Myr up to 120 Myr. In the last 10 Myr, the black hole's separation is seen to be rapidly shrinking due to the gravitational wave emission. Starting from the physical separation observed today, the total merging time in our model is 130 (10) Myr. Conclusions. These results have implications for the statistics of strong sources of gravitational waves at low frequencies, namely, systems engaged in an advanced state of are expected to be prime sources for the LISA mission to observe. △ Less

Submitted 3 October, 2025; originally announced October 2025.

Comments: Contains 7 pages, 7 figures, and 4 Tables. Accepted for publication in A&A

Report number: A&A, Volume 703, Article Number A23, Number of page(s) 8, November 2025

Dynamical model of Praesepe and its tidal tails

Authors: L. Weis, C. West, A. Just, P. Berczik, M. Ishchenko, S. Röser, E. Schilbach, B. Shukirgaliyev

Abstract: Context. The dynamical evolution of open clusters in the tidal field of the Milky Way and the feeding of the disc field star population depend strongly on the initial conditions at the time of gas removal. Detailed dynamical models tailored to individual clusters help us understand the role of open clusters in the Galactic disc evolution. Aims. We present a detailed dynamical model of Praesepe, wh… ▽ More Context. The dynamical evolution of open clusters in the tidal field of the Milky Way and the feeding of the disc field star population depend strongly on the initial conditions at the time of gas removal. Detailed dynamical models tailored to individual clusters help us understand the role of open clusters in the Galactic disc evolution. Aims. We present a detailed dynamical model of Praesepe, which reproduces the mass profile, the stellar mass function, and the mass segregation observed with the help of Gaia EDR3 data. Based on this model, we investigate the kinematic properties of the tidal tail stars in detail. Methods. We used direct N-body simulations along the eccentric orbit of Praesepe in the tidal field of the Milky Way, where each particle represents one star. The initial mass and size of the cluster, the dynamical state, and the initial mass function were adapted to reach the best-fitting model. Based on this model and a comparison model on a circular orbit, we analysed the stars in the tidal tails in terms of density, angular momentum, and orbit shapes. Results. Praesepe can be well reproduced by a cluster model with concentrated star formation in a supervirial state after instantaneous gas expulsion, adopting a global star formation efficiency of 17%. About 75% of the initially 7500 MSol are lost in the violent relaxation phase, and the observed mass segregation can be understood by two-body relaxation. We find that the self-gravity of the tail stars is the dominant force altering the angular momentum of the tail stars. For a typical star, the total change after escaping is about 1.6 kpc km/s. This corresponds to an offset in guiding radius of 7 pc, where tail stars contribute up to 70% to the alteration. The total radial shift of the orbit of the cluster in the Galactic plane can exceed 50 pc. This effect is not a result of the eccentricity of the orbit. △ Less

Submitted 29 September, 2025; originally announced September 2025.

Comments: Contains 13 pages, 12 figures, and 4 Tables. Accepted for publication in A&A

Report number: A&A, Volume 703, Article Number A47, Number of page(s) 13, November 2025

Gravitational influence of the globular cluster NGC 7078 (M 15) flyby of the Oort cloud system

Authors: M. Ishchenko, P. Berczik

Abstract: Context. It is crucial to understand the interaction between globular clusters (GCs) and the Oort cloud, as close flybys of such massive objects can significantly disturb the cloud's structure and redirect comets towards the inner Solar System. This increases the risk of impacts on Earth. Studying such events can teach us about the evolution and stability of the Solar System, as well as the effect… ▽ More Context. It is crucial to understand the interaction between globular clusters (GCs) and the Oort cloud, as close flybys of such massive objects can significantly disturb the cloud's structure and redirect comets towards the inner Solar System. This increases the risk of impacts on Earth. Studying such events can teach us about the evolution and stability of the Solar System, as well as the effect of external gravitational forces on its dynamics over time. Aims. In our study of the gravitational effects of the flyby of the NGC 7078 or M 15 GC on the Oort cloud, we focus on two types of approximation. First, we investigate the impact on the Sun's orbit during close passages, treating the GC as a point mass. At the second stage, we use a complete N-body system representation of the GC comprising over one million particles. Methods. We carried out a dynamical study of the gravitational interaction between Oort cloud particles and galactic GCs within the time-varying galactic external potential. Initially, the GCs are represented as point masses orbiting the Galaxy alongside the Sun and the Oort cloud system. Results. Our study reveals significant variations in the impact of NGC 7078 on the Oort cloud, depending on whether it is modelled as a point mass or a complete N-body system. The N-body system results in much greater stripping of Oort cloud particles, with over 52% stripped during a close pass, compared to a few percent in the point mass model for a flyby at a large distance (>200 pc) and 36% for a closer 10 pc point mass flyby. The N-body system also causes substantial expansion, with particles spreading over 50 pc from the Sun within 30 Myr after the GC's crossing. This creates a twisted and flattened cloud structure with extended outer tails. These stripped cloud particles (more than 10%) spread across the galaxy, reaching distances of up to 16 kpc from the Sun. △ Less

Submitted 18 June, 2025; originally announced June 2025.

Comments: 11 pages, 15 figures, 3 tables. Accepted by Astronomy & Astrophysics

Journal ref: A&A, Volume 699, A248, 2025

Evolution of star clusters with initial bulk rotation via N-body simulations

Authors: Abylay Bissekenov, Xiaoying Pang, Albrecht Kamlah, M. B. N. Kouwenhoven, Rainer Spurzem, Bekdaulet Shukirgaliyev, Mirek Giersz, Abbas Askar, Peter Berczik

Abstract: Young star clusters can inherit bulk rotation from the molecular clouds from which they have formed. This rotation can affect the long-term evolution of a star cluster and its constituent stellar populations. In this study, we aim to characterize the effects of different degrees of initial rotation on star clusters with primordial binaries. The simulations are performed using NBODY6++GPU. We find… ▽ More Young star clusters can inherit bulk rotation from the molecular clouds from which they have formed. This rotation can affect the long-term evolution of a star cluster and its constituent stellar populations. In this study, we aim to characterize the effects of different degrees of initial rotation on star clusters with primordial binaries. The simulations are performed using NBODY6++GPU. We find that initial rotation strongly affects the early evolution of star clusters. Rapidly rotating clusters show angular momentum transport from the inner parts to the outskirts, resulting in a core collapse. Angular momentum transport is accompanied by a highly elongated bar-like structure morphology. The effects of bulk rotation are reduced on the timescale of two-body relaxation. Rotating and non-rotating clusters experience changes in the direction of angular momentum near the dissolution and early evolution due to the tidal field, respectively. We present synthetic observations of simulated clusters for comparison with future observations in filters of Gaia, CSST, and HST. This work shows the effects of bulk rotation on systems with primordial binaries and could be used for the identification of rotation signatures in observed open clusters. △ Less

Submitted 2 July, 2025; v1 submitted 26 May, 2025; originally announced May 2025.

Journal ref: A&A 699, A196 (2025)

Rapid formation of a very massive star >50000 $M_\odot$ and subsequently an IMBH from runaway collisions. Direct N-body and Monte Carlo simulations of dense star clusters

Authors: Marcelo C. Vergara, Abbas Askar, Albrecht W. H. Kamlah, Rainer Spurzem, Francesco Flammini Dotti, Dominik R. G. Schleicher, Manuel Arca Sedda, Arkadiusz Hypki, Mirek Giersz, Jarrod Hurley, Peter Berczik, Andres Escala, Nils Hoyer, Nadine Neumayer, Xiaoying Pang, Ataru Tanikawa, Renyue Cen, Thorsten Naab

Abstract: Context. We present simulations of a massive young star cluster using \textsc{Nbody6++GPU} and \textsc{MOCCA}. The cluster is initially more compact than previously published models, with one million stars, a total mass of $5.86 \times 10^5~\mathrm{M}_{\odot}$, and a half-mass radius of $0.1~\mathrm{pc}$. Aims. We analyse the formation and growth of a very massive star (VMS) through successive s… ▽ More Context. We present simulations of a massive young star cluster using \textsc{Nbody6++GPU} and \textsc{MOCCA}. The cluster is initially more compact than previously published models, with one million stars, a total mass of $5.86 \times 10^5~\mathrm{M}_{\odot}$, and a half-mass radius of $0.1~\mathrm{pc}$. Aims. We analyse the formation and growth of a very massive star (VMS) through successive stellar collisions and investigate the subsequent formation of an intermediate-mass black hole (IMBH) in the core of a dense star cluster. Methods. We use both direct \textit{N}-body and Monte Carlo simulations, incorporating updated stellar evolution prescriptions (SSE/BSE) tailored to massive stars and VMSs. These include revised treatments of stellar radii, rejuvenation, and mass loss during collisions. While the prescriptions represent reasonable extrapolations into the VMS regime, the internal structure and thermal state of VMSs formed through stellar collisions remain uncertain, and future work may require further refinement. Results. We find that runaway stellar collisions in the cluster core produce a VMS exceeding $5 \times 10^4~\mathrm{M}_{\odot}$ within 5 Myr, which subsequently collapses into an IMBH. Conclusions. Our model suggests that dense stellar environments may enable the formation of very massive stars and massive black hole seeds through runaway stellar collisions. These results provide a potential pathway for early black hole growth in star clusters and offer theoretical context for interpreting recent JWST observations of young, compact clusters at high redshift. △ Less

Submitted 17 December, 2025; v1 submitted 12 May, 2025; originally announced May 2025.

Comments: 21 pages, 11 figures, Accepted for publication in A&A

Journal ref: A&A 704, A321 (2025)

Global survey of star clusters in the Milky Way VIII. Cluster formation and evolution

Authors: Jonathan H. Klos, Andreas Just, Evgeny V. Polyachenko, Peter Berczik, Marina Ishchenko

Abstract: We consider tidal masses and ages of Milky Way open clusters, as well as a simple model of their distribution. Our aim is to investigate the space of model parameters and the correspondence between modelled and observed two-dimensional cluster age-mass distributions. The model for cluster evolution is comprised of a two-section cluster initial mass function, constant cluster formation rate, and a… ▽ More We consider tidal masses and ages of Milky Way open clusters, as well as a simple model of their distribution. Our aim is to investigate the space of model parameters and the correspondence between modelled and observed two-dimensional cluster age-mass distributions. The model for cluster evolution is comprised of a two-section cluster initial mass function, constant cluster formation rate, and a mass loss function. This mass loss function represents a supervirial phase after gas expulsion, mass loss due to stellar evolution, and gradual dissolution driven by internal dynamics and the Galactic tidal field. We construct different estimators of model fitness based on $χ^2$-statistics, the Kullback-Leibler divergence (KLD) and a maximum-likelihood approach. Using these estimators and Markov Chain Monte Carlo sampling, we obtain best-fit values and posterior distributions for a selection of model parameters. The KLD returns a superior model compared to the other statistics. The cluster initial mass function is well constrained and we find a clear signature of an enhanced cluster mass loss in the first 50 Myr. In the KLD best model, clusters lose 72% of their initial mass in the violent relaxation phase, after which cluster mass loss slows down, allowing for a relatively low rate of cluster formation of $0.088\mathrm{M_\odot kpc^{-2} Gyr^{-1}}$. The observed upper limit of cluster ages at approx. 5 Gyr is reflected in the model by a shallow lifetime-mass relation for clusters with initial masses above $1000\mathrm{M_\odot}$. The application of the model to an independent cluster sample based on Gaia DR3 data yields similar results except for a systematic shift in age. The observed cluster age-mass distribution is compatible with a constant cluster formation rate. The enhanced number of young massive clusters observed requires an early violent relaxation phase of strong mass loss. △ Less

Submitted 14 April, 2025; v1 submitted 18 March, 2025; originally announced March 2025.

Comments: Accepted for publication in A&A, 21 pages, 14 figures; language edited version

Journal ref: A&A 697, A129 (2025)

Dynamical evolution of the open clusters with different star formation efficiencies and orbital parameters

Authors: M. Ishchenko, V. Masliukh, M. Hradov, P. Berczik, B. Shukirgaliyev, C. Omarov

Abstract: Open star clusters are dynamic systems whose evolution is critically influenced by initial conditions such as star formation efficiency and orbital parameters. Understanding their dissolution mechanisms provides insight into stellar population dynamical mixing in the Milky Way. We aim to investigate the dynamical evolution and dissolution of initially non-virialised open clusters by examining how… ▽ More Open star clusters are dynamic systems whose evolution is critically influenced by initial conditions such as star formation efficiency and orbital parameters. Understanding their dissolution mechanisms provides insight into stellar population dynamical mixing in the Milky Way. We aim to investigate the dynamical evolution and dissolution of initially non-virialised open clusters by examining how different global star formation efficiencies and orbital characteristics impact the cluster longevity and structural changes. We followed the evolution of the clusters up to their dissolution time on the basis of our calculations. We compare our open cluster dynamical evolutionary models with the observed open clusters in our Galaxy's solar vicinity. Using high-order direct N-body simulations, we modelled cluster evolution across different Galactic orbits, systematically varying initial star formation efficiencies to comprehensively explore dissolution mechanisms. Our simulations reveal that open clusters typically survive approximately ten orbital periods, with cluster lifetime being strongly dependent on global star formation efficiency and only marginally influenced by orbital eccentricity. We estimate gas expulsion timescales of 0.9 Myr, with initial supernova explosions efficiently removing gaseous components from the cluster. The expected lifetime of the cluster (in units of orbital periods) strongly depends on the cluster global star-formation efficiency and only slightly on the orbital eccentricities of the cluster. The theoretical models demonstrate a remarkable agreement of the Roche-volobe filling parameter with the recent observed Gaia DR3 cluster catalogues in the solar vicinity. By incorporating a mixed sample of clusters with varying star formation efficiencies, we provide a more nuanced understanding of open cluster evolution in the Galactic disc. △ Less

Submitted 14 January, 2025; originally announced January 2025.

Comments: 15 pages, 12 figures, 3 Tables. Accepted for publication in Astronomy and Astrophysics

Report number: Astronomy & Astrophysics, Volume number 694, Article number A33

Dynamical evolution of massless particles in star clusters with NBODY6++GPU-MASSLESS: I. Free-floating MLPs

Authors: Francesco Flammini Dotti, M. B. N. Kouwenhoven, Peter Berczik, Qi Shu, Rainer Spurzem

Abstract: Context. Low-mass bodies, such as comets, asteroids, planetesimals, and free-floating planets, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems. These can be modeled as massless particles (MLPs, hereafter). The dynamics of large populations of MLPs, however, has yet received little attention in literature. Aims. We investigate the dynam… ▽ More Context. Low-mass bodies, such as comets, asteroids, planetesimals, and free-floating planets, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems. These can be modeled as massless particles (MLPs, hereafter). The dynamics of large populations of MLPs, however, has yet received little attention in literature. Aims. We investigate the dynamical evolution of MLP populations in star clusters, and characterize their kinematics and ejection rates. Methods. We present NBODY6++GPU-MASSLESS, a modified version of the N-body simulation code NBODY6++GPU, that allows fast integration of star clusters that contain large numbers of massless particles (MLPs). NBODY6++GPU-MASSLESS contains routines specifically directed at the dynamical evolution of low-mass bodies, such as planets. Results. Unlike stars, MLPs do not participate in the mass segregation process. Instead, MLPs mostly follow the gravitational potential of the star cluster, which gradually decreases over time due to stellar ejections and stellar evolution. The dynamical evolution of MLPs is primarily affected by the evolution of the core of the star cluster. This is most apparent in the outer regions for clusters with higher initial densities. High escape rates of MLPs are observed before the core-collapse, after which escape rates remain stable. Denser star clusters undergo a more intense core collapse, but this does not impact the dynamical evolution of MLPs. The speeds of escaping stars are similar to those of escaping MLPs, when disregarding the high-velocity ejections of neutron stars during the first 50 Myr. △ Less

Submitted 11 December, 2024; originally announced December 2024.

Comments: 11 Pages, 9 Figures, Accepted for publication in A&A

Cosmological insights into the early accretion of r-process-enhanced stars II. Dynamical identification of lost members of Reticulum II

Authors: P. Berczik, M. Ishchenko, O. Sobodar, M. Mardini

Abstract: Aims. We identify the possible dynamical connection between individual r-process-enhanced stars and the ultra-faint dwarf galaxy Reticulum II based on the current phase-space information for these stars and the dynamical mass-loss model of Reticulum II during its orbital motion for 11.5 Gyr of lookback time. The dynamical orbital modelling together with the chemical abundance analysis proved to be… ▽ More Aims. We identify the possible dynamical connection between individual r-process-enhanced stars and the ultra-faint dwarf galaxy Reticulum II based on the current phase-space information for these stars and the dynamical mass-loss model of Reticulum II during its orbital motion for 11.5 Gyr of lookback time. The dynamical orbital modelling together with the chemical abundance analysis proved to be useful tools for the progenitor identification of the peculiar stars in our Galaxy. Methods. To reproduce the Reticulum II orbital mass loss, we used our high-precision N-body phi-GPU code to integrate almost 1 million stars into the system evolution inside a external Galactic potential. We also investigated the orbits of r-process-enhanced stars using the same code. Results. We present our Reticulum II dynamical modelling results in the context of the stars energies - angular momentum phase-space and phase-space overlapping of the currently observed r-process-enhanced stars with Reticulum II stellar tidal tails. Of the 530 r-stars known today, at least 93 are former members of the Reticulum II dynamical progenitor system. △ Less

Submitted 17 November, 2024; originally announced November 2024.

Comments: 8 pages, 7 figures, 3 Tables. Accepted to publication in Astronomy and Astrophysics

Report number: Astronomy and Astrophysics, Volume: 692, Article Number: A130

Evolution of the disky second generation of stars in globular clusters on cosmological timescale

Authors: Peter Berczik, Taras Panamarev, Maryna Ishchenko, Bence Kocsis

Abstract: Context. Many Milky Way globular clusters (GCs) host multiple stellar populations, challenging the traditional view of GCs as single-population systems. It has been suggested that second-generation stars could form in a disk from gas lost by first-generation stars or from external accreted gas. Aims. We investigate how the introduction of a second stellar generation affects mass loss, internal mix… ▽ More Context. Many Milky Way globular clusters (GCs) host multiple stellar populations, challenging the traditional view of GCs as single-population systems. It has been suggested that second-generation stars could form in a disk from gas lost by first-generation stars or from external accreted gas. Aims. We investigate how the introduction of a second stellar generation affects mass loss, internal mixing, and rotational properties of GCs in a time-varying Galactic tidal field and different orbital configurations. Methods. We conducted direct N-body simulations of GCs on three types of orbits derived from the observed Milky Way GCs. We evolved the clusters for 8 Gyr in the time-varying Galactic potential of the IllustrisTNG-100 cosmological simulation. After 2 Gyr, we introduced a second stellar generation, comprising 5% of the initial mass of the first generation, as a flattened disk of stars. For comparison, we ran control simulations using a static Galactic potential and isolated clusters. Results. We present the mass loss, structural evolution, and kinematic properties of GCs with two stellar generations, focusing on tidal mass, half-mass radii, velocity distributions, and angular momentum. Conclusions. Our results show that the mass loss of GCs depends primarily on their orbital parameters, with tighter orbits leading to higher mass loss. The Galaxy's growth resulted in tighter orbits, meaning GCs lost less mass than if its mass had always been constant. The initially flattened second-generation disk became nearly spherical within one relaxation time. However, whether its distinct rotational signature was retained depends on the orbit: for the long radial orbit, it vanished quickly; for the tube orbit, it lasted several Gyr; but for the circular orbit, rotation persisted until the present day △ Less

Submitted 29 January, 2025; v1 submitted 4 November, 2024; originally announced November 2024.

Comments: 27 pages, 28 figures. Accepted by A&A

Report number: Astronomy & Astrophysics, Volume number 694, Article number A163

Estimating Gamma-Ray Flux from Millisecond Pulsars Originating in Globular Clusters Near the Galactic Center

Authors: Dana Kuvatova, Taras Panamarev, Maryna Ishchenko, Anton Gluchshenko, Peter Berczik

Abstract: In this study, we investigate the contribution of millisecond pulsars (MSPs) to the gamma-ray excess observed in the Galactic Center by analyzing data from high-resolution direct N-body simulations of six globular clusters (GCs) that experience close encounters with the nuclear star cluster. Using the φ-GPU code, we tracked the orbits of individual neutron stars (NSs) formed during the simulations… ▽ More In this study, we investigate the contribution of millisecond pulsars (MSPs) to the gamma-ray excess observed in the Galactic Center by analyzing data from high-resolution direct N-body simulations of six globular clusters (GCs) that experience close encounters with the nuclear star cluster. Using the φ-GPU code, we tracked the orbits of individual neutron stars (NSs) formed during the simulations, assuming a fraction of these NSs evolve into MSPs. Our model includes state-of-the-art single stellar evolution code including prescription for neutron star formation. We estimated the gamma-ray flux from these MSPs, considering known values for their gamma-ray emission. Our results show that MSPs originating from the six modeled GCs contribute a small but non-negligible fraction of the observed gamma-ray flux. This finding suggests that the actual gamma-ray flux from MSPs could be much higher when considering the entire population of GCs, potentially significantly contributing to the gamma-ray excess. This study highlights the importance of considering MSPs in the Galactic Center, originating from nearby globular clusters, as a potential source of the observed gamma-ray excess. Future work will involve more sophisticated simulations incorporating binary stellar evolution and comparing the fraction of MSPs in observed GCs to refine our models and improve the accuracy of our estimates. △ Less

Submitted 21 October, 2024; originally announced October 2024.

Comments: in Russian language

Journal ref: Vol. 90 No. 3 (2024), 14-20: Recent Contributions to Physics (Rec.Contr.Phys.)

The potential for long-lived intermediate mass black hole binaries in the lowest density dwarf galaxies

Authors: Fazeel Mahmood Khan, Fiza Javed, Kelly Holley-Bockelmann, Lucio Mayer, Peter Berczik, Andrea V. Macciò

Abstract: Intermediate Mass Black Hole (IMBH) mergers with masses $10^4 - 10^6$ $M_{\odot}$ are expected to produce gravitational waves (GWs) detectable by the Laser Interferometer Space Antenna (LISA) with high signal to noise ratios out to redshift 20. IMBH mergers are expected to take place within dwarf galaxies, however, the dynamics, timescales, and effect on their hosts are largely unexplored. In a pr… ▽ More Intermediate Mass Black Hole (IMBH) mergers with masses $10^4 - 10^6$ $M_{\odot}$ are expected to produce gravitational waves (GWs) detectable by the Laser Interferometer Space Antenna (LISA) with high signal to noise ratios out to redshift 20. IMBH mergers are expected to take place within dwarf galaxies, however, the dynamics, timescales, and effect on their hosts are largely unexplored. In a previous study, we examined how IMBHs would pair and merge within nucleated dwarf galaxies. IMBHs in nucleated hosts evolve very efficiently, forming a binary system and coalescing within a few hundred million years. Although the fraction of dwarf galaxies ($10^7$ M$_{\odot} \leq$ $M_{\star} \leq 10^{10}$ M$_{\odot}$) hosting nuclear star clusters is between 60-100\%, this fraction drops to 20-70\% for lower-mass dwarfs ($M_{\star}\approx 10^7$ M$_{\odot}$), with the largest drop in low-density environments. Here, we extend our previous study by performing direct $N-$body simulations to explore the dynamics and evolution of IMBHs within non-nucleated dwarf galaxies, under the assumption that IMBHs exist within these dwarfs. To our surprise, none of IMBHs in our simulation suite merge within a Hubble time, despite many attaining high eccentricities $e \sim 0.7-0.95$. We conclude that extremely low stellar density environments in the centers of non-nucleated dwarfs do not provide an ample supply of stars to interact with IMBHs binary resulting in its stalling, in spite of triaxiality and high eccentricity, common means to drive a binary to coalescence. Our findings underline the importance of considering all detailed host properties to predict IMBH merger rates for LISA. △ Less

Submitted 26 August, 2024; originally announced August 2024.

Comments: Submitted to ApJ

Cluster membership analysis with supervised learning and $N$-body simulations

Authors: A. Bissekenov, M. Kalambay, E. Abdikamalov, X. Pang, P. Berczik, B. Shukirgaliyev

Abstract: Membership analysis is an important tool for studying star clusters. There are various approaches to membership determination, including supervised and unsupervised machine learning (ML) methods. We perform membership analysis using the supervised machine learning approach. We train and test our ML models on two sets of star cluster data: snapshots from $N$-body simulations and 21 different cluste… ▽ More Membership analysis is an important tool for studying star clusters. There are various approaches to membership determination, including supervised and unsupervised machine learning (ML) methods. We perform membership analysis using the supervised machine learning approach. We train and test our ML models on two sets of star cluster data: snapshots from $N$-body simulations and 21 different clusters from the Gaia Data Release 3 data. We explore five different ML models: Random Forest (RF), Decision Trees, Support Vector Machines, Feed-Forward Neural Networks, and K-Nearest Neighbors. We find that all models produce similar results, with RF showing slightly better accuracy. We find that a balance of classes in datasets is optional for successful learning. The classification accuracy depends strongly on the astrometric parameters. The addition of photometric parameters does not improve performance. We do not find a strong correlation between the classification accuracy and clusters' age, mass, and half-mass radius. At the same time, models trained on clusters with a larger number of members generally produce better results. △ Less

Submitted 29 July, 2024; originally announced July 2024.

Comments: Accepted for publication in A&A. 10 pages, 12 figures

Journal ref: A&A 689, A282 (2024)

Dynamical evolution timescales for the triple supermassive black hole system in NGC 6240

Authors: P. Berczik, M. Sobolenko, M. Ishchenko

Abstract: Based on the available observational data from the literature, we analysed the dynamics of the NGC 6240 galaxy central supermassive black hole (SMBH) system. For the dynamical modelling of this triple SBMH system, we used the massively parallel and GPU accelerated phi-GPU direct summation N-body code. Following a long-timescale modelling of the triple system, we carried out a very detailed time ou… ▽ More Based on the available observational data from the literature, we analysed the dynamics of the NGC 6240 galaxy central supermassive black hole (SMBH) system. For the dynamical modelling of this triple SBMH system, we used the massively parallel and GPU accelerated phi-GPU direct summation N-body code. Following a long-timescale modelling of the triple system, we carried out a very detailed time output analysis of the von Zeipel-Lidov-Kozai (ZLK) oscillations for the black holes. According to our Newtonian simulation results, for all models and randomisations, the bound system from S1+S2 components formed at ~3.6 Myr. The formation of the bound hierarchical triple system S+N occurred at ~18 Myr. Over the course of these Newtonian simulations of the evolution of the triple SMBH system and the surrounding environment in NGC 6240, ZLK oscillations were detected (in most cases) for the binary components. The inclination angle between the orbital angular momentum of binary components aptly coincides with the theoretical calculations of the ZLK mechanism. In our set of randomised 15 Newtonian $N$-body dynamical galaxy models in 13 systems, we were able to detect a ZLK mechanism. In contrast, our extra few-body post-Newtonian runs (for one randomisation case) show it is only for the large inner binary initial eccentricity (in our case >0.9 that we are able to observe the possibility of the inner binary merging, due to the post-Newtonian energy radiation effects. For the lower eccentricity cases, the test runs show no sign of possible merging or any ZLK oscillations in the system. △ Less

Submitted 29 June, 2024; originally announced July 2024.

Comments: 14 pages, 15 figures, accepted for publication to the Astronomy and Astrophysics

Dynamical evolution of Milky Way globular clusters on the cosmological timescale I. Mass loss and interaction with the nuclear star cluster

Authors: M. Ishchenko, P. Berczik, T. Panamarev, D. Kuvatova, M. Kalambay, A. Gluchshenko, O. Veles, M. Sobolenko, O. Sobodar, C. Omarov

Abstract: Context. Based on the Gaia DR3, we reconstructed the orbital evolution of the known Milky Way globular clusters and found that six objects, NGC 6681, NGC 6981, Palomar 6, NGC 6642, HP 1, and NGC 1904, very likely interact closely with the nuclear star cluster. Aims. We study the dynamical evolution of selected Milky Way globular clusters and their interactions with the Galactic centre over cosmolo… ▽ More Context. Based on the Gaia DR3, we reconstructed the orbital evolution of the known Milky Way globular clusters and found that six objects, NGC 6681, NGC 6981, Palomar 6, NGC 6642, HP 1, and NGC 1904, very likely interact closely with the nuclear star cluster. Aims. We study the dynamical evolution of selected Milky Way globular clusters and their interactions with the Galactic centre over cosmological timescales. We examine the global dynamical mass loss of these globular cluster systems, their close interactions with the Galactic centre, and the potential capture of stars by the Milky Way nuclear star cluster. Methods. For the dynamical modelling of the clusters, we used the parallel N-body code phi-GPU, which allows star-by-star simulations of the systems. Our current code also enabled us to follow the stellar evolution of individual particles, including the formation of high-mass remnants. The modelling was carried out in a Milky Way-like, time-variable potential (with a dynamically changing mass and scale length), obtained from the IllustrisTNG-100 database, with a full integration time of eight billion years. Results. Based on extensive numerical modelling and analysis, we estimated the mass loss and the global and inner structures of the selected six clusters. Over an evolution of eight billion years, the clusters lost 80% of their initial mass. We analysed the phase-space evolution of the individual unbound stars NGC 6681, NGC 6642, HP 1, and NGC 1904. We found that only NGC 6642 could potentially have been a source for populating the Milky Way nuclear star cluster in the past. △ Less

Submitted 27 June, 2024; originally announced June 2024.

Comments: 26 pages, 16 figures, 5 Tables, 4 Appendixes. Accepted for publication to the Astronomy and astrophysics

Star-by-star dynamical evolution of the physical pair of the Collinder 135 and UBC 7 open clusters

Authors: Maryna Ishchenko, Dana A. Kovaleva, Peter Berczik, Nina V. Kharchenko, Anatoly E. Piskunov, Evgeny Polyachenko, Ekaterina Postnikova, Andreas Just, Olga Borodina, Chingis Omarov, Olexandr Sobodar

Abstract: In a previous paper using Gaia DR2 data, we demonstrated that the two closely situated open clusters Collinder 135 and UBC 7 might have formed together about 50 Myr ago. In this work, we performed star-by-star dynamical modelling of the evolution of the open clusters Collinder 135 and UBC 7 from their supposed initial state to their present-day state, reproducing observational distributions of mem… ▽ More In a previous paper using Gaia DR2 data, we demonstrated that the two closely situated open clusters Collinder 135 and UBC 7 might have formed together about 50 Myr ago. In this work, we performed star-by-star dynamical modelling of the evolution of the open clusters Collinder 135 and UBC 7 from their supposed initial state to their present-day state, reproducing observational distributions of members. Modelling of the Collinder 135 and UBC 7 dynamical evolution was done using the high-order parallel N-body code φ-GPU with up-to-date stellar evolution. Membership and characteristics of the clusters were acquired based on Gaia DR3 data. The comparison of the present-day radial cumulative star count obtained from the N-body simulations with the current observational data gave us full consistency of the model with observational data, especially in the central 8 pc, where 80% of the stars reside. The proper motion velocity components obtained from the N-body simulations of the stars are also quite consistent with the observed distributions and error bars. These results show that our numerical modelling is able to reproduce the open clusters' current complex 6D observed phase-space distributions with a high level of confidence. Thus, the model demonstrates that the hypothesis of a common origin of Collinder 135 and UBC 7 complies with present-day observational data. △ Less

Submitted 15 May, 2024; v1 submitted 18 April, 2024; originally announced April 2024.

Comments: Astronomy & Astrophysics, accepted

Milky Way globular clusters on cosmological timescales. IV. Guests in the outer Solar System

Authors: Maryna Ishchenko, Peter Berczik, Margarita Sobolenko

Abstract: The present epoch of the Gaia success gives us a possibility to predict the dynamical evolution of our Solar System in the global Galactic framework with high precision. We statistically investigated the total interaction of globular clusters with the Solar System during six billion years of look-back time. We estimated the gravitational influence of globular clusters' flyby onto the Oort cloud sy… ▽ More The present epoch of the Gaia success gives us a possibility to predict the dynamical evolution of our Solar System in the global Galactic framework with high precision. We statistically investigated the total interaction of globular clusters with the Solar System during six billion years of look-back time. We estimated the gravitational influence of globular clusters' flyby onto the Oort cloud system. To perform the realistic orbital dynamical evolution for each individual cluster, we used our own high-order parallel dynamical $N$ body $\varphi$-GPU code that we developed. To reconstruct the orbital trajectories of clusters, we used five external dynamical time variable galactic potentials selected from the IllustrisTNG-100 cosmological database and one static potential. To detect a cluster's close passages near the Solar System, we adopted a simple distance criterion of below 200 pc. To take into account a cluster's measurement errors (based on Gaia DR3), we generated 1000 initial positions and velocity randomizations for each cluster in each potential. We found 35 globular clusters that have had close passages near the Sun in all the six potentials during the whole lifetime of the Solar System. We can conclude that at a relative distance of 50 pc between a GC and the SolS, we obtain on average $\sim 15$\% of the close passage probability over all six billion years, and at $dR=100$ pc, we get on average $\sim 35$\% of the close passage probability over all six billion years. The globular clusters BH_140, UKS_1, and Djorg_1 have a mean minimum relative distance to the Sun of 9, 19, and 17 pc, respectively. We can assume that a globular cluster with close passages near the Sun is not a frequent occurrence but also not an exceptional event in the Solar System's lifetime. △ Less

Submitted 9 January, 2024; v1 submitted 7 January, 2024; originally announced January 2024.

Comments: 11 pages, 6 figures, 3 tables, accepted to the Astronomy & Astrophysics

Journal ref: Astronomy & Astrophysics, Volume 683, id.A146, (2024)

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

Authors: Maryna Ishchenko, Margaryta Sobolenko, Peter Berczik, Chingis Omarov, Olexander Sobodar, Mukhagali Kalambay, Denis Yurin

Abstract: 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… ▽ More 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. △ Less

Submitted 24 August, 2023; originally announced August 2023.

Comments: 11 pages, 9 figures, 3 tables, accepted for publication in Astronomy and Astrophysics

Journal ref: A&A 678, A69 (2023)

Dynamics of supermassive black hole triples in the ROMULUS25 cosmological simulation

Authors: Hauke Koehn, Andreas Just, Peter Berczik, Michael Tremmel

Abstract: 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 exp… ▽ More 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. △ Less

Submitted 21 August, 2023; originally announced August 2023.

Comments: 11 pages, 6 figures, 4 tables, accepted for publication in A&A

Journal ref: A&A 678, A11 (2023)

Mitigating potentially hazardous asteroid impacts revisited

Authors: Zs. Regaly, V. Frohlich, P. Berczik

Abstract: Context: Potentially hazardous asteroids (PHA) in Earth-crossing orbits pose a constant threat to life on Earth. Several mitigation methods have been proposed, and the most feasible technique appears to be the disintegration of the impactor and the generation of a fragment cloud by explosive penetrators at interception. However, mitigation analyses tend to neglect the effect of orbital dynamics on… ▽ More Context: Potentially hazardous asteroids (PHA) in Earth-crossing orbits pose a constant threat to life on Earth. Several mitigation methods have been proposed, and the most feasible technique appears to be the disintegration of the impactor and the generation of a fragment cloud by explosive penetrators at interception. However, mitigation analyses tend to neglect the effect of orbital dynamics on the trajectory of fragments. Aims: We aim to study the effect of orbital dynamics of the impactor's cloud on the number of fragments that hit the Earth, assuming different interception dates. We investigate the effect of self-gravitational cohesion and the axial rotation of the impactor. Methods: We computed the orbits of 10^5 fragments with a high-precision direct N-body integrator of the eighth order, running on GPUs. We considered orbital perturbations from all large bodies in the Solar System and the self-gravity of the cloud fragments. Results: Using a series of numerical experiments, we show that orbital shear causes the fragment cloud to adopt the shape of a triaxial ellipsoid. The shape and alignment of the triaxial ellipsoid are strongly modulated by the cloud's orbital trajectory and, hence, the impact cross-section of the cloud with respect to the Earth. Therefore, the number of fragments hitting the Earth is strongly influenced by the orbit of the impactor and the time of interception. A minimum number of impacts occur for a well-defined orientation of the impactor rotational axis, depending on the date of interception. Conclusions: To minimise the lethal consequences of an PHA's impact, a well-constrained interception timing is necessary. A too-early interception may not be ideal for PHAs in the Apollo or Aten groups. Thus, we find that the best time to intercept PHA is when it is at the pericentre of its orbit. △ Less

Submitted 18 August, 2023; v1 submitted 3 August, 2023; originally announced August 2023.

Comments: Accepted for publication in A&A Letters (some refs. update)

Journal ref: A&A 677, L6 (2023)

Growth of Seed Black Holes in Galactic Nuclei

Authors: Rainer Spurzem, Francesco Rizzuto, Manuel Arca Sedda, Albrecht Kamlah, Peter Berczik, Qi Shu, Ataru Tanikawa, Thorsten Naab

Abstract: 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 bla… ▽ More 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. △ Less

Submitted 16 July, 2023; originally announced July 2023.

Comments: Article in Proceedings of NIC Symposium 2022, 14 pages, 5 figures

Journal ref: In: NIC Symposium 2022, M.Müller, Ch. Peter, A. Trautmann (Editors), ISBN 978-3-95806-646-5 (Book), DNB Link for this article: https://d-nb.info/1286760135

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

Authors: Manuel Arca Sedda, Albrecht W. H. Kamlah, Rainer Spurzem, Francesco Paolo Rizzuto, Mirek Giersz, Thorsten Naab, Peter Berczik

Abstract: 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 m… ▽ More 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. △ Less

Submitted 10 July, 2023; originally announced July 2023.

Comments: 22 pages, 14 figures, 3 tables. Comments welcome. Submitted to MNRAS

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

Authors: Manuel Arca Sedda, Albrecht W. H. Kamlah, Rainer Spurzem, Francesco Paolo Rizzuto, Mirek Giersz, Thorsten Naab, Peter Berczik

Abstract: 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… ▽ More 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$_\odot$. △ Less

Submitted 10 July, 2023; originally announced July 2023.

Comments: 15 pages, 6 figures, 2 tables, 1 appendix. Comments welcome. Submitted to MNRAS

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

Authors: Manuel Arca Sedda, Albrecht W. H. Kamlah, Rainer Spurzem, Mirek Giersz, Peter Berczik, Sara Rastello, Giuliano Iorio, Michela Mapelli, Massimiliano Gatto, Eva K. Grebel

Abstract: 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 $10-100$… ▽ More 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$_\odot$). △ Less

Submitted 10 July, 2023; originally announced July 2023.

Comments: 22 pages, 21 figures, 4 tables. Comments welcome. Submitted to MNRAS

Evolution of open clusters with or without black holes

Authors: B. Shukirgaliyev, P. Berczik, A. Otebay, M. Kalambay, A. Kamlah, Y. Tleukhanov, E. Abdikamalov, S. Banerjee, A. Just

Abstract: Binary black holes (BHs) can be formed dynamically in the centers of star clusters. The high natal kicks for stellar-mass BHs used in previous works made it hard to retain BHs in star clusters. Recent studies of massive star evolution and supernovae (SN) propose kick velocities that are lower due to the fallback of the SN ejecta. We study the impact of these updates by performing $N$-body simulati… ▽ More Binary black holes (BHs) can be formed dynamically in the centers of star clusters. The high natal kicks for stellar-mass BHs used in previous works made it hard to retain BHs in star clusters. Recent studies of massive star evolution and supernovae (SN) propose kick velocities that are lower due to the fallback of the SN ejecta. We study the impact of these updates by performing $N$-body simulations following instantaneous gas expulsion. For comparison, we simulate two additional model sets with the previous treatment of stars: one with high kicks and another with artificial removal of the kicks. Our model clusters initially consist of about one hundred thousand stars, formed with centrally-peaked efficiency. We find that the updated treatment of stars, due to the fallback-scaled lower natal kicks, allows clusters to retain SN remnants after violent relaxation. The mass contribution of the retained remnants does not exceed a few percent of the total bound cluster mass during the early evolution. For this reason, the first giga year of evolution is not affected significantly by this effect. Nevertheless, during the subsequent long-term evolution, the retained BHs accelerate mass segregation, leading to the faster dissolution of the clusters. △ Less

Submitted 24 April, 2023; originally announced April 2023.

Comments: 8 pages, 7 figures, submitted to MNRAS, comments are welcome

Milky Way globular clusters on cosmological timescales. I. Evolution of the orbital parameters in time-varying potentials

Authors: M. Ishchenko, M. Sobolenko, P. Berczik, S. Khoperskov, C. Omarov, O. Sobodar, M. Makukov

Abstract: Context. Recent observational data show that the Milky Way (MW) galaxy contains about 170 globular clusters (GCs). A fraction of them is likely formed in dwarf galaxies accreted onto the MW in the past, while the remaining of clusters are formed in-situ. Therefore, different parameters, including orbits, of the globular clusters is a valuable tool for studying the Milky Way evolution. However, sin… ▽ More Context. Recent observational data show that the Milky Way (MW) galaxy contains about 170 globular clusters (GCs). A fraction of them is likely formed in dwarf galaxies accreted onto the MW in the past, while the remaining of clusters are formed in-situ. Therefore, different parameters, including orbits, of the globular clusters is a valuable tool for studying the Milky Way evolution. However, since the evolution of the 3D mass distribution of the MW is poorly constrained, the orbits of the clusters are usually calculated in static potentials. Aims. In this work, we study the evolution of the GCs in several external potentials, where we aim to quantify the effects of the evolving galaxy potential on the orbits of the GCs. Methods. For the orbits calculation we used five MW-like potentials from IllustrisTNG-100 simulation. The orbits of 159 GCs were integrated using a high-order N-body parallel dynamic code phi-GPU, with initial conditions obtained from recent Gaia DR3 catalogues. Results. We provide a classification of the GCs orbits according to their 3D shapes and association with different components of the MW (disk, halo, bulge). We also found that the globular clusters in the external potentials have roughly similar energy-angular momentum distributions at the present time. However, both total energy and total angular momentum of the GCs are not conserved due to time-varying nature of the potentials. In some extreme cases, the total energy can change up to 40% (18 objects) over the last 5 Gyr of evolution. We found that the in-situ formed GCs are less affected by the evolution of the TNG potentials as compared to the clusters which are likely formed ex-situ. Therefore, our results suggest that time-varying potentials significantly affect the orbits of the GC, thus making it vital for understanding the formation of the MW. △ Less

Submitted 7 April, 2023; originally announced April 2023.

Comments: 19 pages, 17 figures, 2 tables, accepted for publication in Astronomy and Astrophysics

Journal ref: A&A 673, A152 (2023)

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

Authors: Maryna Ishchenko, Margaryta Sobolenko, Dana Kuvatova, Taras Panamarev, Peter Berczik

Abstract: 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 obse… ▽ More 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. △ Less

Submitted 5 April, 2023; originally announced April 2023.

Comments: 25 pages, 21 figures, 5 tables. Accepted for publication in Astronomy and Astrophysics

Journal ref: A&A 674, A70 (2023)

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

Authors: Shuo Li, Shiyan Zhong, Peter Berczik, Rainer Spurzem, Xian Chen, F. K. Liu

Abstract: 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 interes… ▽ More 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. △ Less

Submitted 20 January, 2023; originally announced January 2023.

Comments: 36 pages, 11 figures, and 1 table. Accepted for publication in ApJ

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

Authors: Maryna Ishchenko, Margaryta Sobolenko, Peter Berczik, Taras Panamarev

Abstract: 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 othe… ▽ More 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. △ Less

Submitted 14 January, 2023; v1 submitted 12 January, 2023; originally announced January 2023.

Comments: 18 pages, 7 figures, 5 tables, accepted in Kinematics and Physics of Celestial Bodies

Report number: Kinematics and Physics of Celestial Bodies, 2023, Vol. 39, No. 1, pp. 33--44

NGC 6240 Supermassive Black Hole Binary dynamical evolution based on Chandra data

Authors: M. Sobolenko, O. Kompaniiets, P. Berczik, V. Marchenko, A. Vasylenko, E. Fedorova, B. Shukirgaliyev

Abstract: The main idea of our research is to estimate the physical coalescence time of the double supermassive black hole (SMBH) system in the centre of NGC 6240 based on the X-ray observations from the Chandra space observatory. The spectra of the Northern and Southern nuclei were fitted by spectral models from Sherpa and both presented the narrow component of the Fe K$α$ emission line. It enabled us to a… ▽ More The main idea of our research is to estimate the physical coalescence time of the double supermassive black hole (SMBH) system in the centre of NGC 6240 based on the X-ray observations from the Chandra space observatory. The spectra of the Northern and Southern nuclei were fitted by spectral models from Sherpa and both presented the narrow component of the Fe K$α$ emission line. It enabled us to apply the spectral model to these lines and to find relative offset $\approx0.02$ keV. The enclosed dynamical mass of the central region of NGC 6240 with radius 1 kpc was estimated $\approx 2.04\times 10^{11} \rm\; M_{\odot}$. These data allowed us to carry on the high resolution direct N-body simulations with Newtonian and post-Newtonian (up to $2.5\mathcal{PN}$ correction) dynamics for this particular double SMBH system. As a result, from our numerical models we approximated the central SMBH binary merging time for the different binary eccentricities. In our numerical parameters range the upper limit for the merging time, even for the very small eccentricities, is still below $\approx70$ Myr. Gravitational waveforms and amplitude-frequency pictures from such events can be detected using Pulsar Timing Array (PTA) projects at the last merging phase. △ Less

Submitted 9 October, 2022; v1 submitted 2 September, 2022; originally announced September 2022.

Comments: 12 pages, 7 figures, 6 tables. Accepted for publication in MNRAS, minor typos were corrected

Apparent counter-rotation in the torus of NGC 1068: influence of an asymmetric wind

Authors: Elena Yu. Bannikova, Nina A. Akerman, Massimo Capaccioli, Peter P. Berczik, Volodymyr S. Akhmetov, Maryna V. Ishchenko

Abstract: The recent ALMA maps together with observations of H$_2$O maser emission seem to suggest the presence of a counter-rotation in the obscuring torus of NGC 1068. We propose to explain this phenomenon as due to the influence of a wind, considered as radiation pressure, and the effects of torus orientation. In order to test this idea: 1. we make $N$-body simulation of a clumpy torus taking into accoun… ▽ More The recent ALMA maps together with observations of H$_2$O maser emission seem to suggest the presence of a counter-rotation in the obscuring torus of NGC 1068. We propose to explain this phenomenon as due to the influence of a wind, considered as radiation pressure, and the effects of torus orientation. In order to test this idea: 1. we make $N$-body simulation of a clumpy torus taking into account mutual forces between particles (clouds); 2. we apply ray-tracing algorithm with the beams from the central engine to choose the clouds in the torus throat that can be under direct influence of the accretion disk emission; 3. we use semi-analytical model to simulate the influence of the asymmetrical radiation pressure (wind) forced on the clouds in the torus throat. An axis of such a wind is tilted with respect to the torus symmetry axis; 4. we orient the torus relative to an observer and again apply ray-tracing algorithm. In this step the beams go from an observer to the optically thick clouds that allows us to take into account the mutual obscuration of clouds; 5. after projecting on the picture plane, we impose a grid on the resulting cloud distribution and find the mean velocity of clouds in each cells to mimic the ALMA observational maps. By choosing the parameters corresponding to NGC 1068 we obtain the model velocity maps that emulate the effect of an apparent counter-rotation and can explain the discovery made by ALMA. △ Less

Submitted 9 November, 2022; v1 submitted 28 May, 2022; originally announced May 2022.

Comments: 11 pages, 11 figures, Accepted for publication in MNRAS

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

Authors: Shiyan Zhong, Shuo Li, Peter Berczik, Rainer Spurzem

Abstract: 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 ful… ▽ More 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. △ Less

Submitted 19 May, 2022; originally announced May 2022.

Comments: 15 pages, 10 figures, accepted for publication in ApJ

The impact of stellar evolution on rotating star clusters: the gravothermal-gravogyro catastrophe and the formation of a bar of black holes

Authors: A. W. H. Kamlah, R. Spurzem, P. Berczik, M. Arca Sedda, F. Flammini Dotti, N. Neumayer, X. Pang, Q. Shu, A. Tanikawa, M. Giersz

Abstract: We present results from a suite of eight direct N-body simulations, performed with \textsc{Nbody6++GPU}, representing realistic models of rotating star clusters with up to $1.1\times 10^5$ stars. Our models feature primordial (hard) binaries, a continuous mass spectrum, differential rotation, and tidal mass loss induced by the overall gravitational field of the host galaxy. We explore the impact o… ▽ More We present results from a suite of eight direct N-body simulations, performed with \textsc{Nbody6++GPU}, representing realistic models of rotating star clusters with up to $1.1\times 10^5$ stars. Our models feature primordial (hard) binaries, a continuous mass spectrum, differential rotation, and tidal mass loss induced by the overall gravitational field of the host galaxy. We explore the impact of rotation and stellar evolution on the star cluster dynamics. In all runs for rotating star clusters we detect a previously predicted mechanism: an initial phase of violent relaxation followed by the so-called gravogyro catastrophe. We find that the gravogyro catastrophe reaches a finite amplitude, which depends in strength on the level of the bulk rotation, and then levels off. After this phase the angular momentum is transferred from high-mass to low-mass particles in the cluster (both stars and compact objects). Simultaneously, the system becomes gravothermally unstable and collapses, thus undergoing the so-called gravothermal-gravogyro catastrophe. Comparing models with and without stellar evolution, we find an interesting difference. When stellar evolution is not taken into account, the whole process proceeds at a faster pace. The population of heavy objects tend to form a triaxial structure that rotates in the cluster centre. When stellar evolution is taken into account, we find that such a {\it rotating bar} is populated by stellar black holes and their progenitors. The triaxial structure becomes axisymmetric over time, but we also find that the models without stellar evolution suffer repeated gravogyro catastrophes as sufficient angular momentum and mass are removed by the tidal field. △ Less

Submitted 31 August, 2022; v1 submitted 9 May, 2022; originally announced May 2022.

Comments: 19 pages, 9 figures, 2 tables, Accepted by MNRAS

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

Authors: Marina Ishchenko, Peter Berczik, Nina Kharchenko

Abstract: 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 E… ▽ More 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. △ Less

Submitted 31 January, 2023; v1 submitted 28 January, 2022; originally announced January 2022.

Comments: 6 pages, 6 figures, 3 tables

Journal ref: Proceedings of the International Astronomical Union, 2020, Volume 16 , pp. 128 - 133

Eccentricity evolution of massive black hole binaries from formation to coalescence

Authors: Alessia Gualandris, Fazeel Mahmood Khan, Elisa Bortolas, Matteo Bonetti, Alberto Sesana, Peter Berczik, Kelly Holley-Bockelmann

Abstract: 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 releva… ▽ More 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. △ Less

Submitted 21 January, 2022; originally announced January 2022.

Comments: 15 pages, 13 figures, accepted for publication in MNRAS

Kinematic characteristics of the Milky Way globular clusters based on Gaia DR2 data

Authors: I. V. Chemerynska, M. V. Ishchenko, M. O. Sobolenko, S. A. Khoperskov, P. P. Berczik

Abstract: Using the data from Gaia (ESA) Data Release 2 we performed the orbital calculations of globular clusters (GCs) of the Milky Way. To explore possible close encounters (or collisions) between the GCs, using our own developed high-order phi-GRAPE code, we integrated backward and forward the orbits of 119 objects with reliable positions and proper motions. In calculations, we adopted a realistic axisy… ▽ More Using the data from Gaia (ESA) Data Release 2 we performed the orbital calculations of globular clusters (GCs) of the Milky Way. To explore possible close encounters (or collisions) between the GCs, using our own developed high-order phi-GRAPE code, we integrated backward and forward the orbits of 119 objects with reliable positions and proper motions. In calculations, we adopted a realistic axisymmetric Galactic potential (bulge + disk + halo). Using different impact conditions, we found four pairs of the six GCs that may have experienced an encounter within twice the sum of the half-mass radii (collisions) over the last 5Gyr: Terzan3 - NGC 6553, Terzan 3 - NGC 6218, Liller 1 - NGC 6522 and Djorg 2 - NGC 6553. △ Less

Submitted 17 January, 2023; v1 submitted 16 January, 2022; originally announced January 2022.

Comments: Accepted for publication in Advances in Astronomy and Space Physics (http://aasp.kiev.ua). arXiv admin note: substantial text overlap with arXiv:2201.06891

Journal ref: Advances in Astronomy and Space Physics, 12, 18-24 (2022)

Milky Way Globular Clusters: close encounter rates with each other and with the Central Supermassive Black Hole

Authors: Maryna V. Ishchenko, Margarita O. Sobolenko, Mukhagali T. Kalambay, Bekdaulet T. Shukirgaliyev, Peter P. Berczik

Abstract: Using the data from Gaia (ESA) Data Release 2 we performed the orbital calculations of globular clusters (GCs) of the Milky Way. To explore possible collisions between the GCs, using our developed highorder φ-GRAPE code, we integrated (backwards and forward) the orbits of 119 objects with reliable positions and proper motions. In calculations, we adopted a realistic axisymmetric Galactic potential… ▽ More Using the data from Gaia (ESA) Data Release 2 we performed the orbital calculations of globular clusters (GCs) of the Milky Way. To explore possible collisions between the GCs, using our developed highorder φ-GRAPE code, we integrated (backwards and forward) the orbits of 119 objects with reliable positions and proper motions. In calculations, we adopted a realistic axisymmetric Galactic potential (bulge + disk + halo). Using different impact conditions, we found five pairs of the GCs that likely experienced collisions: Terzan 3 - NGC 6553, Terzan 3 - NGC 6218, Liller 1 - NGC 6522, Djorg 2 - NGC 6552 and NGC 6355 - NGC 6637. We analyzed the GCs interaction rates with the central supermassive black hole. Assuming the maximum 100 pc distance criteria for separation between them we estimated 11 close encounter events. From our numerical simulations, we estimate the close interaction rate as at least one event per Gyr with the impact parameter less than 30 pc; and one event per Myr with the impact parameter less than 60 pc. Our calculations show one very close encounter of NGC 6121 with the central SMBH near 5.5 pc (practically direct collision). Based on the extended literature search for the possible progenitor of our selected 11 GCs, we found that most of them have a Milky Way main bulge origin. △ Less

Submitted 19 January, 2022; v1 submitted 18 January, 2022; originally announced January 2022.

Comments: 9 pages, 9 figures, accepted for publication in Reports of National academy of sciences of the Republic of Kazakhstan

Journal ref: Volume 6, Number 340 (2021), 94-105