arXiv subjects

Peter Berczik

Publications and source records attributed to Peter Berczik.

At least 19 recordsLinked to original sources

arXiv2026

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

The hierarchical nature of galaxy formation in the Lambda cold dark matter ($\Lambda$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.

astro-ph.GA↗

arXiv2026

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

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.

astro-ph.GA↗

arXiv2026

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

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 S\'ersic 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.

astro-ph.GA↗

arXiv2026

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

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 ({\phi}-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.

astro-ph.GA↗

arXiv2026

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

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.

astro-ph.GA↗

arXiv2025

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

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

astro-ph.EP↗

arXiv2025

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

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.

astro-ph.GA↗

arXiv2025

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

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.

astro-ph.GA↗

arXiv2025

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

The hierarchical nature of galaxy formation in the $\Lambda$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.

astro-ph.GA↗

arXiv2025

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

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.

astro-ph.GA↗

arXiv2025

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

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.

astro-ph.GA↗

arXiv2025

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

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 $\chi^2$-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.

astro-ph.GA↗

arXiv2024

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

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.

astro-ph.SR↗

arXiv2024

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

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

astro-ph.GA↗

arXiv2024

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

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 {\phi}-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.

astro-ph.HE↗

arXiv2024

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

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.

astro-ph.GA↗

arXiv2024

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

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 \phi-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.

astro-ph.GA↗

arXiv2024

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

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.

astro-ph.GA↗