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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, Comment: 27 pages, 28 figures. Submitted to A&A

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., Comment: in Russian language

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., Comment: Submitted to ApJ

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., Comment: Astronomy & Astrophysics, accepted

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

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

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

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

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

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 $\chi_{\rm IMBH} > 0.6$. 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$_\odot$., Comment: 15 pages, 6 figures, 2 tables, 1 appendix. Comments welcome. Submitted to MNRAS

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$_\odot$)., Comment: 22 pages, 21 figures, 4 tables. Comments welcome. Submitted to MNRAS

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

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

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

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., Comment: 11 pages, 11 figures, Accepted for publication in MNRAS

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., Comment: 15 pages, 10 figures, accepted for publication in ApJ

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., Comment: 6 pages, 6 figures, 3 tables

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., Comment: 15 pages, 13 figures, accepted for publication in MNRAS

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 {\phi}-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., Comment: 9 pages, 9 figures, accepted for publication in Reports of National academy of sciences of the Republic of Kazakhstan

Aims: We study the impact of Post-Newtonian correction terms on the energetic interaction between a gravitational wave (GW)-emitting supermassive black hole (SMBH) binary system and incoming stars via three-body scattering experiments. Methods: We use the AR-chain code to simulate with high accuracy the interactions between stars and an SMBH binary at separations of$\sim 1000\,R_{sch}$. For all of the interactions, we investigate in detail the energy balance of the three-body systems, using both Newtonian and Post-Newtonian expressions for the SMBH binary orbital energy, taking into account the GW emission by the binary. Results: We find that at these separations, purely Newtonian treatment of the binary orbital energy is insufficient to properly account for the SMBH binary orbital evolution. Instead, along with GW emission, even terms in the PN-corrections must be included in order to describe the energy change of the binary during the stellar interaction.es, 2, Comment: 8 pages, 2 figures, 1 table. Submitted to A&A

One of the main possible way of creating the supermassive black hole (SMBH) is a so call hierarchical merging scenario. Central SMBHs at the final phase of interacting and coalescing host-galaxies are observed as SMBH binary (SMBHB) candidates at different separations from hundreds of pc to mpc. Today one of the strongest SMBHB candidate is a ULIRG galaxy NGC 6240 which was X-ray spatially and spectroscopically resolved by Chandra. Dynamical calculation of central SMBHBs merging in a dense stellar environment allows us to retrace their evolution from kpc to mpc scales. The main goal of our dynamical modeling was to reach the final, gravitational wave (GW) emission regime for the model BHs. We present the direct N-body simulations with up to one million particles and relativistic post-Newtonian corrections for the SMBHs particles up to 3.5 post-Newtonian terms. Generally speaking, the set of initial physical conditions can strongly effect of our merging time estimations. But in a range of our parameters, we did not find any strong correlation between merging time and BHs mass or BH to bulge mass ratios. Varying the model numerical parameters (such as particle number - N) makes our results quite robust and physically more motivated. From our 20 models we found the upper limit of merging time for central SMBHB is less than $\sim$55 Myr. This concrete number are valid only for our set of combination of initial mass ratios. Further detailed research of rare dual/multiple BHs in dense stellar environment (based on observations data) can clarify the dynamical co-evolution of central BHs and their host-galaxies., Comment: 11 pages, 6 figures, 3 tables, Accepted for publication in Astronomy & Astrophysics

Tidal disruption events (TDEs) provide a clue to the properties of a central supermassive black hole (SMBH) and an accretion disk around it, and to the stellar density and velocity distributions in the nuclear star cluster surrounding the SMBH. Deviations of TDE light curves from the standard occurring at a parabolic encounter with the SMBH depends on whether the stellar orbit is hyperbolic or eccentric (Hayasaki et al. 2018) and the penetration factor ($\beta$, tidal disruption radius to orbital pericenter ratio). We study the orbital parameters of bound and unbound stars being tidally disrupted by comparison of direct $N$-body simulation data with an analytical model. Starting from the classical steady-state Fokker-Planck model of Cohn & Kulsrud (1978), we develop an analytical model of the number density distribution of those stars as a function of orbital eccentricity ($e$) and $\beta$. To do so fittings of the density and velocity distribution of the nuclear star cluster and of the energy distribution of tidally disrupted stars are required and obtained from $N$-body data. We confirm that most of the stars causing TDEs in a spherical nuclear star cluster originate from the full loss-cone region of phase space, derive analytical boundaries in eccentricity-$\beta$ space, and find them confirmed by $N$-body data. Since our limiting eccentricities are much smaller than critical eccentricities for full accretion or full escape of stellar debris, we conclude that those stars are only very marginally eccentric or hyperbolic, close to parabolic., Comment: 28 pages, 10 figures, 1 table. Accepted for publication in ApJ

Aims: We investigate the orbital and phase space properties of loss cone stars that interact strongly with a hard, high-redshift binary supermassive black hole (SMBH) system formed in a cosmological scenario. Methods: We use a novel hybrid integration approach that combines the direct N-body code $\varphi$-GRAPE with ETICS, a collisionless code that employs the self-consistent field method for force calculation. The hybrid approach shows considerable speed-up over direct summation for particle numbers $> 10^6$, while retaining accuracy of direct N-body for a subset of particles. During the SMBH binary evolution we monitor individual stellar interactions with the binary in order to identify stars that noticeably contribute to the SMBH binary hardening. Results: We successfully identify and analyze in detail the properties of stars that extract energy from the binary. We find that the summed energy changes seen in these stars match very well with the overall binary energy change, demonstrating that stellar interactions are the primary drivers of SMBH binary hardening in triaxial, gas-poor systems. The slight triaxiality of our system results in efficient loss cone refilling, avoiding the final parsec problem. We distinguish three different populations of interactions based on their apocenter. We find a clear prevalence of interactions co-rotating with the binary. Nevertheless, retrograde interactions are the most energetic, contributing only slightly less than the prograde population to the overall energy exchange. The most energetic interactions are also likely to result in a change of sign in the angular momentum of the star. We estimate the merger timescale of the binary to be $\approx 20$ $\mathrm{Myr}$, a value larger by a factor of two than the timescale reported in a previous study., Comment: 17 pages, 13 figures, 2 tables; accepted for publication in Astronomy & Astrophysics

Modern galaxy formation theory suggests that the misalignment between stellar and gaseous components usually results from an external gas accretion and/or interaction with other galaxies. The extreme case of the kinematic misalignment is demonstrated by so-called galaxies with counterrotation that possess two distinct components rotating in opposite directions with respect to each other. We provide an in-deep analysis of galaxies with counterrotation from IllustrisTNG100 cosmological simulations. We have found $25$ galaxies with substantial stellar counterrotation in the stellar mass range of $2\times10^{9}-3\times10^{10}$~\Msun. In our sample the stellar counterrotation is a result of an external gas infall happened $\approx 2-8$~Gyr ago. The infall leads to the initial removal of pre-existing gas, which is captured and mixed together with the infalling component. The gas mixture ends up in the counterrotating gaseous disc. We show that $\approx 90\%$ of the stellar counterrotation formed in-situ, in the counterrotating gas. During the early phases of the infall, gas can be found in inclined extended and rather thin disc-like structures, and in some galaxies they are similar to (nearly-)~polar disc or ring-like structures. We discuss a possible link between the gas infall, AGN activity and the formation of misaligned components. In particular, we suggest that the AGN activity does not cause the counterrotation, although it is efficiently triggered by the retrograde gas infall, and it correlates well with the misaligned component appearance. We also find evidence of the stellar disc heating visible as an increase of the vertical-to-radial velocity dispersion ratio above unity in both co- and counterrotating components, which implies the importance of the kinematical misalignment in shaping the velocity ellipsoids in disc galaxies., Comment: 20 pages, 20 figures, accepted for publication in MNRAS

This study presents a comprehensive chemo-dynamical analysis of LAMOST J1109+0754, a bright (V = 12.8), extremely metal-poor (\abund{Fe}{H} = $-3.17$) star, with a strong \textit{r}-process enhancement (\abund{Eu}{Fe} = +0.94 $\pm$ 0.12). Our results are based on the 7-D measurements supplied by $Gaia$ and the chemical composition derived from a high-resolution ($R\sim 110,000$), high signal-to-noise ratio ($S/N \sim 60)$ optical spectrum obtained by the 2.4\,m Automated Planet Finder Telescope at Lick Observatory. We obtain chemical abundances of 31 elements (from lithium to thorium). The abundance ratios (\abund{X}{Fe}) of the light-elements (Z $\leqslant 30$) suggest a massive Population\,III progenitor in the 13.4-29.5\,M$_\odot$ mass range. The heavy-element ($30 <$ Z $\leqslant 90$) abundance pattern of J1109+075 agrees extremely well with the scaled-Solar \textit{r}-process signature. We have developed a novel approach to trace the kinematic history and orbital evolution of J1109+0754 with a c\textbf{O}smologically de\textbf{RI}ved tim\textbf{E}-varyi\textbf{N}g Galactic po\textbf{T}ential (the ORIENT) constructed from snapshots of a simulated Milky-Way analog taken from the \texttt{Illustris-TNG} simulation. The orbital evolution within this Milky Way-like galaxy, along with the chemical-abundance pattern implies that J1109+0754 likely originated in a low-mass dwarf galaxy located $\sim$ 60\,kpc from the center of the Galaxy, which was accreted $\sim$ 6 - 7\,Gyr ago, and that the star now belongs to the outer-halo population.

Given the closeness of the two open clusters Cr 135 and UBC 7 on the sky, we investigate the possibility of the two clusters to be physically related. We aim to recover the present-day stellar membership in the open clusters Collinder 135 and UBC 7 (300 pc from the Sun), to constrain their kinematic parameters, ages and masses, and to restore their primordial phase space configuration. The most reliable cluster members are selected with our traditional method modified for the use of Gaia DR2 data. Numerical simulations use the integration of cluster trajectories backwards in time with our original high order Hermite4 code \PGRAPE. We constrain the age, spatial coordinates and velocities, radii and masses of the clusters. We estimate the actual separation of the cluster centres equal to 24 pc. The orbital integration shows that the clusters were much closer in the past if their current line-of-sight velocities are very similar and the total mass is more than 7 times larger the mass of the determined most reliable members. We conclude that the two clusters Cr 135 and UBC 7 might very well have formed a physial pair, based on the observational evidence as well as numerical simulations. The probability of a chance coincidence is only about $2\%$., Comment: Accepted for publication as a Letter in Astronomy and Astrophysics. 5 pages, 2 figures

Young dense massive star clusters are a promising environment for the formation of intermediate mass black holes (IMBHs) through collisions. We present a set of 80 simulations carried out with Nbody6++GPU of 10 initial conditions for compact $\sim 7 \times 10^4 M_{\odot}$ star clusters with half-mass radii $R_\mathrm{h} \lesssim 1 pc$, central densities $\rho_\mathrm{core} \gtrsim 10^5 M_\odot pc^{-3}$, and resolved stellar populations with 10\% primordial binaries. Very massive stars (VMSs) with masses up to $\sim 400 M_\odot$ grow rapidly by binary exchange and three-body scattering events with main sequences stars in hard binaries. Assuming that in VMS - stellar BH collisions all stellar material is accreted onto the BH, IMBHs with masses up to $M_\mathrm{BH} \sim 350 M_\odot$ can form on timescales of $\lesssim 15$ Myr. This process was qualitatively predicted from Monte Carlo MOCCA simulations. Despite the stochastic nature of the process - typically not more than 3/8 cluster realisations show IMBH formation - we find indications for higher formation efficiencies in more compact clusters. Assuming a lower accretion fraction of 0.5 for VMS - BH collisions, IMBHs can also form. The process might not work for accretion fractions as low as 0.1. After formation, the IMBHs can experience occasional mergers with stellar mass BHs in intermediate mass-ratio inspiral events (IMRIs) on a 100 Myr timescale. Realised with more than $10^5$ stars, 10 \% binaries, the assumed stellar evolution model with all relevant evolution processes included and 300 Myr simulation time, our large suite of simulations indicates that IMBHs of several hundred solar masses might form rapidly in massive star clusters right after their birth while they are still compact., Comment: Submitted

In this work, we study the stellar-dynamical hardening of unequal mass supermassive black hole (SMBH) binaries in the central regions of merging galactic nuclei. We present a comprehensive set of direct $N$-body simulations of the problem, varying both the total mass and the mass ratio of the SMBH binary (SMBHB). Simulations were carried out with the $\varphi-$GPU $N$-body code, which enabled us to fully exploit supercomputers equipped with graphic processing units (GPUs). As a model for the galactic nuclei, we adopted initial axisymmetric, rotating models, aimed at reproducing the properties of a galactic nucleus emerging from a galaxy merger event, containing two SMBHs which were unbound initially. We found no 'final-parsec problem', as our SMBHs tend to pair and shrink without showing significant signs of stalling. This confirms earlier results and extends them to large particle numbers and rotating systems. We find that the SMBHB hardening depends on the binary-reduced mass ratio via a single parameter function. Our results suggest that, at a fixed value for the SMBHB primary mass, the merger time of highly asymmetric binaries is up to four order of magnitudes smaller than the equal-mass binaries. This can significantly affect the population of SMBHs potentially detectable as gravitational wave sources., Comment: 7 pages, 5 figures, accepted to A&A

We present a set of self-consistent chemo-dynamical simulations of MW-type galaxies formation to study the origin of the bimodality of $\alpha$-elements in stellar populations. We explore how the bimodality is related to the geometrically and kinematically defined stellar discs, gas accretion and radial migration. We find that the two $\alpha$-sequences are formed in quite different physical environments. The high-$\alpha$ sequence is formed early from a burst of star formation (SF) in a turbulent, compact gaseous disc which forms a thick disc. The low-$\alpha$ stellar populations is the result of quiescent SF supported by the slow accretion of enriched gas onto a radially extended thin disc. Stellar feedback-driven outflows during the formation of the thick disc are responsible for the enrichment of the surrounding gaseous halo, which subsequently feeds the disc on a longer time-scale. During the thin disc phase, chemical evolution reaches an equilibrium metallicity and abundance, where the stars pile-up. This equilibrium metallicity decreases towards the outer disc, generating the ridgeline that forms the low-$\alpha$ sequence. We identify a second mechanism capable of creating a low-$\alpha$ sequence in one of our simulations. Rapid shutdown of the SF, provoked by the feedback at the end of the thick disc phase, suppresses the chemical enrichment of the halo gas, which, once accreted onto the star-forming disc, dilutes the ISM at the beginning of the thin disc formation. Both mechanisms can operate in a galaxy, but the former is expected to occur when SF efficiency ceases to be dominated by the formation of the thick disc, while the latter can occur in the inner regions. Being the result of the presence of low and high gas density environments, the bimodality is independent of any particular merger history, suggesting that it could be much more widespread than has been claimed., Comment: 22 pages, 19 figures, accepted for publication in MNRAS

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

The hierarchical galaxy formation model predicts supermassive black hole binaries (SMBHBs) in galactic nuclei. Due to the gas poor environment and the limited spatial resolution in observations they may hide in the center of many a galaxy. However, a close encounter of a star with one of the supermassive black holes (SMBHs) may tidally disrupt it to produce a tidal disruption event (TDE) and temporarily light up the SMBH. In a previous work, we investigated with direct N-BODY simulations the evolution of TDE rates of SMBHB systems in galaxy mergers of equal mass. In this work we extend to unequal mass mergers. Our results show that, when two SMBHs are far away from each other, the TDE rate of each host galaxy is similar as in an isolated galaxy. As the two galaxies and their SMBHs separation shrinks, the TDE rate is increasing gradually until it reaches a maximum shortly after the two SMBHs become bound. In this stage, the averaged TDE rate can be enhanced by several times to an order of magnitude relative to isolated single galaxies. Our simulations show that the dependence of the TDE accretion rate on the mass ratio in this stage can be well fitted by power law relations for both SMBHs. After the bound SMBHB forms, the TDE rate decreases with its further evolution. We also find that in minor mergers TDEs of the secondary SMBH during and after the bound binary formation are mainly contributed by stars from the other galaxy., Comment: 27 pages, 6 figures, accepted by ApJ

We study the evolution of star clusters in the Galactic tidal field starting from their birth in molecular clumps. Our model clusters form according to the local-density-driven cluster formation model in which the stellar density profile is steeper than that of gas. As a result, clusters resist the gas expulsion better than predicted by earlier models. We vary the impact of the Galactic tidal field {\lambda}, considering different Galactocentric distances (3-18 kpc), as well as different cluster sizes. Our model clusters survive the gas expulsion independent of {\lambda}. We investigated the relation between the cluster mass at the onset of secular evolution and their dissolution time. The model clusters formed with a high star-formation efficiency (SFE) follow a tight mass-dependent dissolution relation, in agreement with previous theoretical studies. However, the low-SFE models present a shallower mass-dependent relation than high-SFE clusters, and most dissolve before reaching 1 Gyr (cluster teenage mortality)., Comment: 4 pages, 2 figures. Submitted for publication in the Proceedings of IAU Symposium 351

The masses of stellar-remnant black holes (BH), as a result of their formation via massive single- and binary-stellar evolution, is of high interest in this era of gravitational-wave detection from binary black hole (BBH) and binary neutron star (BNS) mergers. Here we present new developments in the N-body evolution program NBODY7 in regards to its stellar-remnant formation and related schemes. We demonstrate that the newly-implemented stellar-wind and remnant-formation schemes in the NBODY7 code's BSE sector, such as the 'rapid' and the 'delayed' supernova (SN) schemes along with an implementation of pulsational-pair-instability and pair-instability supernova (PPSN/PSN), now produces neutron star (NS) and BH masses that agree nearly perfectly, over large ranges of zero-age-main sequence (ZAMS) mass and metallicity, with those from the StarTrack population-synthesis program. We also demonstrate the new implementations of various natal-kick mechanisms on NSs and BHs such as the 'convection-asymmetry-driven', 'collapse-asymmetry-driven', and 'neutrino-emission-driven' kicks, in addition to a fully consistent implementation of the standard, fallback-dependent, momentum-conserving natal kick. We find that the SN material fallback causes the convection-asymmetry kick to effectively retain similar number and mass of BHs in clusters as for the standard, momentum-conserving kick. The collapse-asymmetry kick would cause nearly all BHs to retain in clusters irrespective of remnant formation model and metallicity, whereas the inference of a large number of BHs in GCs would potentially rule out the neutrino-driven kick mechanism. Pre-SN mergers of massive primordial binaries would cause BH masses to deviate from the single-star ZAMS mass-remnant mass relation. Such mergers, at low metallicities, can produce low-spinning BHs within the PSN mass gap that can be retained in a stellar cluster., Comment: 27 pages, 15 figures, 2 tables. Accepted for publication in Astronomy and Astrophysics

Using a single N-body simulation ($N=0.14\times 10^9$) we explore the formation, evolution and spatial variation of the phase-space spirals similar to those recently discovered by Antoja et al. in the Milky Way disk, with Gaia DR2. For the first time in the literature, we use a self-consistent N-body simulation of an isolated Milky Way-type galaxy to show that the phase-space spirals develop naturally from vertical oscillations driven by the buckling of the stellar bar. We claim that the physical mechanism standing behind the observed incomplete phase-space mixing process can be internal and not necessarily due to the perturbation induced by a massive satellite. In our model, the bending oscillations propagate outwards and produce axisymmetric variations of the mean vertical coordinate and of the vertical velocity component. As a consequence, the phase-space wrapping results in the formation of patterns with various morphology across the disk, depending on the bar orientation, distance to the galactic center and time elapsed since the bar buckling. Once bending waves appear, they are supported for a long time via disk self-gravity. The underlying physical mechanism implies the link between in-plane and vertical motion that leads directly to phase-space structures whose amplitude and shape are in remarkable agreement with those of the phase-space spirals observed in the Milky Way disk. In our isolated galaxy simulation, phase-space spirals are still distinguishable, at the solar neighbourhood, 3 Gyr after the buckling phase. The long-lived character of the phase-space spirals generated by the bar buckling instability cast doubts on the timing argument used so far to get back at the time of the onset of the perturbation: phase-space spirals may have been caused by perturbations originated several Gyrs ago, and not as recent as suggested so far., Comment: 7 pages, 6 figures; accepted for publication by A&A Letters on Dec 14, 2018

The Laser Interferometer Space Antenna (LISA) will detect gravitational-wave (GW) signals from merging supermassive black holes (BHs) with masses below $10^7$~M$_{\odot}$. It is thus of paramount importance to understand the orbital dynamics of these relatively light central BHs, which typically reside in disc-dominated galaxies, in order to produce reliable forecasts of merger rates. To this aim, realistic simulations probing BH dynamics in unequal-mass disc galaxy mergers, into and beyond the binary hardening stage, are performed by combining smooth particle hydrodynamics and direct $N$-body codes. The structural properties and orbits of the galaxies are chosen to be consistent with the results of galaxy formation simulations. Stellar and dark matter distributions are triaxial down to the central 100 pc of merger remnant. In all cases, a BH binary forms and hardens on time-scales of at most 100~Myr, coalescing on another few hundred Myr time-scale, depending on the characteristic density and orbital eccentricity. Overall, the sinking of the BH binary takes no more than $\sim$0.5~Gyr after the merger of the two galaxies is completed, but can be much faster for very plunging orbits. Comparing with previous numerical simulations following the decay of BHs in massive early-type galaxies at $z \sim 3$, we confirm that the characteristic density is the most crucial parameter determining the overall BH merging time-scale, despite the structural diversity of the host galaxies. Our results lay down the basis for robust forecasts of LISA event rates in the case of merging BHs., Comment: ApJ submitted

We have studied the long-term evolution of star clusters of the solar neighborhood, starting from their birth in gaseous clumps until their complete dissolution in the Galactic tidal field. We have combined the "local-density-driven cluster formation model" of Parmentier & Pfalzner (2013) with direct N-body simulations of clusters following instantaneous gas expulsion. We have studied the relation between cluster dissolution time, $t_{dis}$, and cluster "initial" mass, $M_{init}$, defined as the cluster {mass at the end of the dynamical response to gas expulsion (i.e. violent relaxation), when the cluster age is 20-30 Myr}. We consider the "initial" mass to be consistent with other works which neglect violent relaxation. The model clusters formed with a high star formation efficiency (SFE -- i.e. gas mass fraction converted into stars) follow a tight mass-dependent relation, in agreement with previous theoretical studies. However, the low-SFE models present a large scatter in both the "initial" mass and the dissolution time, and a shallower mass-dependent relation than high-SFE clusters. Both groups differ in their structural properties on the average. Combining two populations of clusters, high- and low-SFE ones, with domination of the latter, yields a cluster dissolution time for the solar neighborhood in agreement with that inferred from observations, without any additional destructive processes such as giant molecular cloud encounters. An apparent mass-independent relation may emerge for our low-SFE clusters when we neglect low-mass clusters (as expected for extra-galactic observations), although more simulations are needed to investigate this aspect., Comment: Acceped for publication in Astrophysical Journal (ApJ), 17 pages, 9 figures

We study the dynamics and evolution of the Milky Way nuclear star cluster performing a high resolution direct one-million-body simulation. Focusing on the interactions between such stellar system and the central supermassive black hole, we find that different stellar components adapt their overall distribution differently. After 5 Gyr, stellar mass black holes are characterized by a spatial distribution with power-slope $-1.75$, fully consistent with the prediction of Bahcall-Wolf pioneering work. Using the vast amount of data available, we infer the rate for tidal disruption events, being $4 \times 10^{-6}$ per yr, and estimate the number of objects that emit gravitational waves during the phases preceding the accretion onto the super-massive black hole, $\sim 270$ per Gyr. We show that some of these sources could form extreme mass-ratio inspirals. We follow the evolution of binary stars population, showing that the initial binary fraction of $5\%$ drops down to $2.5\%$ inside the inner parsec. Also, we explored the possible formation of binary systems containing a compact object, discussing the implications for millisecond pulsars formation and the development of Ia Supernovae., Comment: Accepted by MNRAS after a major revision

The evolution of Supermassive Black Holes (SMBHs) initially embedded in the centres of merging galaxies realised with a stellar mass function (SMF) is studied from the onset of galaxy mergers till coalescence. We performed a large set of direct N-body simulations with three different slopes of the central stellar cusp and different random seeds. Post Newtonian terms up to order 3.5 are used to drive the SMBH binary evolution in the relativistic regime. The impact of a SMF on the hardening rate and the coalescence time is investigated. We find that SMBH binaries coalesce well within one billion years when our models are scaled to galaxies with a steep cusp at low redshift. Here higher central densities provide larger supply of stars to efficiently extract energy from the SMBH binary orbit and shrink it to the phase where gravitational wave (GW) emission becomes dominant leading to the coalescence of the SMBHs. Mergers of models with shallow cusps that are representative for giant elliptical galaxies having central cores result in less efficient extraction of binary orbital energy due to the lower stellar densities in the centre. However, high values of eccentricity witnessed for SMBH binaries in such galaxy mergers ensure that the GW emission dominated phase sets in earlier at larger values of the semi-major axis. This helps to compensate for the less efficient energy extraction during the phase dominated by stellar encounters resulting in mergers of SMBHs in about one Gyr after the formation of the binary. Additionally, we witness mass segregation in the merger remnant resulting in enhanced SMBH binary hardening rates. We show that at least the final phase of the merger in cuspy low mass galaxies would be observable with the GW detector eLISA., Comment: Accepted for publication in Astronomy & Astrophysics

We study the rates of tidal disruption of stars by intermediate-mass to supermassive black holes on bound to unbound orbits by using high-accuracy direct N-body experiments. The approaching stars from the star cluster to the black hole can take three types of orbit: eccentric, parabolic, and hyperbolic orbits. Since the mass fallback rate shows a different variability depending on these orbital types, we can classify tidal disruption events (TDEs) into three main categories: eccentric, parabolic, and hyperbolic TDEs. Respective TDEs are characterized by two critical values of the orbital eccentricity: the lower critical eccentricity is the one below which the stars on eccentric orbits cause the finite, intense accretion, and the higher critical eccentricity above which the stars on hyperbolic orbits cause no accretion. Moreover, we find that the parabolic TDEs are divided into three subclasses: precisely parabolic, marginally eccentric, and marginally hyperbolic TDEs. We analytically derive that the mass fallback rate of the marginally eccentric TDEs can be flatter and slightly higher than the standard fallback rate proportional to $t^{-5/3}$, whereas it can be flatter and lower for the marginally hyperbolic TDEs. We confirm by N-body experiments that only few eccentric, precisely parabolic, and hyperbolic TDEs can occur in a spherical stellar system with a single intermediate-mass to supermassive black hole. A substantial fraction of the stars approaching to the black hole would cause the marginally eccentric or marginally hyperbolic TDEs., Comment: 37 pages, 2 tables, 7 figures, accepted for publication in ApJ

We perform high resolution direct $N$-body simulations to study the effect of an accretion disc on stellar dynamics in an active galactic nucleus (AGN). We show that the interaction of the nuclear stellar cluster (NSC) with the gaseous disc (AD) leads to formation of a stellar disc in the central part of the NSC. The accretion of stars from the stellar disc onto the super-massive black hole is balanced by the capture of stars from the NSC into the stellar disc, yielding a stationary density profile. We derive the migration time through the AD to be 3\% of the half-mass relaxation time of the NSC. The mass and size of the stellar disc are 0.7\% of the mass and 5\% of the influence radius of the super-massive black hole. An AD lifetime shorter than the migration time would result in a less massive nuclear stellar disc. The detection of such a stellar disc could point to past activity of the hosting galactic nucleus., Comment: submitted to MNRAS after revision

A large fraction of galactic nuclei is expected to host supermassive black hole binaries (BHB), likely formed during the early phase of galaxies assembly and merging. In this paper, we use a large set of state-of-art numerical models to investigate the interplay between a BHB and a massive star cluster (GCs) driven toward the galactic centre by dynamical friction. Varying the BHB mass and mass ratio and the GC orbit, we show that the reciprocal feedback exerted between GCs and the BHB shapes their global properties. We show that, at GC-to-BHB mass ratios above 0.1, the GC affects notably the BHB orbital evolution, possibly boosting its coalescence. This effect is maximized if the GC moves on a retrograde orbit, and for a non-equal mass BHB. We show that the GC debris dispersed around the galactic nucleus can lead to the formation of a nuclear cluster, depending on the BHB tidal field, and that the distribution of compact remnants resulting from the GC disruption can carry information about the BHB orbital properties. We find that red giant stars delivered by the spiralling GC can be disrupted at a rate of $\simeq (0.7-7)\times 10^{-7}$ yr$^{-1}$ for BHB masses $\sim 10^7{\rm M}_\odot$, while tens to hundreds of stars can be possibly observed in the galactic halo as high-velocity stars, with velocities up to $\sim 2000$ km s$^{-1}$, depending on the BHB orbital properties., Comment: 26 pages, 27 figures, 2 tables. Resubmitted to MNRAS after minor revision

Numerical simulations were carried out to study the origin of multiple stellar populations in the intermediate-age clusters NGC 411 and NGC 1806 in the Magellanic Clouds. We performed NBODY6++ simulations based on two different formation scenarios, an ad hoc formation model where second-generation (SG) stars are formed inside a cluster of first-generation (FG) stars using the gas accumulated from the external intergalactic medium and a minor merger model of unequal mass ($M_{SG}$/$M_{FG}$ ~5-10%) clusters with an age difference of a few hundred million years. We compared our results such as the radial profile of the SG-to-FG number ratio with observations on the assumption that the SG stars in the observations are composed of cluster members, and confirmed that both the ad hoc formation and merger scenarios reproduce the observed radial trend of the SG-to-FG number ratio which shows less centrally concentrated SG than FG stars. It is difficult to constrain the formation scenario for the multiple populations by only using the spatial distribution of the SG stars. SG stars originating from the merger scenario show a significant velocity anisotropy and rotational features compared to those from the ad hoc formation scenario. Thus, observations aimed at kinematic properties like velocity anisotropy or rotational velocities for SG stars should be obtained to better understand the formation of the multiple populations in these clusters. This is, however, beyond current instrumentation capabilities., Comment: 11 pages, 8 figures, 1 table; accepted for publication in MNRAS

We study the effect of the instantaneous gas expulsion on star clusters wherein the residual gas has a density profile shallower than that of the embedded cluster. This is expected if star formation proceeds with a given SFE per free-fall time in a centrally-concentrated molecular clump. We perform direct N-body simulations whose initial conditions are generated by the program "mkhalo" "falcON" adapted for our models. Our model clusters initially have a Plummer profile and are in virial equilibrium with the gravitational potential of the cluster-forming clump. The residual gas contribution is computed based on the model of Parmentier&Pfalzner(2013). Our simulations include mass loss by stellar evolution and the tidal field of the Galaxy. We find that a star cluster with a minimum global SFE of 15% is able to survive instantaneous gas expulsion and to produce a bound cluster. Its violent relaxation lasts no longer than 20 Myr, independently of its global SFE and initial stellar mass. At the end of violent relaxation the bound fractions of surviving clusters with the same global SFEs are similar regardless of their initial stellar mass. Their subsequent lifetime in the gravitational field of the Galaxy depends on their bound stellar masses. We therefore conclude that the critical SFE needed to produce a bound cluster is 15%, which is twice smaller than earlier estimates of 33%. Thus we have improved the survival likelihood of young clusters after instantaneous gas expulsion. Those can now survive instantaneous gas expulsion with global SFEs as low as those observed for embedded clusters of Solar Neighbourhood (15-30%). This is the consequence of the star cluster having a density profile steeper than that of the residual gas. However, in terms of the effective SFE, measured by the virial ratio of the cluster at gas expulsion, our results are in agreement with previous studies., Comment: Accepted for publication in Astronomy&Astrophysics, 13 pages, 10 figures

Supermassive black hole (SMBH) binaries residing at the core of merging galaxies are recently found to be strongly affected by the rotation of their host galaxies. The highly eccentric orbits that form when the host is counterrotating emit strong bursts of gravitational waves that propel rapid SMBH binary coalescence. Most prior work, however, focused on planar orbits and a uniform rotation profile, an unlikely interaction configuration. However, the coupling between rotation and SMBH binary evolution appears to be such a strong dynamical process that it warrants further investigation. This study uses direct N-body simulations to isolate the effect of galaxy rotation in more realistic interactions. In particular, we systematically vary the SMBH orbital plane with respect to the galaxy rotation axis, the radial extent of the rotating component, and the initial eccentricity of the SMBH binary orbit. We find that the initial orbital plane orientation and eccentricity alone can change the inspiral time by an order of magnitude. Because SMBH binary inspiral and merger is such a loud gravitational wave source, these studies are critical for the future gravitational wave detector, LISA, an ESA/NASA mission currently set to launch by 2034., Comment: 9 pages, 9 figures and 3 tables. Accepted for publication in MNRAS

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

Supermassive black holes (SMBHs) are ubiquitous in galaxies with a sizable mass. It is expected that a pair of SMBHs originally in the nuclei of two merging galaxies would form a binary and eventually coalesce via a burst of gravitational waves. So far theoretical models and simulations have been unable to predict directly the SMBH merger timescale from ab-initio galaxy formation theory, focusing only on limited phases of the orbital decay of SMBHs under idealized conditions of the galaxy hosts. The predicted SMBH merger timescales are long, of order Gyrs, which could be problematic for future gravitational wave searches. Here we present the first multi-scale $\Lambda$CDM cosmological simulation that follows the orbital decay of a pair of SMBHs in a merger of two typical massive galaxies at $z\sim3$, all the way to the final coalescence driven by gravitational wave emission. The two SMBHs, with masses $\sim10^{8}$ M$_{\odot}$, settle quickly in the nucleus of the merger remnant. The remnant is triaxial and extremely dense due to the dissipative nature of the merger and the intrinsic compactness of galaxies at high redshift. Such properties naturally allow a very efficient hardening of the SMBH binary. The SMBH merger occurs in only $\sim10$ Myr after the galactic cores have merged, which is two orders of magnitude smaller than the Hubble time., Comment: 8 pages, 7 figures, accepted for publication in ApJ

Introducing the DRAGON simulation project, we present direct $N$-body simulations of four massive globular clusters (GCs) with $10^6$ stars and 5$\%$ primordial binaries at a high level of accuracy and realism. The GC evolution is computed with NBODY6++GPU and follows the dynamical and stellar evolution of individual stars and binaries, kicks of neutron stars and black holes, and the effect of a tidal field. We investigate the evolution of the luminous (stellar) and dark (faint stars and stellar remnants) GC components and create mock observations of the simulations (i.e. photometry, color-magnitude diagrams, surface brightness and velocity dispersion profiles). By connecting internal processes to observable features we highlight the formation of a long-lived 'dark' nuclear subsystem made of black holes (BHs), which results in a two-component structure. The inner core is dominated by the BH subsystem and experiences a core collapse phase within the first Gyr. It can be detected in the stellar (luminous) line-of-sight velocity dispersion profiles. The outer extended core - commonly observed in the (luminous) surface brightness profiles - shows no collapse features and is continuously expanding. We demonstrate how a King (1966) model fit to observed clusters might help identify the presence of post core-collapse BH subsystems. For global observables like core and half-mass radii the direct simulations agree well with Monte-Carlo models. Variations in the initial mass function can result in significantly different GC properties (e.g. density distributions) driven by varying amounts of early mass loss and the number of forming BHs., Comment: 18 pages, 8 figures, MNRAS accepted

We show by numerical simulations that a purely stellar dynamical model composed of an exponential disc, a cuspy bulge, and an NFW halo with parameters relevant to the Milky Way Galaxy is subject to bar formation. Taking into account the finite disc thickness, the bar formation can be explained by the usual bar instability, in spite of the presence of an inner Lindblad resonance, that is believed to damp any global modes. The effect of replacing the live halo and bulge by a fixed external axisymmetric potential (rigid models) is studied. It is shown that while the e-folding time of bar instability increases significantly (from 250 to 500 Myr), the bar pattern speed remains almost the same. For the latter, our average value of 55 km/s/kpc agrees with the assumption that the Hercules stream in the solar neighbourhood is an imprint of the bar--disc interaction at the outer Lindblad resonance of the bar. Vertical averaging of the radial force in the central disc region comparable to the characteristic scale length allows us to reproduce the bar pattern speed and the growth rate of the rigid models, using normal mode analysis of linear perturbation theory in a razor thin disc. The strong increase of the e-folding time with decreasing disc mass predicted by the mode analysis suggests that bars in galaxies similar to the Milky Way have formed only recently., Comment: 13 pages, 15 figures, submitted to MNRAS Dec 2015, accepted Jul 29, 2016

Supermassive black hole binaries (SMBHBs) are productions of the hierarchical galaxy formation model. There are many close connections between central SMBH and its host galaxy because the former plays very important roles on the formation and evolution of a galaxy. For this reason, the evolution of SMBHBs in merging galaxies is an essential problem. Since there are many discussions about SMBHB evolution in gas rich environment, we focus on the quiescent galaxy, using tidal disruption as a diagnostic tool. Our study is based on a series of numerical large particle number direct N-body simulations for dry major mergers. According to the simulation results, the evolution can be divided into three phases. In phase I, the tidal disruption rate for two well separated SMBHs in merging system has similar level to single SMBH in isolate galaxy. After two SMBHs getting close enough to form a bound binary in phase II, the disruption rate can be enhanced for ~ 2 order of magnitudes within a short time. This "boosted" disruption stage finishes after the SMBHB evolving to compact binary system in phase III, corresponding to a drop back of disruption rate to a level of a few times higher than that in Phase I. How to correctly extrapolate our N-body simulation results to reality, and implications of our results to observations, are discussed too., Comment: 16 pages, Accepted for publication in ApJ