Search

Context. Recent observational data show that the Milky Way (MW) galaxy contains about 170 globular clusters (GCs). A fraction of them is likely formed in dwarf galaxies accreted onto the MW in the past, while the remaining of clusters are formed in-situ. Therefore, different parameters, including orbits, of the globular clusters is a valuable tool for studying the Milky Way evolution. However, since the evolution of the 3D mass distribution of the MW is poorly constrained, the orbits of the clusters are usually calculated in static potentials. Aims. In this work, we study the evolution of the GCs in several external potentials, where we aim to quantify the effects of the evolving galaxy potential on the orbits of the GCs. Methods. For the orbits calculation we used five MW-like potentials from IllustrisTNG-100 simulation. The orbits of 159 GCs were integrated using a high-order N-body parallel dynamic code phi-GPU, with initial conditions obtained from recent Gaia DR3 catalogues. Results. We provide a classification of the GCs orbits according to their 3D shapes and association with different components of the MW (disk, halo, bulge). We also found that the globular clusters in the external potentials have roughly similar energy-angular momentum distributions at the present time. However, both total energy and total angular momentum of the GCs are not conserved due to time-varying nature of the potentials. In some extreme cases, the total energy can change up to 40% (18 objects) over the last 5 Gyr of evolution. We found that the in-situ formed GCs are less affected by the evolution of the TNG potentials as compared to the clusters which are likely formed ex-situ. Therefore, our results suggest that time-varying potentials significantly affect the orbits of the GC, thus making it vital for understanding the formation of the MW., 19 pages, 17 figures, 2 tables, accepted for publication in Astronomy and Astrophysics

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

Understanding the formation of star clusters with low star-formation efficiency (SFE) is very important to know about the star-formation history. In N-body models of star cluster evolution after gas expulsion, the Plummer model with outer power law density profile has been used massively. We study the impact of the density profile slopes on the survivability of the low-SFE star clusters after instantaneous gas expulsion. We compare cases when stellar cluster has Plummer profile and Dehnen profiles with cusp of different slopes at the time of formation. We determine the corresponding density profile of the residual gas for a given global SFE, assuming that our model clusters formed with a constant efficiency per free-fall time and hence have shallower density profile of gas than that of stars. We perform direct $N$-body simulations of evolution of clusters initially in virial equilibrium within gas potential after gas removal. We find that the violent relaxation lasts no longer than 20~Myr independently of the density profile power law slopes. Dehnen model clusters survive after violent relaxation with significantly lower SFEs when the global SFE measured within the Jacobi radius or within a half-mass radius. Dehnen $\gamma=0$ model clusters show similar final bound fraction with the Plummer model clusters if global SFE is measured within 10 scale radii. The final bound fraction increases with $\gamma$ values for a given global SFE. We conclude that Dehnen clusters better resist the consequences of the violent relaxation followed the instantaneous gas expulsion than the Plummer clusters. Thus the shallower the outer density slope of the low-SFE clusters, the better for their survivability after gas expulsion. Among Dehnen clusters we find that the steeper the inner slope (cusp) the higher the bound mass fraction is retained after violent relaxation for a given global SFE., Comment: 14 pages, 10 figures. Accepted for publication in Astronomy and Astrophysics (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., 11 pages, 6 figures, 3 tables, Accepted for publication in Astronomy & Astrophysics

MS acknowledge the financial support by the NASU under the Grant for young researchers. MS and PB acknowledge also the special support by the NASU under the Main Astronomical Observatory GRID/GPU computing cluster golowood project. RS and PB acknowledge support by Chinese Academy of Sciences through the Silk Road Project at NAOC, through the “Qianren” special foreign experts program of China. MS gratefully acknowledges support for collaboration visits in Beijing under the same program. Supported by the Strategic Priority Research Program “The Emergence of Cosmological Structures” of the Chinese Academy of Sciences, Grant N XDB09000000. The main part of the simulations presented here was performed on the dedicated GPU clusters kepler at the ARI. funded under the grants 1/80 041-043 and 1/81 396 of the Volkswagen Foundation and the grants 823.219-439/30 and /36 of the Ministry of Science, Research and the Arts of Baden-Wurttemberg, Germany. The authors are acknowledges the support of the Volkswagen Foundation under the Trilateral Partnerships grant No. 90411. Part of the code development work was conducted using the resources of the GPU cluster laohu at the Center of Information and Computing at the National Astronomical Observatories, Chinese Academy of Sciences, funded by the Ministry of Finance of People’s Republic of China under the grant ZDYZ2008-2. We also acknowledge the helpful comments made by Stephen Justham.

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

We present a set of, large scale direct N-body simulations of the galaxy collision with the central Supermassive Black Hole Binary (SMBHB) system. Based on our simulations which include the accurate Post Newtonian (PN) relativistic dynamical corrections we can estimated the merging time for the real astrophysical object. Each galaxy initially was represented as a set of particles (up to N=500k) with Plummer distribution. The SMBHBs system is described using the two special high mass, i.e. “relativistic”, particles. The interaction between these two particles have an extra PN correction terms (up to 3.5PN). Merging time upper limit was obtained for the closely interacting galaxy system NGC 6240.