The star cluster survivability after gas expulsion is independent of the impact of the Galactic tidal field

We study the impact of the tidal field on the survivability of star clusters following instantaneous gas expulsion. Our model clusters are formed with a centrally-peaked star-formation efficiency profile as a result of star-formation taking place with a constant efficiency per free-fall time. We define the impact of the tidal field as the ratio of the cluster half-mass radius to its Jacobi radius immediately after gas expulsion, $\lambda = r_{h}/R_{J}$. We vary $\lambda$ by varying either the Galactocentric distance, or the size (hence volume density) of star clusters. We propose a new method to measure the violent relaxation duration, in which we compare the total mass-loss rate of star clusters with their stellar evolutionary mass-loss rate. That way, we can robustly estimate the bound mass fraction of our model clusters at the end of violent relaxation. The duration of violent relaxation correlates linearly with the Jacobi radius, when considering identical clusters at different Galactocentric distances. In contrast, it is nearly constant for the solar neighbourhood clusters, slightly decreasing with $\lambda$. The violent relaxation does not last longer than 50 Myr in our simulations. Identical model clusters placed at different Galactocentric distances have the same final bound fraction, despite experiencing different impacts of the tidal field. The solar neighbourhood clusters with different densities experience only limited variations of their final bound fraction. In general, we conclude that the cluster survivability after instantaneous gas expulsion, as measured by their bound mass fraction at the end of violent relaxation, $F_{bound}$, is independent of the impact of the tidal field, $\lambda$.Comment: accepted for publication in MNRAS, 8 pages, 5 figures,3 table

Evolution of open clusters with or without black holes

Binary black holes (BHs) can be formed dynamically in the centers of star clusters. The high natal kicks for stellar-mass BHs used in previous works made it hard to retain BHs in star clusters. Recent studies of massive star evolution and supernovae (SN) propose kick velocities that are lower due to the fallback of the SN ejecta. We study the impact of these updates by performing $N$-body simulations following instantaneous gas expulsion. For comparison, we simulate two additional model sets with the previous treatment of stars: one with high kicks and another with artificial removal of the kicks. Our model clusters initially consist of about one hundred thousand stars, formed with centrally-peaked efficiency. We find that the updated treatment of stars, due to the fallback-scaled lower natal kicks, allows clusters to retain SN remnants after violent relaxation. The mass contribution of the retained remnants does not exceed a few percent of the total bound cluster mass during the early evolution. For this reason, the first giga year of evolution is not affected significantly by this effect. Nevertheless, during the subsequent long-term evolution, the retained BHs accelerate mass segregation, leading to the faster dissolution of the clusters.Comment: 8 pages, 7 figures, submitted to MNRAS, comments are welcom

The star cluster survivability after gas expulsion is independent of the impact of the Galactic tidal field

We study the impact of the tidal field on the survivability of star clusters following instantaneous gas expulsion. Our model clusters are formed with a centrally peaked star formation efficiency profile as a result of star formation taking place with a constant efficiency per free-fall time. We define the impact of the tidal field as the ratio of the cluster half-mass radius to its Jacobi radius immediately after gas expulsion, λ = rh/RJ. We vary λ by varying either the Galactocentric distance, or the size (hence volume density) of star clusters. We propose a new method to measure the violent relaxation duration, in which we compare the total mass-loss rate of star clusters with their stellar evolutionary mass-loss rate. That way, we can robustly estimate the bound mass fraction of our model clusters at the end of violent relaxation. The duration of violent relaxation correlates linearly with the Jacobi radius, when considering identical clusters at different Galactocentric distances. In contrast, it is nearly constant for the solar neighbourhood clusters, slightly decreasing with λ. The violent relaxation does not last longer than 50 Myr in our simulations. Identical model clusters placed at different Galactocentric distances have the same final bound fraction, despite experiencing different impacts of the tidal field. The solar neighbourhood clusters with different densities experience only limited variations of their final bound fraction. In general, we conclude that the cluster survivability after instantaneous gas expulsion, as measured by their bound mass fraction at the end of violent relaxation, Fbound, is independent of the impact of the tidal field, λ

Star-disc interaction in galactic nuclei: formation of a central stellar disc

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 accretion disc (AD) leads to formation of a stellar disc in the central part of the NSC. The accretion of stars from the stellar disc on to 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 per cent of the half-mass relaxation time of the NSC. The mass and size of the stellar disc are 0.7 per cent of the mass and 5 per cent 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

Bound mass of Dehnen models with a centrally peaked star formation efficiency

Context. Understanding the formation of bound star clusters with a low star formation efficiency (SFE) is important for improving our knowledge of the star-formation history of galaxies. In N-body models of star-cluster evolution after gas expulsion, the Plummer model with an outer power law density profile has been used in a broad range of studies. Aims. Here, 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 a stellar cluster exhibits a Plummer profile to those with Dehnen profiles, including cuspy ones of different slopes at the time of formation. Methods. We determined 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, with a shallower density profile for the gas than that of the stars. We performed direct N-body simulations of evolution of clusters initially in virial equilibrium within the gas potential following gas removal. Results. 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 a similar final bound fraction with the Plummer model clusters if the global SFE is measured within ten scale radii. The final bound fraction increases with the gamma values for a given global SFE. Conclusions. We conclude that Dehnen clusters better resist the consequences of the violent relaxation that follows the instantaneous gas expulsion, as compared to the Plummer clusters. Therefore, the shallower the outer density slope of the low-SFE clusters, the better their prospects for survival after gas expulsion. Among the Dehnen clusters, we find that the steeper the inner slope, the higher the bound mass fraction that is retained, following the violent relaxation for a given global SFE

NGC 6240 supermassive black hole binary dynamical evolution based on Chandra data

The main idea of our research is to estimate the physical coalescence time of the double supermassive black hole (SMBH) system in the centre of NGC 6240 based on the X-ray observations from the Chandra space observatory. The spectra of the Northern and Southern nuclei were fitted by spectral models from Sherpa and both presented the narrow component of the Fe K$\alpha$ emission line. It enabled us to apply the spectral model to these lines and to find relative offset $\approx0.02$ keV. The enclosed dynamical mass of the central region of NGC 6240 with radius 1 kpc was estimated $\approx 2.04\times 10^{11} \rm\; M_{\odot}$. These data allowed us to carry on the high resolution direct N-body simulations with Newtonian and post-Newtonian (up to $2.5\mathcal{PN}$ correction) dynamics for this particular double SMBH system. As a result, from our numerical models we approximated the central SMBH binary merging time for the different binary eccentricities. In our numerical parameters range the upper limit for the merging time, even for the very small eccentricities, is still below $\approx70$ Myr. Gravitational waveforms and amplitude-frequency pictures from such events can be detected using Pulsar Timing Array (PTA) projects at the last merging phase.Comment: 12 pages, 7 figures, 6 tables. Accepted for publication in MNRAS, minor typos were correcte

Discovery of Tidal Tails in Disrupting Open Clusters: Coma Berenices and a Neighbor Stellar Group

We report the discovery of tidal structures around the intermediate-aged (∼700-800 Myr), nearby (∼85 pc) star cluster Coma Berenices. The spatial and kinematic grouping of stars is determined with the Gaia DR2 parallax and proper motion data, by a clustering analysis tool, STARGO, to map 5D parameters (X, Y, Z, {μ }α \cos δ ,{μ }δ ) onto a 2D neural network. Leading and trailing tails, each with an extension of ∼50 pc are revealed for the first time around this disrupting star cluster. The cluster members, totaling ∼ {115}-3+5 {M}ȯ , are clearly mass-segregated, and exhibit a flat mass function with α ∼ 0.79 ± 0.16, in the sense of dN/dm ∝ m −α , where N is the number of member stars and m is stellar mass, in the mass range of m = 0.25-2.51 M ☉. Within the tidal radius of ∼6.9 pc, there are 77 member candidates with an average position, i.e., the cluster center, of R.A. = 186.°8110, and decl. = 25.°8112, and an average distance of 85.8 pc. Additional 120 member candidates reside in the tidal structures, i.e., outnumbering those in the cluster core. The expansion of escaping members lead to an anisotropy in the velocity field of the tidal tails. Our analysis also serendipitously uncovers an adjacent stellar group, part of which has been cataloged in the literature. We identify 218 member candidates, 10 times more than previously known. This star group is some 65 pc away from, and ∼400 Myr younger than, Coma Ber, but is already at the final stage of disruption

Bound mass of Dehnen models with a centrally peaked star formation efficiency

Context. Understanding the formation of bound star clusters with a low star formation efficiency (SFE) is important for improving our knowledge of the star-formation history of galaxies. In N-body models of star-cluster evolution after gas expulsion, the Plummer model with an outer power law density profile has been used in a broad range of studies. Aims. Here, 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 a stellar cluster exhibits a Plummer profile to those with Dehnen profiles, including cuspy ones of different slopes at the time of formation. Methods. We determined 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, with a shallower density profile for the gas than that of the stars. We performed direct N-body simulations of evolution of clusters initially in virial equilibrium within the gas potential following gas removal. Results. 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 γ = 0 model clusters show a similar final bound fraction with the Plummer model clusters if the global SFE is measured within ten scale radii. The final bound fraction increases with the γ values for a given global SFE. Conclusions. We conclude that Dehnen clusters better resist the consequences of the violent relaxation that follows the instantaneous gas expulsion, as compared to the Plummer clusters. Therefore, the shallower the outer density slope of the low-SFE clusters, the better their prospects for survival after gas expulsion. Among the Dehnen clusters, we find that the steeper the inner slope, the higher the bound mass fraction that is retained, following the violent relaxation for a given global SFE