Dynamical evolution of stellar-mass black holes in dense stellar clusters: estimate for merger rate of binary black holes originating from globular clusters

We have performed N-body simulations of globular clusters (GCs) in order to estimate a detection rate of mergers of Binary stellar-mass Black Holes (BBHs) by means of gravitational wave (GW) observatories. For our estimate, we have only considered mergers of BBHs which escape from GCs (BBH escapers). BBH escapers merge more quickly than BBHs inside GCs because of their small semi-major axes. N-body simulation can not deal with a GC with the number of stars N ~ 10^6 due to its high calculation cost. We have simulated dynamical evolution of small-N clusters (10^4 <~ N <~ 10^5), and have extrapolated our simulation results to large-N clusters. From our simulation results, we have found the following dependence of BBH properties on N. BBHs escape from a cluster at each two-body relaxation time at a rate proportional to N. Semi-major axes of BBH escapers are inversely proportional to N, if initial mass densities of clusters are fixed. Eccentricities, primary masses, and mass ratios of BBH escapers are independent of N. Using this dependence of BBH properties, we have artificially generated a population of BBH escapers from a GC with N ~ 10^6, and have estimated a detection rate of mergers of BBH escapers by next-generation GW observatories. We have assumed that all the GCs are formed 10 or 12Gyrs ago with their initial numbers of stars N_i=5 x 10^5 -- 2 x 10^6 and their initial stellar mass densities inside their half-mass radii \rho_h,i=6 x 10^3 -- 10^6M_sun pc^-3. Then, the detection rate of BBH escapers is 0.5 -- 20 yr^-1 for a BH retention fraction R_BH=0.5. A few BBH escapers are components of hierarchical triple systems, although we do not consider secular perturbation on such BBH escapers for our estimate. Our simulations have shown that BHs are still inside some of GCs at the present day. These BHs may marginally contribute to BBH detection.Comment: 20 pages, 19 figures, 3 tables, accepted for publication in MNRA

Correlation of macroscopic instability and Lyapunov times in the general three-body problem

We conducted extensive numerical experiments of equal mass three-body systems until they became disrupted. The system lifetimes, as a bound triple, and the Lyapunov times show a correlation similarto what has been earlier obtained for small bodies in the Solar System. Numerical integrations of several sets of differently randomised initial conditions produced the same relationship of the instability time and Lyapunov time. Marginal probability densities of the various times in the three-body experiments are also discussed. Our high accuracy numerical method for three-body orbit computations and Lyapunov time determinations is concisely described.Comment: 4 pages, 7 figures. accepted for publication in MNRA

High-resolution hydrodynamic simulation of tidal detonation of a helium white dwarf by an intermediate mass black hole

We demonstrate tidal detonation during a tidal disruption event (TDE) of a helium (He) white dwarf (WD) with $0.45M_\odot$ by an intermediate mass black hole (IMBH) by extremely high-resolution simulations. Tanikawa et al. (2017) have showed tidal detonation in previous studies results from unphysical heating due to low-resolution simulations, and such unphysical heating occurs in 3-dimensional (3D) smoothed particle hydrodynamics (SPH) simulations even with $10$ million SPH particles. In order to avoid such unphysical heating, we perform 3D SPH simulations up to $300$ million SPH particles, and 1D mesh simulations using flow structure in the 3D SPH simulations for 1D initial conditions. The 1D mesh simulations have higher resolution than the 3D SPH simulations. We show tidal detonation occurs, and confirm this result is perfectly converged with different space resolution in both 3D SPH and 1D mesh simulations. We find detonation waves independently arises in leading parts of the WD, and yield large amounts of $^{56}$Ni. Although detonation waves are not generated in trailing parts of the WD, the trailing parts receive detonation waves generated in the leading parts, and leave large amounts of Si group elements. Eventually, this He WD TDE would synthesize $^{56}$Ni of $0.30M_\odot$ and Si group elements of $0.08M_\odot$, and could be observed as a luminous thermonuclear transient comparable to type Ia supernovae.Comment: 13 pages, 14 figure

Mass-Loss Timescale of Star Clusters in an External Tidal Field. II. Effect of Mass Profile of Parent Galaxy

We investigate the long-term dynamical evolution of star clusters in a steady tidal field produced by its parent galaxy. In this paper, we focus on the influence of mass profile of the parent galaxy. The previous studies were done with the simplification where the parent galaxy was expressed by point mass. We express different mass profiles of the parent galaxy by the tidal fields in which the ratios of the epicyclic frequency to the angular velocity are different. We compare the mass-loss timescale of star clusters whose tidal radii are identical but in parent galaxies with different mass profile, by means of orbits calculations in fixed cluster potential and N-body simulations. In this situation, a cluster rotates around the parent galaxy more rapidly as the parent galaxy has shallower mass profile. We found that the mass-loss timescale increase 20% and 50% for the cases that the mass density profile of the parent galaxies are proportional to R^-2 and R^-1.5 where R is the distance from the galaxy center, compared to the point-mass case, in moderately strong tidal field. Counterintuitively, a cluster which rotates around the parent galaxy more rapidly has a longer lifetime. The increase of lifetime is due to the fact that the fraction occupied by regular-like orbit increases in shallower profile. Finally, we derive an evaluation formula for the mass-loss timescale of clusters. Our formula can explain a property of the population of the observed galactic globular clusters that their half-mass radii become smaller as their distances from the galactic center become smaller.Comment: Submitted to PAS