We present a set of 148 independent N -body simulations of globular clusters (GCs) computed using the code CMC (Cluster Monte Carlo). At an age of ∼ 10−13 Gyr, the resulting models cover nearly the full range of cluster properties exhibited by the Milky Way GCs, including total mass, core and half-light radii, metallicity, and galactocentric distance. We use our models to investigate the role that stellarmass black holes play in the process of core collapse. Furthermore, we study how dynamical interactions affect the formation and evolution of several important types of sources in GCs, including low-mass X-ray binaries, millisecond pulsars, blue stragglers, cataclysmic variables, Type Ia supernovae, calciumrich transients, and merging compact binaries. While our focus here is on old, low-metallicity GCs, our CMC simulations follow the evolution of clusters over a Hubble time, and they include a wide range of metallicities (up to solar), so that our results can also be used to study younger and higher-metallicity star clusters.2. METHODS 2.1. Summary of CMC

The first detection of gravitational waves from a neutron star -neutron star (NS-NS) merger, GW170817, and the increasing number of observations of short gamma-ray bursts (SGRBs) have greatly motivated studies of the origins of NS-NS and neutron star -black hole (NS-BH) binaries. We calculate the merger rates of NS-NS and NS-BH binaries from globular clusters (GCs) using realistic GC simulations with the CMC cluster catalog. We use a large sample of models with a range of initial numbers of stars, metallicities, virial radii and galactocentric distances, representative of the present-day Milky Way GCs, to quantify the inspiral times and volumetric merger rates as a function of redshift, both inside and ejected from clusters. We find that over the complete lifetime of most GCs, stellar BHs dominate the cluster cores and prevent the mass segregation of NSs, thereby reducing the dynamical interaction rates of NSs so that at most a few NS binary mergers are ever produced. We estimate the merger rate in the local universe to be ∼ 0.02 Gpc −3 yr −1 for both NS-NS and NS-BH binaries, or a total of ∼ 0.04 Gpc −3 yr −1 for both populations. These rates are about 5 orders of magnitude below the current empirical merger rate from LIGO/Virgo. We conclude that dynamical interactions in GCs do not play a significant role in enhancing the NS-NS and NS-BH merger rates.

The high rate of black hole (BH) mergers detected by LIGO/Virgo opened questions on their astrophysical origin. One possibility is the dynamical channel, in which binary formation and hardening is catalyzed by dynamical encounters in globular clusters (GCs). Previous studies have shown that the BH merger rate from the present day GC density in the Universe is lower than the observed rate. In this Letter, we study the BH merger rate by accounting for the first time for the evolution of GCs within their host galaxies. The mass in GCs was initially ∼ 8× higher, which decreased to its present value due to evaporation and tidal disruption. Many BH binaries that were ejected long before their merger, originated in GCs that no longer exist. We find that the comoving merger rate in the dynamical channel from GCs varies between 18 to 35 Gpc −3 yr −1 between redshift z = 0.5 to 2, and the total rate is 1, 5, 24 events per day within z = 0.5, 1, and 2, respectively. The cosmic evolution and disruption of GCs systematically increases the present-day merger rate by a factor ∼ 2 relative to isolated clusters. Gravitational wave detector networks offer an unique observational probe of the initial number of GC populations and their subsequent evolution across cosmic time.

Nuclear star clusters surrounding supermassive black holes (SMBHs) in galactic nuclei contain large numbers of stars, black holes (BHs) and neutron stars (NSs), a fraction of which are likely to form binaries. These binaries were suggested to form a triple system with the SMBH, which acts as a perturber and may enhance BH and NS mergers via the Lidov-Kozai mechanism. We follow-up previous studies, but for the first time perform an extensive statistical study of BH-BH, NS-NS and BH-NS binary mergers by means of direct high-precision regularized N -body simulations, including Post-Newtonian (PN) terms up to order PN2.5. We consider different SMBH masses, slopes for the BH mass function, binary semi-major axis and eccentricity distributions, and different spatial distributions for the binaries. We find that the merger rates are a decreasing function of the SMBH mass and are in the ranges ∼ 0.17-0.52 Gpc −3 yr −1 , ∼ 0.06-0.10 Gpc −3 yr −1 and ∼ 0.04-0.16 Gpc −3 yr −1 for BH-BH, BH-NS and NS-NS binaries, respectively. However, the rate estimate from this channel remains highly uncertain and depends on the specific assumptions regarding the star-formation history in galactic nuclei and the supply rate of compact objects. We find that ∼ 10%-20% of the mergers enter the LIGO band with eccentricities 0.1. We also compare our results to the secular approximation, and show that N -body simulations generally predict a larger number of mergers. Finally, these events can also be observable via their electromagnetic counterparts, thus making these compact object mergers especially valuable for cosmological and astrophysical purposes.

In hierarchical triple systems, the inner binary is perturbed by a distant companion. For large mutual inclinations, the Lidov-Kozai mechanism secularly excites large eccentricity and inclination oscillations of the inner binary. The maximal eccentricity attained, e max is simply derived and widely used. However, for mildly hierarchical systems (i.e. the companion is relatively close and massive), non-secular perturbations affect the evolution. Here we account for fast non-secular variations and find new analytic formula for e max , in terms of the system's hierarchy level, correcting previous work and reproducing the orbital flip criteria. We find that e max is generally enhanced, allowing closer encounters between the inner binary components, thus significantly changing their interaction and its final outcome. We then extend our approach to include additional relativistic and tidal forces. Using our results, we show that the merger time of gravitational-wave (GW) sources orbiting massive black-holes in galactic nuclei is enhanced compared with previous analysis accounting only for the secular regime. Consequently, this affects the distribution and rates of such GW sources in the relevant mild-hierarchy regime. We test and confirm our predictions with direct N-body and 2.5-level Post-Newtonian codes. Finally, we calculate the formation and disruption rates of hot-Jupiters (HJ) in planetary systems using a statistical approach, which incorporates our novel results for e max . We find that more HJ migrate from further out, but they are also tidally disrupted more frequently. Remarkably, the overall formation rate of HJs remains similar to that found in previous studies. Nevertheless, the different rates could manifest in different underlying distribution of observed warm-Jupiters.

Theoretical modeling of massive stars predicts a gap in the black hole (BH) mass function above ∼40-50 M e for BHs formed through single star evolution, arising from (pulsational) pair-instability supernovae (PISNe). However, in dense star clusters, dynamical channels may exist that allow construction of BHs with masses in excess of those allowed from single star evolution. The detection of BHs in this so-called "upper-mass gap" would provide strong evidence for the dynamical processing of BHs prior to their eventual merger. Here, we explore in detail the formation of BHs with masses within or above the pair-instability gap through collisions of young massive stars in dense star clusters. We run a suite of 68 independent cluster simulations, exploring a variety of physical assumptions pertaining to growth through stellar collisions, including primordial cluster mass segregation and the efficiency of envelope stripping during collisions. We find that as many as ∼20% of all BH progenitors undergo one or more collisions prior to stellar collapse and up to ∼1% of all BHs reside within or above the pair-instability gap through the effects of these collisions. We show that these BHs readily go on to merge with other BHs in the cluster, creating a population of massive BH mergers at a rate that may compete with the "multiple-generation" merger channel described in other analyses. This has clear relevance for the formation of very massive BH binaries as recently detected by the Laser Interferometer Gravitational-Wave Observatory/Virgo in GW190521. Finally, we describe how stellar collisions in clusters may provide a unique pathway to PISNe and briefly discuss the expected rate of these events and other electromagnetic transients.

The recent discovery of gravitational waves (GW) has opened new horizons for physics. Current and upcoming missions, such as LIGO, VIRGO, KAGRA, and LISA, promise to shed light on black holes of every size from stellar mass (SBH) sizes up to supermassive black holes. The intermediate mass black hole (IMBH) family has not been detected beyond any reasonable doubt. Recent analyses suggest observational evidence for the presence of IMBHs in the centers of two Galactic globular clusters. In this paper, we investigate the possibility that globular clusters were born with a central IMBH, which undergo repeated merger events with SBHs in the cluster core. By means of a semi-analytical method, we follow the evolution of the primordial cluster population in the galactic potential and the mergers of the binary IMBH-SBH systems. Our models predict ≈ 1000 IMBHs within 1 kpc from the galactic center and show that the IMBH-SBH merger rate density changes from R ≈ 1000 Gpc −3 yr −1 beyond z ≈ 2 to R ≈ 1−10 Gpc −3 yr −1 at z ≈ 0. The rates at low redshifts may be significantly higher if young massive star clusters host IMBHs. The merger rates are dominated by IMBHs with masses between 10 3 and 10 4 M . Currently there are no LIGO/VIRGO upper limits for GW sources in this mass range, but our results show that at design sensitivity these instruments will detect IMBH-SBH mergers in the coming years. LISA and the Einstein Telescope will be best suited to detect these events. The inspirals of IMBH-SBH systems may also generate an unresolved GW background.

With the hundreds of merging binary black hole (BH) signals expected to be detected by LIGO/Virgo, LISA and other instruments in the next few years, the modeling of astrophysical channels that lead to the formation of compact-object binaries has become of fundamental importance. In this paper, we carry out a systematic statistical study of quadruple BHs consisting of two binaries in orbit around their center of mass, by means of high-precision direct N -body simulations including Post-Newtonian (PN) terms up to 2.5PN order. We found that most merging systems have high initial inclinations and the distributions peak at ∼ 90 • as for triples, but with a more prominent broad distribution tail. We show that BHs merging through this channel have a significant eccentricity in the LIGO band, typically much larger than BHs merging in isolated binaries and in binaries ejected from star clusters, but comparable to that of merging binaries formed via the GW capture scenario in clusters, mergers in hierarchical triples, or BH binaries orbiting intermediate-mass black holes in star clusters. We show that the merger fraction can be up to ∼ 3-4× higher for quadruples than for triples. Thus even if the number of quadruples is 20%-25% of the number of triples, the quadruple scenario can represent an important contribution to the events observed by LIGO/VIRGO.