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Abstract:

Mergers of binary black holes on eccentric orbits are among the targets for second-generation ground-based gravitational-wave detectors. These sources may commonly form in galactic nuclei due to gravitational-wave emission during close flyby events of single objects. We determine the distributions of initial orbital parameters for a population of these gravitational-wave sources. Our results show that the initial dimensionless pericenter distance systematically decreases with the binary component masses and the mass of the central supermassive black hole, and its distribution depends sensitively on the highest possible black hole mass in the nuclear star cluster. For a multi-mass black hole population with masses between 5 Msun and 80 Msun, we find that between 43-69% (68-94%) of 30 Msun - 30 Msun (10 Msun - 10 Msun) sources have an eccentricity greater than 0.1 when the gravitational-wave signal reaches 10 Hz, but less than 10% of the sources with binary component masses less than 30 Msun remain eccentric at this level near the last stable orbit (LSO). The eccentricity at LSO is typically between 0.005-0.05 for the lower-mass BHs, and 0.1 - 0.2 for the highest-mass BHs. Thus, due to the limited low-frequency sensitivity, the six currently known quasi-circular LIGO/Virgo sources could still be compatible with this originally highly eccentric source population. However, at the design sensitivity of these instruments, the measurement of the eccentricity and mass distribution of merger events may be a useful diagnostic to identify the fraction of GW sources formed in this channel.

Abstract:

Nuclear star clusters around massive black holes are expected to be abundant in stellar mass black holes and black hole binaries. These binaries form a hierarchical triple system with the massive black hole at the center. Gravitational perturbations from the massive black hole can cause high eccentricity excitation. During this process, the eccentricity may approach unity, and the pericenter distance may become sufficiently small that gravitational wave emission drives the binary to merge. In this paper, we consider a simple proof of concept and explore the effect of the eccentric Kozai-Lidov mechanism for unequal mass binaries. We perform a set of Monte Carlo simulations on BH-BH binaries in galactic nuclei with quadrupole and octupole-level secular perturbations, general relativistic precession, and gravitational wave emission. For a nominal number of steady-state BH-BH binaries, our model gives a total merger rate $\sim 1 - 3$$Gpc^{-3} yr^{-1}$, depending on the assumed density profile. Thus, our model potentially competes with other dynamical mechanisms, such as the dynamical formations and mergers of BH binaries in globular clusters or dense nuclear clusters without a massive black hole. We provide predictions for the distributions of these LIGO sources in galactic nuclei.

Abstract:

The gravitational interaction among bodies orbiting in a spherical potential leads to the rapid relaxation of the orbital planes' distribution, a process called vector resonant relaxation. We examine the statistical equilibrium of this process for a system of bodies with similar semimajor axes and eccentricities. We extend the previous model of Roupas et al. (2017) by accounting for the multipole moments beyond the quadrupole, which dominate the interaction for radially overlapping orbits. Nevertheless, we find no qualitative differences between the behavior of the system with respect to the model restricted to the quadrupole interaction. The equilibrium distribution resembles a counterrotating disk at low temperature and a spherical structure at high temperature. The system exhibits a first order phase transition between the disk and the spherical phase in the canonical ensemble if the total angular momentum is below a critical value. We find that the phase transition erases the high order multipoles, i.e. small-scale structure in angular momentum space, most efficiently. The system admits a maximum entropy and a maximum energy, which lead to the existence of negative temperature equilibria.