Nuclear star clusters around a central massive black hole (MBH) are expected to be abundant in stellar black hole (BH) remnants and BH-BH binaries. These binaries form a hierarchical triple system with the central MBH and gravitational perturbations from the MBH can cause high-eccentricity excitation in the BH-BH binary orbit. During this process, the eccentricity may approach unity, and the pericenter distance may become sufficiently small that gravitational-wave emission drives the BH-BH binary to merge. In this paper, we construct a simple proof-of-concept model for this process and, specifically, we study the eccentric Kozai-Lidov mechanism in unequal-mass, soft BH-BH binaries. Our model is based on a set of Monte Carlo simulations for BH-BH binaries in galactic nuclei, taking into account quadrupole-and octupole-level secular perturbations, general relativistic precession, and gravitational-wave emission. For a typical steady-state number of BH-BH binaries, our model predicts a total merger rate ∼ 1 − 3 Gpc −3 yr −1 , depending on the assumed density profile in the nucleus. Thus, our mechanism could potentially compete with other dynamical formation processes for merging BH-BH binaries, such as interactions of stellar BHs in globular clusters, or in nuclear star clusters without a MBH.

The supermassive black holes originally in the nuclei of two merging galaxies will form a binary in the remnant core. The early evolution of the massive binary is driven by dynamical friction before the binary becomes "hard" and eventually reaches coalescence through gravitational wave emission. We consider the dynamical friction evolution of massive binaries consisting of a secondary hole orbiting inside a stellar cusp dominated by a more massive central black hole. In our treatment we include the frictional force from stars moving faster than the inspiralling object which is neglected in the standard Chandrasekhar's treatment. We show that the binary eccentricity increases if the stellar cusp density profile rises less steeply than ρ ∝ r −2 . In cusps shallower than ρ ∝ r −1 the frictional timescale can become very long due to the deficit of stars moving slower than the massive body. Although including the fast stars increases the decay rate, low mass-ratio binaries (q 10 −3 ) in sufficiently massive galaxies have decay timescales longer than one Hubble time. During such minor mergers the secondary hole stalls on an eccentric orbit at a distance of order one tenth the influence radius of the primary hole (i.e., ≈ 10 − 100pc for massive ellipticals). We calculate the expected number of stalled satellites as a function of the host galaxy mass, and show that the brightest cluster galaxies should have 1 of such satellites orbiting within their cores. Our results could provide an explanation to a number of observations, which include multiple nuclei in core ellipticals, off-center AGNs and eccentric nuclear disks.

ESA and NASA are moving forward with plans to launch LISA around 2034. With data from the Illustris cosmological simulation, we provide analysis of LISA detection rates accompanied by characterization of the merging massive black hole population. Massive black holes of total mass ∼ 10 5 − 10 10 M are the focus of this study. We evolve Illustris massive black hole mergers, which form at separations on the order of the simulation resolution (∼kpc scales), through coalescence with two different treatments for the binary massive black hole evolutionary process. The coalescence times of the population, as well as physical properties of the black holes, form a statistical basis for each evolutionary treatment. From these bases, we Monte Carlo synthesize many realizations of the merging massive black hole population to build mock LISA detection catalogs. We analyze how our massive black hole binary evolutionary models affect detection rates and the associated parameter distributions measured by LISA. With our models, we find massive black hole binary detection rates with LISA of ∼ 0.5 − 1 yr −1 for massive black holes with masses greater than 10 5 M . This should be treated as a lower limit primarily because our massive black hole sample does not include masses below 10 5 M , which may significantly add to the observed rate. We suggest reasons why we predict lower detection rates compared to much of the literature.

Finite eccentricities in mass-transferring eccentric binary systems can be explained by taking into account mass-loss and mass-transfer processes that often occur in these systems. These processes can be treated as perturbations to the general two-body problem. The time-evolution equations for the semi-major axis and the eccentricity derived from perturbative methods are in general phasedependent. The osculating semi-major axis and eccentricity change over the orbital timescale and they are not easy to implement in binary evolution codes like MESA. However, the secular orbital element evolution equations can be simplified averaging over the rapidly varying true anomalies. In this paper, we derive the secular time-evolution equations for the semi-major axis and the eccentricity for various mass-loss/transfer processes using either the adiabatic approximation or the assumption of deltafunction mass-loss/transfer at periastron. We begin with the cases of isotropic and anisotropic wind mass-loss. We continue with conservative and non-conservative non-isotropic mass ejection/accretion (including RLOF) for both point-masses and extended bodies. We conclude with the case of phasedependent mass accretion. Comparison of the derived equations with similar work in the literature is included and explanation of the existing discrepancies is provided.

Most studies of mass transfer in binary systems assume circular orbits at the onset of Roche lobe overflow. However, there are theoretical and observational indications that mass transfer could occur in eccentric orbits. In particular, eccentricity could be produced via sudden mass loss and velocity kicks during supernova explosions, or Lidov-Kozai (LK) oscillations in hierarchical triple systems, or, more generally, secular evolution in multiple-star systems. However, current analytic models of eccentric mass transfer are faced with the problem that they are only well defined in the limit of very high eccentricities, and break down for less eccentric and circular orbits. This provides a major obstacle to implementing such models in binary and higher-order population synthesis codes, which are useful tools for studying the long-term evolution of a large number of systems. Here, we present a new analytic model to describe the secular orbital evolution of binaries undergoing conservative mass transfer. The main improvement of our model is that the mass transfer rate is a smoothly varying function of orbital phase, rather than a delta function centered at periapsis. Consequently, our model is in principle valid for any eccentricity, thereby overcoming the main limitation of previous works. We implement our model in an easy-to-use and publicly available code that can be used as a basis for implementations of our model into population synthesis codes. We investigate the implications of our model in a number of applications with circular and eccentric binaries, and triples undergoing LK oscillations.