Coalescing massive black hole binaries, formed during galaxy mergers, are expected to be a primary source of low frequency gravitational waves. Yet in isolated gas-free spherical stellar systems, the hardening of the binary stalls at parsec-scale separations owing to the inefficiency of relaxation-driven loss-cone refilling. Repopulation via collisionless orbit diffusion in triaxial systems is more efficient, but published simulation results are contradictory. While sustained hardening has been reported in simulations of galaxy mergers with N ∼ 10 6 stars and in early simulations of rotating models, in isolated non-rotating triaxial models the hardening rate continues to fall with increasing N , a signature of spurious two-body relaxation.We present a novel approach for studying loss cone repopulation in galactic nuclei. Since loss cone repopulation in triaxial systems owes to orbit diffusion, it is a purely collisionless phenomenon and can be studied with an approximated force calculation technique, provided the force errors are well behaved and sufficiently small. We achieve this using an accurate fast multipole method and define a proxy for the hardening rate that depends only on stellar angular momenta. We find that the loss cone is efficiently replenished even in very mildly triaxial models (with axis ratios 1 : 0.9 : 0.8). Such triaxiality is unavoidable following galactic mergers and can drive binaries into the gravitational wave regime. We conclude that there is no 'final parsec problem'.

AM CVn binaries consist of a WD accreting from a hydrogen-deficient star (or WD) companion (Warner, 1995;Solheim, 2010). In their formation history (Fig. 1.6 and Section 1.3.1.1), AM CVns form after at least one CE phase of their progenitor system. The current RLO is initiated, due to orbital damping caused by GW radiation, at orbital periods of typically 5−20 min (depending on the nature and the temperature of the companion star), and the mass-transfer rate is determined

Massive black hole binaries (BHBs) are expected to be one of the most powerful sources of gravitational waves (GWs) in the frequency range of the pulsar timing array and of forthcoming space-borne detectors. They are believed to form in the final stages of galaxy mergers, and then harden by slingshot ejections of passing stars. However, evolution via the slingshot mechanism may be ineffective if the reservoir of interacting stars is not readily replenished, and the binary shrinking may come to a halt at roughly a parsec separation. Recent simulations suggest that the departure from spherical symmetry, naturally produced in merger remnants, leads to efficient loss cone refilling, preventing the binary from stalling. However, current N-body simulations able to accurately follow the evolution of BHBs are limited to very modest particle numbers. Brownian motion may artificially enhance the loss cone refilling rate in low-N simulations, where the binary encounters a larger population of stars due its random motion. Here we study the significance of Brownian motion of BHBs in merger remnants in the context of the final parsec problem. We simulate mergers with various particle numbers (from 8k to 1M) and with several density profiles. Moreover, we compare simulations where the BHB is fixed at the centre of the merger remnant with simulations where the BHB is free to random walk. We find that Brownian motion does not significantly affect the evolution of BHBs in simulations with particle numbers in excess of one million, and that the hardening measured in merger simulations is due to collisionless loss cone refilling.

One of the most promising gravitational wave (GW) sources detectable by the forthcoming LISA observatory are the so-called extreme-mass ratio inspirals (EMRIs), i.e. GW-driven inspirals of stellar-mass compact objects onto supermassive black holes (SMBHs). In this paper, we suggest that supernova (SN) kicks may trigger EMRIs in galactic nuclei by scattering newborn stellar black holes and neutron stars on extremely eccentric orbits; as a consequence, the time-scale over which these compact objects are expected to inspiral onto the central SMBH via GW emission may become shorter than the time-scale for other orbital perturbations to occur. By applying this argument to the Galactic Centre, we show that the S-cluster and the clockwise disc are optimal regions for the generation of such events: one SN out of ∼ 10 4 (∼ 10 5 ) occurring in the S-cluster (clockwise disc) is expected to induce an EMRI. If we assume that the natal kicks affecting stellar black holes are significantly slower than those experienced by neutron stars, we find that most SN-driven EMRIs involve neutron stars. We further estimate the time spanning from the SN to the final plunge onto the SMBH to be of the order of few Myr. Finally, we extrapolate the rate of SN-driven EMRIs per Milky Way to be up to 10 −8 yr −1 , thus we expect that LISA will detect up to a few tens of SN-driven EMRIs every year.