Binary supermassive black holes (SBHs) form naturally in galaxy mergers, but their long-term evolution is uncertain. In spherical galaxies, N-body simulations show that binary evolution stalls at separations much too large for significant emission of gravitational waves (the "final-parsec problem"). Here we follow the long-term evolution of a massive binary in more realistic, triaxial and rotating galaxy models with particle numbers as high as 10 6 . We find that the binary does not stall. The binary hardening rates that we observe are sufficient to allow complete coalescence of binary SBHs in 10 Gyr or less, even in the absence of collisional loss-cone refilling or gasdynamical torques, thus providing a potential solution to the final-parsec problem.

Introducing the DRAGON simulation project, we present direct N -body simulations of four massive globular clusters (GCs) with 10 6 stars and 5% primordial binaries at a high level of accuracy and realism. The GC evolution is computed with NBODY6++GPU and follows the dynamical and stellar evolution of individual stars and binaries, kicks of neutron stars and black holes, and the effect of a tidal field. We investigate the evolution of the luminous (stellar) and dark (faint stars and stellar remnants) GC components and create mock observations of the simulations (i.e. photometry, color-magnitude diagrams, surface brightness and velocity dispersion profiles). By connecting internal processes to observable features we highlight the formation of a long-lived 'dark' nuclear subsystem made of black holes (BHs), which results in a two-component structure. The inner core is dominated by the BH subsystem and experiences a core collapse phase within the first Gyr. It can be detected in the stellar (luminous) line-of-sight velocity dispersion profiles. The outer extended corecommonly observed in the (luminous) surface brightness profiles -shows no collapse features and is continuously expanding. We demonstrate how a King (1966) model fit to observed clusters might help identify the presence of post core-collapse BH subsystems. For global observables like core and half-mass radii the direct simulations agree well with Monte-Carlo models. Variations in the initial mass function can result in significantly different GC properties (e.g. density distributions) driven by varying amounts of early mass loss and the number of forming BHs.

We use a gaseous model and a semi-analytical approach to study the evolution of a super-massive central gaseous object (a super-massive star, SMS from now on) in an AGN and its evolution by interactions with the surrounding stellar system. Our future work in this field is outlined, which aims at a more detailed study of energy flows in the interstellar medium, stellar evolution and the relation between QSOs and galaxy formation.

The influence of rotation on the dynamical evolution of collisional stellar systems is investigated by solving the orbit-averaged Fokker-Planck equation in (E, J z )-space. We find that large amounts of initial rotation drive the system into a phase of strong mass loss while it is moderately contracting. The core is rotating even faster than before although angular momentum is transported outwards. At the same time the core is heating. Given these features this phase can be associated with the gravo-gyro 'catastrophe' found by Hachisu (1979). The increase in central angular momentum levels off after about 2-3 initial half-mass relaxation times indicating that the source of this 'catastrophe' is depleted. Finally, the central angular velocity increases again, but with a rather small power of the central density -the same power as for the central velocity dispersion during self-similar contraction towards the collapse. The rotation curves flatten and the ellipticity variations decrease with time, but their shapes are very similar. These results suggest the existence of a self-similar solution for a rotating cluster as well. The maximum values of rotational velocity and ellipticity occur at about the half mass radius.

Accurate direct N -body simulations help to obtain detailed information about the dynamical evolution of star clusters. They also enable comparisons with analytical models and Fokker-Planck or Monte-Carlo methods. NBODY6 is a well-known direct N -body code for star clusters, and NBODY6++ is the extended version designed for large particle number simulations by supercomputers. We present NBODY6++GPU, an optimized version of NBODY6++ with hybrid parallelization methods (MPI, GPU, OpenMP, and AVX/SSE) to accelerate large direct N -body simulations, and in particular to solve the million-body problem. We discuss the new features of the NBODY6++GPU code, benchmarks, as well as the first results from a simulation of a realistic globular cluster initially containing a million particles. For million-body simulations, NBODY6++GPU is 400 − 2000 times faster than NBODY6 with 320 CPU cores and 32 NVIDIA K20X GPUs. With this computing cluster specification, the simulations of million-body globular clusters including 5% primordial binaries require about an hour per half-mass crossing time.

We investigate a purely stellar dynamical solution to the Final Parsec Problem. Galactic nuclei resulting from major mergers are not spherical, but show some degree of triaxiality. With N-body simulations, we show that equal-mass massive black hole binaries (MBHBs) hosted by them will continuously interact with stars on centrophilic orbits and will thus inspiral-in much less than a Hubble time-down to separations at which gravitational-wave (GW) emission is strong enough to drive them to coalescence. Such coalescences will be important sources of GWs for future space-borne detectors such as the Laser Interferometer Space Antenna (LISA). Based on our results for equal-mass mergers, and given that the hardening rate of unequal-mass binaries is similar, we expect that LISA will see between ∼10 and ∼ few × 10 2 such events every year, depending on the particular massive black hole (MBH) seed model as obtained in recent studies of merger trees of galaxy and MBH co-evolution. Orbital eccentricities in the LISA band will be clearly distinguishable from zero with e 0.001-0.01.

Direct-summation N -body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O(N 2 ). Performance can be greatly enhanced via the use of special-purpose accelerator boards like the GRAPE-6A. However the memory of the GRAPE boards is limited. Here, we present a performance analysis of direct N -body codes on two parallel supercomputers that incorporate special-purpose boards, allowing as many as four million particles to be integrated. Both computers employ high-speed, Infiniband interconnects to minimize communication overhead, which can otherwise become significant due to the small number of "active" particles at each time step. We find that the computation time scales well with processor number; for 2×10 6 particles, efficiencies greater than 50% and speeds in excess of 2 TFlops are reached.

We study the compact binary population in star clusters, focusing on binaries containing black holes, using a self-consistent Monte Carlo treatment of dynamics and full stellar evolution. We find that the black holes experience strong mass segregation and become centrally concentrated. In the core the black holes interact strongly with each other and black hole-black hole binaries are formed very efficiently. The strong interactions, however, also destroy or eject the black hole-black hole binaries. We find no black hole-black hole mergers within our simulations but produce many hard escapers that will merge in the Galactic field within a Hubble time. We also find several highly eccentric black hole-black hole binaries that are potential Laser Interferometer Space Antenna (LISA) sources, suggesting that star clusters are interesting targets for space-based detectors. We conclude that star clusters must be taken into account when predicting compact binary population statistics.