Peter Berczik

EFFICIENT MERGER OF BINARY SUPERMASSIVE BLACK HOLES IN NON- AXISYMMETRIC GALAXIES

Binary supermassive black holes 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 pars ec problem”). Here, we follow the long-term evolution of a massive binary in more realistic, triaxial and rota ting galaxy models. We find that the binary does not stall. The binary hardening rates that we observe are suffici ent to allow complete coalescence of binary SBHs in 10 Gyr or less, even in the absence of collisional loss-con e refilling or gas-dynamical torques, thus providing a potential solution to the final parsec problem. Subject headings:

FAST COALESCENCE OF MASSIVE BLACK HOLE BINARIES FROM MERGERS OF GALACTIC NUCLEI: IMPLICATIONS FOR LOW-FREQUENCY GRAVITATIONAL-WAVE ASTROPHYSICS

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.

Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies

We use direct-summation N-body integrations to follow the evolution of binary black holes at the centers of galaxy models with large, constant-density cores. Particle numbers as large as 0.4 × 106 are considered. The results are compared with the predictions of loss-cone theory under the assumption that the supply of stars to the binary is limited by the rate at which they can be scattered into the binarys influence sphere by gravitational encounters. The agreement between theory and simulation is quite good; in particular, we are able to quantitatively explain the observed dependence of binary hardening rate on N. We do not verify a recent claim that the hardening rate of the binary stabilizes when N exceeds a particular value or that Brownian wandering of the binary has a significant effect on its evolution. When scaled to real galaxies, our results suggest that massive black hole binaries in gas-poor nuclei would be unlikely to reach gravitational wave coalescence in a Hubble time.

Supermassive Black Hole Binary Evolution in Axisymmetric Galaxies: The Final Parsec Problem is Not a Problem

During a galaxy merger, the supermassive black hole (SMBH) in each galaxy is thought to sink to the center of the potential and form an SMBH binary; this binary can eject stars via three-body scattering, bringing the SMBHs ever closer. In a static spherical galaxy model, the binary stalls at a separation of about a parsec after ejecting all the stars in its loss cone—this is the well-known final parsec problem. Earlier work has shown that the centrophilic orbits in triaxial galaxy models are key in refilling the loss cone at a high enough rate to prevent the black holes from stalling. However, the evolution of binary SMBHs has never been explored in axisymmetric galaxies, so it is not clear if the final parsec problem persists in these systems. Here we use a suite of direct N-body simulations to follow SMBH binary evolution in galaxy models with a range of ellipticity. For the first time, we show that mere axisymmetry can solve the final parsec problem; we find the SMBH evolution is independent of N for an axis ratio of c/a = 0.8, and that the SMBH binary separation reaches the gravitational radiation regime for c/a = 0.75.

BINARY BLACK HOLE MERGER IN GALACTIC NUCLEI: POST-NEWTONIAN SIMULATIONS

This paper studies the formation and evolution of binary supermassive black holes (SMBHs) in rotating galactic nuclei, focusing on the role of stellar dynamics. We present the first N-body simulations that follow the evolution of the SMBHs from kiloparsec separations all the way to their final relativistic coalescence, and that can robustly be scaled to real galaxies. The N-body code includes post-Newtonian corrections to the binary equations of motion up to order 2.5; we show that the evolution of the massive binary is only correctly reproduced if the conservative and terms are included. The orbital eccentricities of the massive binaries in our simulations are often found to remain large until shortly before coalescence. This directly affects not only their orbital evolution rates, but has important consequences as well for the gravitational waveforms emitted during the relativistic inspiral. We estimate gravitational wave amplitudes when the frequencies fall inside the band of the (planned) Laser Interferometer Space Antennae (LISA). We find significant contributions?well above the LISA sensitivity curve?from the higher-order harmonics.

The dragon simulations: globular cluster evolution with a million stars

Introducing the dragon simulation project, we present direct N-body simulations of four massive globular clusters (GCs) with 106 stars and 5 per cent 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 (BHs), 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, colour–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 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 core – commonly observed in the (luminous) surface brightness profiles – shows no collapse features and is continuously expanding. We demonstrate how a King 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. (Less)

Quantitative analysis of clumps in the tidal tails of star clusters

Tidal tails of star clusters are not homogeneous but show well-defined clumps in observations as well as in numerical simulations. Recently, an epicyclic theory for the formation of these clumps was presented. A quantitative analysis was still missing. We present a quantitative derivation of the angular momentum and energy distribution of escaping stars from a star cluster in the tidal field of the Milky Way and derive the connection to the position and width of the clumps. For the numerical realization we use star-by-star N-body simulations. We find a very good agreement of theory and models. We show that the radial offset of the tidal arms scales with the tidal radius, which is a function of cluster mass and the rotation curve at the cluster orbit. The mean radial offset is 2.77 times the tidal radius in the outer disc. Near the Galactic Centre the circumstances are more complicated, but to lowest order the theory still applies. We have also measured the Jacobi energy distribution of bound stars and showed that there is a large fraction of stars (about 35 per cent) above the critical Jacobi energy at all times, which can potentially leave the cluster. This is a hint that the mass loss is dominated by a self-regulating process of increasing Jacobi energy due to the weakening of the potential well of the star cluster, which is induced by the mass loss itself.

Orbital evolution of the Carina dwarf galaxy and self-consistent determination of star formation history

We present a new study of the evolution of the Carina dwarf galaxy that includes a simultaneous derivation of its orbit and star formation history. The structure of the galaxy is constrained through orbital parameters derived from the observed distance, proper motions, radial velocity, and star formation history. The different orbits admitted by the large proper motion errors are investigated in relation to the tidal force exerted by an external potential representing the Milky Way. Our analysis is performed with the aid of fully consistent N-body simulations that are able to follow the dynamics and the stellar evolution of the dwarf system in order to determine the star formation history of Carina self-consistently. We also find a star formation history characterized by several bursts, partially matching the observational expectation. We find also compatible results between dynamical projected quantities and the observational constraints. The possibility of a past interaction between Carina and the Magellanic Clouds is also separately considered and deemed unlikely.

Dynamical friction of massive objects in galactic centres

Dynamical friction leads to an orbital decay of massive objects like young compact star clusters or massive black holes in central regions of galaxies. The dynamical friction force can be well approximated by Chandrasekhars standard formula, but recent investigations show that corrections to the Coulomb logarithm are necessary. With a large set of N-body simulations we show that the improved formula for the Coulomb logarithm fits the orbital decay very well for circular and eccentric orbits. The local scalelength of the background density distribution serves as the maximum impact parameter for a wide range of power-law indices of -1 ... -5. For each type of code the numerical resolution must be compared to the effective minimum impact parameter in order to determine the Coulomb logarithm. We also quantify the correction factors by using self-consistent velocity distribution functions instead of the standard Maxwellian often used. These factors enter directly the decay time-scale and cover a range of 0.5 ... 3 for typical orbits. The new Coulomb logarithm combined with self-consistent velocity distribution functions in the Chandrasekhar formula provides a significant improvement of orbital decay times with correction up to one order of magnitude compared to the standard case. We suggest the general use of the improved formula in parameter studies as well as in special applications.

FORMATION AND HARDENING OF SUPERMASSIVE BLACK HOLE BINARIES IN MINOR MERGERS OF DISK GALAXIES

We model for the first time the complete orbital evolution of a pair of supermassive black holes (SMBHs) in a 1:10 galaxy merger of two disk-dominated gas-rich galaxies, from the stage prior to the formation of the binary up to the onset of gravitational wave (GW) emission when the binary separation has shrunk to 1 mpc. The high-resolution smoothed particle hydrodynamics (SPH) simulations used for the first phase of the evolution include star formation, accretion onto the SMBHs as well as feedback from supernovae explosions, and radiative heating from the SMBHs themselves. Using the direct N-body code -GPU, we evolve the system further without including the effect of gas, which in the mean time has been mostly consumed by star formation. We start at the time when the separation between two SMBHs is ~700 pc and the two black holes are still embedded in their galaxy cusps. We use three million particles to study the formation and evolution of the SMBH binary until it becomes hard. After a hard binary is formed, we reduce (reselect) the particles to 1.15 million and follow the subsequent shrinking of the SMBH binary due to three-body encounters with the stars. We find approximately constant hardening rates and that the SMBH binary rapidly develops a high eccentricity. Similar hardening rates and eccentricity values were reported in earlier studies of SMBH binary evolution in the merging of dissipationless spherical galaxy models. The estimated coalescence time is ~5.5 Gyr, significantly smaller than a Hubble time. We discuss why this timescale should be regarded as an upper limit. Since 1:10 mergers are among the most common interaction events for galaxies at all cosmic epochs, we argue that several SMBH binaries should be detected with currently planned space-borne GW interferometers, whose sensitivity will be especially high for SMBHs in the mass range considered here.