by Li, Shuo and Liu, F. K. and Berczik, Peter and Chen, Xian and Spurzem, Rainer
38 pages, 10 figues; accepted for publication in ApJ

Supermassive black hole binaries (SMBHBs) are the products of frequent galaxy mergers. The coalescence of the SMBHBs is a distinct source of gravitational wave (GW) radiation. The detections of the strong GW radiation and their possible electromagnetic counterparts are essential. Numerical relativity suggests that the post-merger supermassive black hole (SMBH) gets a kick velocity up to 4000 km/s due to the anisotropic GW radiations. Here we investigate the dynamical co-evolution and interaction of the recoiling SMBHs and their galactic stellar environments with one million direct N-body simulations including the stellar tidal disruption by the recoiling SMBHs. Our results show that the accretion of disrupted stars does not significantly affect the SMBH dynamical evolution. We investigate the stellar tidal disruption rates as a function of the dynamical evolution of oscillating SMBHs in the galactic nuclei. Our simulations show that most of stellar tidal disruptions are contributed by the unbound stars and occur when the oscillating SMBHs pass through the galactic center. The averaged disruption rate is ~10^{-6} M_\odot yr^{-1}, which is about an order of magnitude lower than that by a stationary SMBH at similar galactic nuclei. Our results also show that a bound star cluster is around the oscillating SMBH of about ~ 0.7% the black hole mass. In addition, we discover a massive cloud of unbound stars following the oscillating SMBH. We also investigate the dependence of the results on the SMBH masses and density slopes of the galactic nuclei.

by Farr, Will M. and Ames, Jeff and Hut, Piet and Makino, Junichiro and McMillan, Steve and Muranushi, Takayuki and Nakamura, Koichi and Nitadori, Keigo and Zwart, Simon Portegies
5 pages; submitted to New Astronomy

We present a data format for the output of general N-body simulations, allowing the presence of individual time steps. By specifying a standard, different N-body integrators and different visualization and analysis programs can all share the simulation data, independent of the type of programs used to produce the data. Our Particle Stream Data Format, PSDF, is specified in YAML, based on the same approach as XML but with a simpler syntax. Together with a specification of PSDF, we provide background and motivation, as well as specific examples in a variety of computer languages. We also offer a web site from which these examples can be retrieved, in order to make it easy to augment existing codes in order to give them the option to produce PSDF output.

by Vasiliev, E. and Athanassoula, E.
13 pages, 10 figures

We use both N-body simulations and integration in fixed potentials to explore the stability and the long-term secular evolution of self-consistent, equilibrium, non-rotating, triaxial spheroidal galactic models. More specifically, we consider Dehnen models built with the Schwarzschild method. We show that short-term stability depends on the degree of velocity anisotropy (radially anisotropic models are subject to rapid development of radial-orbit instability). Long-term stability, on the other hand, depends mainly on the properties of the potential, and in particular, on whether it admits a substantial fraction of strongly chaotic orbits. We show that in the case of a weak density cusp (gamma=1 Dehnen model) the N-body model is remarkably stable, while the strong-cusp (gamma=2) model exhibits substantial evolution of shape away from triaxiality, which we attribute to the effect of chaotic diffusion of orbits. The different behaviour of these two cases originates from the different phase space structure of the potential; in the weak-cusp case there exist numerous resonant orbit families that impede chaotic diffusion. We also find that it is hardly possible to affect the rate of this evolution by altering the fraction of chaotic orbits in the Schwarzschild model, which is explained by the fact that the chaotic properties of an orbit are not preserved by the N-body evolution. There are, however, parameters in Schwarzschild modelling that do affect the stability of an N-body model, so we discuss the recipes how to build a `good’ Schwarzschild model.

by Giersz, Mirek and Heggie, Douglas C. and Hurley, Jarrod and Hypki, Arkadiusz
15 pages, 24 figures

We describe a major upgrade of a Monte Carlo code which has previously been used for many studies of dense star clusters. We outline the steps needed in order to calibrate the results of the new Monte Carlo code against N-body simulations for large $latex N$ systems, up to N=200000. The new version of the Monte Carlo code (called MOCCA), in addition to the old version, incorporates direct FewBody integrator for three- and four-body interactions, and new treatment of the escape process based on Fokushige and Heggie (2000). Now stars which fulfil the escape criterion are not removed immediately, but can stay in the system for a certain time which depends on the excess of the energy of a star above the critical energy. They are called potential escapers. FewBody integrator allows to follow all interaction channels, which are important for the rate of creation of various types of objects observed in star clusters, and assures that the energy generation by binaries is treated in a meaner similar to the N-body model.

There are at most three parameters which have to be adjusted against N-body simulations for large N. Two (or one, depends on the chosen approach) connected with the escape process and one responsible for determination of the interaction probabilities. The adopted free parameters are independent on N. They allow MOCCA code to reproduce N-body results, in a reasonably precision, not only for the rate of cluster evolution and the cluster mass distribution, but also for the detailed distributions of mass and binding energy of binaries.

The MOCCA code is at present the most advanced code for simulations of real star clusters. It can follow the cluster evolution in details comparable to N-body code, but orders of magnitude faster.

by Marx, Jay and Danzmann, Karsten and Hough, James and Kuroda, Kazuaki and McClelland, David and Mours, Benoit and Phinney, Sterl and Rowan, Sheila and Sathyaprakash, B. and Vetrano, Flavio and Vitale, Stefano and Whitcomb, Stan and Will, Clifford
116 pages. Original document in higher resolution can be found at https://gwic.ligo.org/roadmap/

Gravitational wave science is on the verge of direct observation of the waves predicted by Einstein’s General Theory of Relativity and opening the exciting new field of gravitational wave astronomy. In the coming decades, ultra-sensitive arrays of ground-based instruments and complementary spaced-based instruments will observe the gravitational wave sky, inevitably discovering entirely unexpected phenomena while providing new insight into many of the most profound astrophysical phenomena known. in July 2007 the Gravitational Wave International Committee (GWIC) initiated the development of a strategic roadmap for the field of gravitational wave science with a 30-year horizon. The goal of this roadmap is to serve the international gravitational wave community and its stakeholders as a tool for the development of capabilities and facilities needed to address the exciting scientific opportunities on the intermediate and long-term horizons.

by Banerjee, Sambaran and Kroupa, Pavel
14 pages, 4 figures. Published in The Astrophysical Journal Letters

Among the most explored directions in the study of dense stellar systems is the investigation of the effects of the retention of supernova remnants, especially that of the massive stellar remnant black holes (BHs), in star clusters. By virtue of their eventual high central concentration, these stellar mass BHs potentially invoke a wide variety of physical phenomena, the most important ones being emission of gravitational waves (GWs), formation of X-ray binaries, and modification of the dynamical evolution of the cluster. Here we propose, for the first time, that rapid removal of stars from the outer parts of a cluster by the strong tidal field in the inner region of our Galaxy can unveil its BH sub-cluster, which appears as a star cluster that is gravitationally bound by an invisible mass. We study the formation and properties of such systems through direct N-body computations and estimate that they can be present in significant numbers in the inner region of the Milky Way. We call such objects “dark star clusters” (DSCs) as they appear dimmer than normal star clusters of similar mass and they comprise a predicted, new class of entities. The finding of DSCs will robustly cross-check BH retention; they will not only constrain the uncertain natal kicks of BHs, thereby the widely debated theoretical models of BH formation, but will also pinpoint star clusters as potential sites for GW emission for forthcoming ground-based detectors such as the Advanced LIGO. Finally, we also discuss the relevance of DSCs for the nature of IRS 13E.

by Meiron, Yohai and Laor, Ari
12 pages, 9 figures

We present a new approach to studying the evolution of massive black hole binaries in a stellar environment. By imposing conservation of total energy and angular momentum in scattering experiments, we find the dissipation forces that are exerted on the black holes by the stars, and thus obtain the decaying path of the binary from the classical dynamical friction regime down to subparsec scales. Our scheme lies between scattering experiments and N-body simulations. While still resolving collisions between stars and black holes, it is fast enough and allows to use a large enough number of particles to reach a smooth and convergent result. We studied both an equal mass and a 10:1 mass ratio binaries under various initial conditions. We show that while an equal mass binary stalls at a nearly circular orbit, a runaway growth of eccentricity occurs in the unequal mass case. This effect reduces the timescale for black hole coalescence through gravitational radiation to well below the Hubble time, even in spherical and gasless systems formed by dry mergers.

by Antonini, Fabio and Capuzzo-Dolcetta, Roberto and Mastrobuono-Battisti, Alessandra and Merritt, David
15 pages, 14 figure. Submitted to ApJ

In one widely discussed model for the formation of nuclear star clusters (NSCs), massive globular clusters spiral into the center of a galaxy and merge to form the nucleus. It is now known that at least some NSCs coexist with supermassive black holes (SBHs); this is the case, for instance, in the Milky Way (MW). In this paper, we investigate how the presence of a SMBH at the center of the MW impacts the merger hypothesis for the formation of its NSC. Starting from a model consisting of a low-density nuclear stellar disk and the SMBH, we use N-body simulations to follow the successive inspiral and merger of (12) globular clusters. The clusters are started on circular orbits of radius 20 pc, and their initial masses and radii are set up in such a way as to be consistent with the galactic tidal field at that radius. The total accumulated mass is about 1.5×10^7 Solar masses. Each cluster is disrupted by the SMBH at a distance of roughly one parsec. The density profile that results after the final inspiral event is characterized by a core of roughly this radius, and an envelope with density that falls off rho \sim r^-2. These properties are similar to those of the MW NSC, with the exception of the core size, which in the MW is a little smaller. But by continuing the evolution of the model after the final inspiral event, we find that the core shrinks substantially via gravitational encounters in a time (when scaled to the MW) of 10 Gyr as the stellar distribution evolves toward a Bahcall-Wolf cusp. We also show that the luminosity function of the MW NSC is consistent with the hypothesis that a large fraction of the mass comes from (~10Gyr) old stars, brought in by globular clusters. We conclude that a model in which a large fraction of the mass of the MW NSC arose from infalling globular clusters is consistent with existing observational constraints.

by Rein, Hanno and Liu, Shang-Fei
10 pages, 9 figures, re-submitted to A&A, source code available at https://github.com/hannorein/rebound

REBOUND is a new multi-purpose N-body code which is freely available under an open-source license. It was designed for collisional dynamics such as planetary rings but can also solve the classical N-body problem. It is highly modular and can be customized easily to work on a wide variety of different problems in astrophysics and beyond.

REBOUND comes with three symplectic integrators: leap-frog, the symplectic epicycle integrator (SEI) and a Wisdom-Holman mapping (WH). It supports open, periodic and shearing-sheet boundary conditions. REBOUND can use a Barnes-Hut tree to calculate both self-gravity and collisions. These modules are fully parallelized with MPI as well as OpenMP. The former makes use of a static domain decomposition and a distributed essential tree. Two new collision detection modules based on a plane-sweep algorithm are also implemented. The performance of the plane-sweep algorithm is superior to a tree code for simulations in which one dimension is much longer than the other two and in simulations which are quasi-two dimensional with less than one million particles.

In this work, we discuss the different algorithms implemented in REBOUND, the philosophy behind the code’s structure as well as implementation specific details of the different modules. We present results of accuracy and scaling tests which show that the code can run efficiently on both desktop machines and large computing clusters.

by Noyola, Eva and Baumgardt, Holger
Accepted for publication in ApJ

Surface photometry is a necessary tool to establish the dynamical state of stars clusters. We produce realistic HST-like images from N-body models of star clusters with and without central intermediate-mass black holes (IMBHs) in order to measure their surface brightness profiles. The models contain ~600,000 individual stars, black holes of various masses between 0% to 2% of the total mass, and are evolved for a Hubble time. We measure surface brightness and star count profiles for every constructed image in order to test the effect of intermediate mass black holes on the central logarithmic slope, the core radius, and the half-light radius. We use these quantities to test diagnostic tools for the presence of central black holes using photometry. We find that the the only models that show central shallow cusps with logarithmic slopes between -0.1 and -0.4 are those containing central black holes. Thus, the central logarithmic slope seems to be a good way to choose clusters suspect of containing intermediate-mass black holes. Clusters with steep central cusps can definitely be ruled out to host an IMBH. The measured r_c/r_h ratio has similar values for clusters that have not undergone core-collapse, and those containing a central black hole. We notice that observed Galactic globular clusters have a larger span of values for central slope and r_c/r_h than our modeled clusters, and suggest possible reasons that could account for this and contribute to improve future models.

by Fiestas, Jose and Porth, Oliver and Berczik, Peter and Spurzem, Rainer
15 pages, 7 figures,accepted by MNRAS

NBody realizations of axisymmetric collisional galaxy cores (e.g. M32, M33, NGC205, Milky Way) with embedded growing black holes are presented. Stars which approach the disruption sphere are disrupted and accreted to the black hole. We measure the zone of influence of the black hole and disruption rates in relaxation time scales. We show that secular gravitational instabilities dominate the initial core dynamics, while the black hole is small and growing due to consumption of stars. Later, the black hole potential dominates the core, and loss cone theory can be applied. Our simulations show that central rotation in galaxies can not be neglected for relaxed systems, and compare and discuss our results with the standard theory of spherically symmetric systems.

by Khan, Fazeel and Just, Andreas and Merritt, David
9 pages, 11 figures. Accepted for publication in The Astrophysical Journal

In spherical galaxies, binary supermassive black holes (SMBHs) have difficulty reaching sub-parsec separations due to depletion of stars on orbits that intersect the massive binary – the final-parsec problem. Galaxies that form via major mergers are substantially nonspherical, and it has been argued that the centrophilic orbits in triaxial galaxies might provide stars to the massive binary at a high enough rate to avoid stalling. Here we test that idea by carrying out fully self-consistent merger simulations of galaxies containing central SMBHs. We find hardening rates of the massive binaries that are indeed much higher than in spherical models, and essentially independent of the number of particles used in the simulations. Binary eccentricities remain high throughout the simulations. Our results constitute a fully stellar-dynamical solution to the final-parsec problem and imply a potentially high rate of events for low-frequency gravitational wave detectors like LISA.

by Merritt, David and Alexander, Tal and Mikkola, Seppo and Will, Clifford
28 pages, 16 figures

Inspiral of compact stellar remnants into massive black holes (MBHs) is accompanied by the emission of gravitational waves at frequencies that are potentially detectable by the proposed laser interferometer space antenna. Event rates computed from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due to uncertaintities about the rate coefficients. Here we present results from direct integration of the post-Newtonian N-body equations of motion descrbing dense clusters of compact stars around Schwarzschild and Kerr MBHs. These simulations embody an essentially exact (at the post-Newtonian level) treatment of the interplay between stellar dynamical relaxation, relativistic precession, and gravitational-wave energy loss. The rate of capture of stars by the MBH is found to be greatly reduced by relativistic precession, which limits the ability of torques from the stellar potential to change orbital angular momenta. Penetration of this “Schwarzschild barrier” does occasionally occur, resulting in capture of stars onto orbits that gradually inspiral due to gravitational wave emission; we discuss two mechanisms for barrier penetration and find evidence for both in the simulations. We derive an approximate formula for the capture rate, which predicts that captures would be strongly disfavored from orbits with semi-major axes below a certain value; this prediction, as well as the predicted rate, are verified in the N-body integrations. Adding spin to the MBH does not substantially change the capture rate; the back-reaction of the stellar torques on the spin of the MBH is evaluated and shown to be potentially observable. We discuss the implications of our results for the detection of extreme-mass-ratio inspirals from galactic nuclei with a range of physical properties.

by Preto, Miguel and Berentzen, Ingo and Berczik, Peter and Spurzem, Rainer
6 pages, 4 figures, 1 table. Submitted to ApJL

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 $latex N$-body simulations, we show that massive black hole binaries (MBHB) 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 {\it Laser Interferometer Space Antenna} (LISA). Based on our results, we expect that LISA will see between $latex \sim 10$ to $latex \sim {\rm few} \times 10^2$ such events every year, depending on the particular 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 $latex e \gtrsim 0.001-0.01$.

by Amaro-Seoane, Pau and Preto, Miguel
Submitted to Class. Quantum Grav.; based on the invited plenary talk of P. Amaro-Seoane at the LISA Symposium 2010

One of the most interesting sources of gravitational waves (GWs) for LISA is the inspiral of compact objects on to a massive black hole (MBH), commonly referred to as an “extreme-mass ratio inspiral” (EMRI). The small object, typically a stellar black hole (bh), emits significant amounts of GW along each orbit in the detector bandwidth. The slowly, adiabatic inspiral of these sources will allow us to map space-time around MBHs in detail, as well as to test our current conception of gravitation in the strong regime. The event rate of this kind of source has been addressed many times in the literature and the numbers reported fluctuate by orders of magnitude. On the other hand, recent observations of the Galactic center revealed a dearth of giant stars inside the inner parsec relative to the numbers theoretically expected for a fully relaxed stellar cusp. The possibility of unrelaxed nuclei (or, equivalently, with no or only a very shallow cusp) adds substantial uncertainty to the estimates. Having this timely question in mind, we run a significant number of direct-summation $latex N-$body simulations with up to half a million particles to calibrate a much faster orbit-averaged Fokker-Planck code. We then investigate the regime of strong mass segregation (SMS) for models with two different stellar mass components. We show that, under quite generic initial conditions, the time required for the growth of a relaxed, mass segregated stellar cusp is shorter than a Hubble time for MBHs with $latex M_\bullet \lesssim 5 \times 10^6 M_\odot$ (i.e. nuclei in the range of LISA). SMS has a significant impact boosting the EMRI rates by a factor of $latex \sim 10$ for our fiducial models of Milky Way type galactic nuclei.

by Madigan, Ann-Marie and Hopman, Clovis and Levin, Yuri
22 pages, 27 figures, submitted to ApJ

The angular momentum evolution of stars close to massive black holes (MBHs) is driven by secular torques. In contrast to two-body relaxation, where interactions between stars are incoherent, the resulting resonant relaxation (RR) process is characterized by coherence times of hundreds of orbital periods. In this paper, we show that all the statistical properties of RR can be reproduced in an autoregressive moving average (ARMA) model. We use the ARMA model, calibrated with extensive N-body simulations, to analyze the long-term evolution of stellar systems around MBHs with Monte Carlo simulations. We show that for a single mass system in steady state, a depression is carved out near a MBH as a result of tidal disruptions. In our Galactic center, the size of the depression is about 0.2 pc, consistent with the size of the observed “hole” in the distribution of bright late-type stars. We also find that the velocity vectors of stars around a MBH are locally not isotropic. In a second application, we evolve the highly eccentric orbits that result from the tidal disruption of binary stars, which are considered to be plausible precursors of the “S-stars” in the Galactic center. We find that in this scenario more highly eccentric (e > 0.9) S-star orbits are produced than have been observed to date.

by Vesperini, Enrico and Trenti, Michele
14 pages, 3 figures, Accepted for publication in The Astrophysical Journal, Letters

Surface brightness profiles of globular clusters with shallow central cusps (Sigma ~ R^v with -0.3<~ v ~ -0.3 in the pre-core-collapse and core-collapse phases. Post-core-collapse clusters without an IMBH transition to steeper cusps, -0.7<~ v <~ -0.4, only if the primordial binary fraction is very small, f_{bin} -0.3 even when <~ -0.4. Overall our analysis shows that a shallow cusp is not an unequivocal signature of a central IMBH and casts serious doubts on the usefulness of measuring v in the context of the hunt for IMBHs in globular clusters.

by Madigan, Ann-Marie
Proceedings article to be published in “The Galactic Center: A Window on the Nuclear Environment of Disk Galaxies”, ed. Mark Morris, Daniel Q. Wang and Feng Yuan

In this paper we revisit the “eccentric disc instability”, an instability which occurs in coherently eccentric discs of stars orbiting massive black holes (MBHs) embedded in stellar clusters, which results in stars achieving either very high or low eccentricities. The preference for stars to attain higher or lower eccentricities depends significantly on the density distribution of the surrounding stellar cluster. Here we discuss its mechanism and the implications for the Galactic Centre, home to at least one circum-MBH stellar disc.

by Merritt, David and Alexander, Tal and Mikkola, Seppo and Will, Clifford M.
18 pages, 9 figures

The spin and quadrupole moment of the supermassive black hole at the Galactic center can in principle be measured via astrometric monitoring of stars orbiting at milliparsec (mpc) distances, allowing tests of general relativistic “no-hair” theorems (Will 2008). One complicating factor is the presence of perturbations from other stars, which may induce orbital precession of the same order of magnitude as that due to general relativistic effects. The expected number of stars in this region is small enough that full N-body simulations can be carried out. We present the results of a comprehensive set of such simulations, which include a post-Newtonian treatment of spin-orbit effects. A number of possible models for the distribution of stars and stellar remnants are considered. We find that stellar perturbations are likely to obscure the signal due to frame-dragging for stars beyond ~0.5 mpc from the black hole, while measurement of the quadrupole moment is likely to require observation of stars inside ~0.2 mpc. A high fraction of stellar remnants, e.g. 10-Solar-mass black holes, in this region would make tests of GR problematic at all radii. We discuss the possibility of separating the effects of stellar perturbations from those due to GR.

by Sari, Re’em and Kobayashi, Shiho and Rossi, Elena M.
10 pages, 10 Figures, Apj submitted

Motivated by detections of hypervelocity stars that may originate from the Galactic Center, we revist the problem of a binary disruption by a passage near a much more massive point mass. The six order of magnitude mass ratio between the Galactic Center black hole and the binary stars allows us to formulate the problem in the restricted parabolic three-body approximation. In this framework, results can be simply rescaled in terms of binary masses, its initial separation and binary-to-black hole mass ratio. Consequently, an advantage over the full three-body calculation is that a much smaller set of simulations is needed to explore the relevant parameter space. Contrary to previous claims, we show that, upon binary disruption, the lighter star does not remain preferentially bound to the black hole. In fact, it is ejected exactly in 50% of the cases. Nonetheless, lighter objects have higher ejection velocities, since the energy distribution is independent of mass. Focusing on the planar case, we provide the probability distributions for disruption of circular binaries and for the ejection energy. We show that even binaries that penetrate deeply into the tidal sphere of the black hole are not doomed to disruption, but survive in 20% of the cases. Nor do these deep encounters produce the highest ejection energies, which are instead obtained for binaries arriving to 0.1-0.5 of the tidal radius in a prograde orbit. Interestingly, such deep-reaching binaries separate widely after penetrating the tidal radius, but always approach each other again on their way out from the black hole.[shortened]

by Loeckmann, Ulf and Baumgardt, Holger and Kroupa, Pavel
MNRAS, accepted, 8 pages, 4 figures

(abridged) Here we discuss the question whether the extreme circumstances in the centre of the Milky Way may be the reason for a significant variation of the IMF. By means of stellar evolution models using different codes we show that the observed luminosity in the central parsec is too high to be explained by a long-standing top-heavy IMF, considering the limited amount of mass inferred from stellar kinematics in this region. In contrast, continuous star formation over the Galaxy’s lifetime following a canonical IMF results in a mass-to-light ratio and a total mass of stellar black holes (SBHs) consistent with the observations. Furthermore, these SBHs migrate towards the centre due to dynamical friction, turning the cusp of visible stars into a core as observed in the Galactic Centre. For the first time here we explain the luminosity and dynamical mass of the central cluster and both the presence and extent of the observed core, since the number of SBHs expected from a canonical IMF is just enough to make up for the missing luminous mass. We conclude that the Galactic Centre is consistent with the canonical IMF and do not suggest a systematic variation as a result of the region’s properties such as high density, metallicity, strong tidal field etc.

by Preto, Miguel and Amaro-Seoane, Pau
5 pages, 4 figures, 1 table, submitted to ApJL

We present, for the first time, a clear $latex N$-body realization of the {\it strong mass segregation} solution for the stellar distribution around a massive black hole. We compare our $latex N$-body results with those obtained by solving the orbit-averaged Fokker-Planck (FP) equation in energy space. The $latex N$-body segregation is slightly stronger than in the FP solution, but both confirm the {\it robustness} of the regime of strong segregation when the number fraction of heavy stars is a (realistically) small fraction of the total population. In view of recent observations revealing a dearth of giant stars in the sub-parsec region of the Milky Way, we show that the time scales associated with cusp re-growth are not longer than $latex (0.1-0.25) \times T_{rlx}(r_h)$. These time scales are shorter than a Hubble time for black holes masses $latex \mbul \lesssim 4 \times 10^6 M_\odot$ and we conclude that quasi-steady, mass segregated, stellar cusps may be common around MBHs in this mass range. Since EMRI rates scale as $latex \mbul^{-\alpha}$, with $latex \alpha \in [1\4,1]$, a good fraction of these events should originate from strongly segregated stellar cusps.

by Amaro-Seoane, Pau and Sesana, Alberto and Hoffman, Loren and Benacquista, Matthew and Eichhorn, Christoph and Makino, Junichiro and Spurzem, Rainer
Submitted to MNRAS

Supermassive black holes (SMBHs) found in the centers of many galaxies have been recognized to play a fundamental active role in the cosmological structure formation process. In hierarchical formation scenarios, SMBHs are expected to form binaries following the merger of their host galaxies. If these binaries do not coalesce before the merger with a third galaxy, the formation of a black hole triple system is possible. Numerical simulations of the dynamics of triples within galaxy cores exhibit phases of very high eccentricity (as high as $latex e \sim 0.99$). During these phases, intense bursts of gravitational radiation can be emitted at orbital periapsis. This produces a gravitational wave signal at frequencies substantially higher than the orbital frequency. The likelihood of detection of these bursts with pulsar timing and the Laser Interferometer Space Antenna ({\it LISA}) is estimated using several population models of SMBHs with masses $latex \gtrsim 10^7 {\rm M_\odot}$. Assuming a fraction of binaries $latex \ge 0.1$ in triple system, we find that few to few dozens of these bursts will produce residuals $latex >1$ ns, within the sensitivity range of forthcoming pulsar timing arrays (PTAs). However, most of such bursts will be washed out in the underlying confusion noise produced by all the other ’standard’ SMBH binaries emitting in the same frequency window. A detailed data analysis study would be required to assess resolvability of such sources. Implementing a basic resolvability criterion, we find that the chance of catching a resolvable burst at a one nanosecond precision level is 2-50%, depending on the adopted SMBH evolution model. On the other hand, the probability of detecting bursts produced by massive binaries (masses $latex \gtrsim 10^7\msun$) with {\it LISA} is negligible.

by Amaro-Seoane, Pau and Santamaria, Lucia
Submitted to ApJ; abstract abridged, figure 1 has a lower resolution

Even though the existence of intermediate-mass black holes has not yet been corroborated observationally, these objects are of high interest for astrophysics. Our understanding of formation and evolution of supermassive black holes (SMBHs), as well as galaxy evolution modeling and cosmography would dramatically change if an IMBH was observed. The prospect of detection and, possibly, observation and characterization of an IMBH has good chances in lower-frequency gravitational-wave (GW) astrophysics with ground-based detectors such as LIGO, Virgo and the future Einstein Telescope (ET). We present an analysis of the signal of a system of a binary of IMBHs based on a waveform model obtained with numerical relativity simulations coupled with post-Newtonian calculations at the highest available order so as to extend the waveform to lower frequencies. We find that initial LIGO and Virgo are in the position of detecting IMBHs with a signal-to-noise ratio (SNR) of $latex \sim 10$ for systems with total mass between 100 and $latex 500 M_{\odot}$ situated at a distance of 100 Mpc. Nevertheless, the event rate is too low and the possibility that these signals are mistaken with a glitch is, unfortunately, non-negligible. When going to second- and third-generation detectors, such as Advanced LIGO or the proposed ET, the event rate becomes much more promising (tens per year for the first and thousands per year for the latter) and the SNR at 100 Mpc is as high as 100 — 1000 and 1000 — $latex 10^{5}$ respectively. The prospects for IMBH detection and characterization with ground-based GW observatories would not only provide us with a robust test of general relativity, but would also corroborate the existence of these systems. Such detections would be a probe to the stellar environments of IMBHs and their formation.

by Fregeau, J. M. and Ivanova, N. and Rasio, F. A.
8 pages, 7 figures in emulateapj format. Submitted to ApJ

Using our recently improved Monte Carlo evolution code, we study the evolution of the binary fraction in globular clusters. In agreement with previous N-body simulations, we find generally that the hard binary fraction in the core tends to increase with time over a range of initial cluster central densities for initial binary fractions <~ 90%. The dominant processes driving the evolution of the core binary fraction are mass segregation of binaries into the cluster core and preferential destruction of binaries there. On a global scale, these effects and the preferential tidal stripping of single stars tend to roughly balance, leading to overall cluster binary fractions that are roughly constant with time. Our findings suggest that the current hard binary fraction near the half-mass radius is a good indicator of the hard primordial binary fraction. However, the relationship between the true binary fraction and the fraction of main-sequence stars in binaries (which is typically what observers measure) is non-linear and rather complicated. We also consider the importance of soft binaries, which not only modify the evolution of the binary fraction, but can drastically change the evolution of the cluster as a whole. Finally, we describe in some detail the recent addition of single and binary stellar evolution to our cluster evolution code.

by Ernst, Andreas and Just, Andreas and Spurzem, Rainer
18 pages, 20 figures; accepted by MNRAS

We present N-body simulations of dissolving star clusters close to galactic centres. For this purpose, we developed a new N-body program called nbody6gc based on Aarseth’s series of N-body codes. We describe the algorithm in detail. We report about the density wave phenomenon in the tidal arms which has been recently explained by Kuepper et al. (2008). Standing waves develop in the tidal arms. The wave knots or clumps develop at the position, where the emerging tidal arm hits the potential wall of the effective potential and is reflected. The escaping stars move through the wave knots further into the tidal arms. We show the consistency of the positions of the wave knots with the theory in Just et al. (2009). We also demonstrate a simple method to study the properties of tidal arms. By solving many eigenvalue problems along the tidal arms, we construct numerically a 1D coordinate system whose direction is always along a principal axis of the local tensor of inertia. Along this coordinate system, physical quantities can be evaluated. The half-mass or dissolution times of our models are almost independent of the particle number which indicates that two-body relaxation is not the dominant mechanism leading to the dissolution. This may be a typical situation for many young star clusters. We propose a classification scheme which sheds light on the dissolution mechanism.

by Preto, Miguel and Saha, Prasenjit
21 pages, 5 figures, submitted to Astrophysical Journal

Stars near the Galactic center reach a few percent of light speed during pericenter passage, which makes post-Newtonian effects potentially detectable. We formulate the orbit equations in Hamiltonian form such that the $latex O(v^2/c^2)$ and $latex O(v^3/c^3)$ post-Newtonian effects of the Kerr metric appear as a simple generalization of the Kepler problem. A related perturbative Hamiltonian applies to photon paths. We then derive a symplectic integrator with adaptive time-steps, for fast and accurate numerical calculation of post-Newtonian effects. Using this integrator, we explore relativistic effects. Taking the star S2 as an example, we find that general relativity would contribute tenths of mas in astrometry and tens of $latex \rm km s^{-1}$ in kinematics. (For eventual comparison with observations, redshift and time-delay contributions from the gravitational field on light paths will need to be calculated, but we do attempt these in the present paper.) The contribution from stars, gas, and dark matter in the Galactic center region is still poorly constrained observationally, but current models suggest that the resulting Newtonian perturbation on the orbits could plausibly be of the same order as the relativistic effects for stars with semi-major axes $latex \gtrsim 0.01$ pc (or 250 mas). Nevertheless, the known and distinctive {\it time dependence} of the relativistic perturbations may make it possible to disentangle and extract both effects from observations.

by Sijacki, Debora and Springel, Volker and Haehnelt, Martin G.
26 pages, 19 figures, MNRAS submitted

We employ cosmological hydrodynamical simulations to study the growth of massive black holes (BHs) at high redshifts subject to BH merger recoils from gravitational wave emission. We select the most massive dark matter halo at z=6 from the Millennium simulation, and resimulate its formation at much higher resolution including gas physics and a model for BH seeding, growth and feedback. Assuming that the initial BH seeds are relatively massive, of the order of $latex 10^5 M_{\odot}$, and that seeding occurs around z~15 in dark matter haloes of mass $latex 10^9-10^{10} M_{\odot}$, we find that it is possible to build up supermassive BHs (SMBHs) by z=6 that assemble most of their mass during extended Eddington-limited accretion periods. The properties of the simulated SMBHs are consistent with observations of z=6 quasars in terms of the estimated BH masses and bolometric luminosities, the amount of star formation occurring within the host halo, and the presence of highly enriched gas in the innermost regions of the host galaxy. After a peak in the BH accretion rate at z=6, the most massive BH has become sufficiently massive for the growth to enter into a much slower phase of feedback-regulated accretion. We explore the full range of expected recoils and radiative efficiencies, and also consider models with spinning BHs. In the most `pessimistic’ case where BH spins are initially high, we find that the growth of the SMBHs can be potentially hampered if they grow mostly in isolation and experience only a small number of mergers. Whereas BH kicks can expel a substantial fraction of low mass BHs, they do not significantly affect the build up of the SMBHs. On the contrary, a large number of BH mergers has beneficial consequences for the growth of the SMBHs by considerably reducing their spin. [Abridged]

by Amaro-Seoane, Pau and Miller, Cole and Freitag, Marc
Accepted for publication by ApJ Letts

If binary intermediate-mass black holes (IMBHs; with masses between 100 and $latex 10^4 \Msun$) form in dense stellar clusters, their inspiral will be detectable with the planned Laser Interferometer Space Antenna (LISA) out to several Gpc. Here we present a study of the dynamical evolution of such binaries using a combination of direct $latex N$-body techniques (when the binaries are well separated) and three-body relativistic scattering experiments (when the binaries are tight enough that interactions with stars occur one at a time). We find that for reasonable IMBH masses there is only a mild effect on the structure of the surrounding cluster even though the binary binding energy can exceed the binding energy of the cluster. We demonstrate that, contrary to standard assumptions, the eccentricity in the LISA band can be in {\em some} cases as large as $latex \sim 0.2 – 0.3$ and that it induces a measurable phase difference from circular binaries in the last year before merger. We also show that, even though energy input from the binary decreases the density of the core and slows down interactions, the total time to coalescence is short enough (typically less than a hundred million years) that such mergers will be unique snapshots of clustered star formation.