by Anders, P. and Baumgardt, H. and Gaburov, E. and Zwart, S. Portegies
14 pages incl. 3 pages with figures and 4 pages of tables (analysis results), MNRAS in press

Most recent progress in understanding the dynamical evolution of star clusters relies on direct N-body simulations. Owing to the computational demands, and the desire to model more complex and more massive star clusters, hardware calculational accelerators, such as GRAPE special-purpose hardware or, more recently, GPUs (i.e. graphics cards), are generally utilised. In addition, simulations can be accelerated by adjusting parameters determining the calculation accuracy (i.e. changing the internal simulation time step used for each star).

We extend our previous thorough comparison (Anders et al. 2009) of basic quantities as derived from simulations performed either with STARLAB/KIRA or NBODY6. Here we focus on differences arising from using different hardware accelerations (including the increasingly popular graphic card accelerations/GPUs) and different calculation accuracy settings.

We use the large number of star cluster models (for a fixed stellar mass function, without stellar/binary evolution, primordial binaries, external tidal fields etc) already used in the previous paper, evolve them with STARLAB/KIRA (and NBODY6, where required), analyse them in a consistent way and compare the averaged results quantitatively. For this quantitative comparison, we apply the bootstrap algorithm for functional dependencies developed in our previous study.

In general we find very high comparability of the simulation results, independent of the used computer hardware (including the hardware accelerators) and the used N-body code. For the tested accuracy settings we find that for reduced accuracy (i.e. time step at least a factor 2.5 larger than the standard setting) most simulation results deviate significantly from the results using standard settings. The remaining deviations are comprehensible and explicable.

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 Zocchi, A. and Bertin, G. and Varri, A. L.
18 pages, 7 figures. Accepted for publication in Astronomy & Astrophysics

We perform a systematic combined photometric and kinematic analysis of a sample of globular clusters under different relaxation conditions, based on their core relaxation time (as listed in available catalogs), by means of two well-known families of spherical stellar dynamical models. Systems characterized by shorter relaxation time scales are expected to be better described by isotropic King models, while less relaxed systems might be interpreted by means of non-truncated, radially-biased anisotropic f^(\nu) models, originally designed to represent stellar systems produced by a violent relaxation formation process and applied here for the first time to the study of globular clusters. The comparison between dynamical models and observations is performed by fitting simultaneously surface brightness and velocity dispersion profiles. For each globular cluster, the best-fit model in each family is identified, along with a full error analysis on the relevant parameters. Detailed structural properties and mass-to-light ratios are also explicitly derived. We find that King models usually offer a good representation of the observed photometric profiles, but often lead to less satisfactory fits to the kinematic profiles, independently of the relaxation condition of the systems. For some less relaxed clusters, f^(\nu) models provide a good description of both observed profiles. Some derived structural characteristics, such as the total mass or the half-mass radius, turn out to be significantly model-dependent. The analysis confirms that, to answer some important dynamical questions that bear on the formation and evolution of globular clusters, it would be highly desirable to acquire larger numbers of accurate kinematic data-points, well distributed over the cluster field.

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 Nakasato, Naohito
Journal of Computational Science, 2011; See our recent update at http://galaxy.u-aizu.ac.jp/trac/note/wiki/Octree_On_GPU

The kd-tree is a fundamental tool in computer science. Among other applications, the application of kd-tree search (by the tree method) to the fast evaluation of particle interactions and neighbor search is highly important, since the computational complexity of these problems is reduced from O(N^2) for a brute force method to O(N log N) for the tree method, where N is the number of particles. In this paper, we present a parallel implementation of the tree method running on a graphics processing unit (GPU). We present a detailed description of how we have implemented the tree method on a Cypress GPU. An optimization that we found important is localized particle ordering to effectively utilize cache memory. We present a number of test results and performance measurements. Our results show that the execution of the tree traversal in a force calculation on a GPU is practical and efficient.

by Lauer, Tod R. and Bender, Ralf and Kormendy, John and Rosenfield, Philip and Green, Richard F.
29 pages, 11 figures (3 color); Astrophysical Journal accepted

We obtained U_330 and B band images of the M31 nucleus using the High Resolution Camera of the Advanced Camera for Surveys on board the Hubble Space Telescope (HST). The spatial resolution in the U_330-band, 0.03″ FWHM, or 0.1 pc at M31, is sufficient to resolve the outskirts of the compact cluster (P3) of UV-bright stars surrounding the M31 black hole. The center of the cluster is marked by an extended source that is both brighter and redder than the other point sources within P3; it is likely to be a blend of several bright stars. We hypothesize that it marks the location of the M31 black hole. Both stellar photometry and a surface brightness fluctuation analysis, show that the P3 stellar population is consistent with early-type main sequence stars formed in a ~100 – ~200 Myr old starburst population. Evolutionary tracks of post early asymptotic giant-branch stars, associated with late-stage evolution of an old population, also traverse the U and U-B domain occupied by the P3 stars; but we argue that only a few stars could be accounted for that way. PEAGB evolution is very rapid, and there is no progenitor population of red giants associated with P3. The result that P3 comprises young stars is consistent with inferences from earlier HST observations of the integrated light of the cluster. Like the Milky Way, M31 harbors a black hole closely surrounded by apparently young stars.

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 Jalali, B. and Baumgardt, H. and Kissler-Patig, M. and Gebhardt, K. and Noyola, E. and Lützgendorf, N. and de Zeeuw, P. T.
Accepted for publication in A&A

Supermassive black holes (SMBHs) are fundamental keys to understand the formation and evolution of their host galaxies. However, the formation and growth of SMBHs are not yet well understood. One of the proposed formation scenarios is the growth of SMBHs from seed intermediate-mass black holes (IMBHs, 10^2 to 10^5 M_{\odot}) formed in star clusters. In this context, and also with respect to the low mass end of the M-sigma relation for galaxies, globular clusters are in a mass range that make them ideal systems to look for IMBHs. Among Galactic star clusters, the massive cluster $latex \omega$ Centauri is a special target due to its central high velocity dispersion and also its multiple stellar populations. We study the central structure and dynamics of the star cluster $latex \omega$ Centauri to examine whether an IMBH is necessary to explain the observed velocity dispersion and surface brightness profiles. We perform direct N-body simulations to follow the dynamical evolution of $latex \omega$ Centauri. The simulations are compared to the most recent data-sets in order to explain the present-day conditions of the cluster and to constrain the initial conditions leading to the observed profiles. We find that starting from isotropic spherical multi-mass King models and within our canonical assumptions, a model with a central IMBH mass of 2% of the cluster stellar mass, i.e. a 5×10^4 M_{\odot} IMBH, provides a satisfactory fit to both the observed shallow cusp in surface brightness and the continuous rise towards the center of the radial velocity dispersion profile. In our isotropic spherical models, the predicted proper motion dispersion for the best-fit model is the same as the radial velocity dispersion one. (abridged)

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 Touma, Jihad R. and Sridhar, S.
41 pages, 5 figures, Submitted to MNRAS

We formulate the collisionless Boltzmann equation (CBE) for dense star clusters that lie within the radius of influence of a massive black hole in galactic nuclei. Our approach to these nearly Keplerian systems follows that of Sridhar and Touma (1999): Delaunay canonical variables are used to describe stellar orbits and we average over the fast Keplerian orbital phases. The stellar distribution function (DF) evolves on the longer time scale of precessional motions, whose dynamics is governed by a Hamiltonian, given by the orbit-averaged self-gravitational potential of the cluster. We specialize to razor-thin, planar discs and consider two counter-rotating (”$latex \pm$”) populations of stars. To describe discs of small eccentricities, we expand the $latex \pm$ Hamiltonian to fourth order in the eccentricities, with coefficients that depend self-consistently on the $latex \pm$ DFs. We construct approximate $latex \pm$ dynamical invariants and use Jeans’ theorem to construct time-dependent $latex \pm$ DFs, which are completely described by their centroid coordinates and shape matrices. When the centroid eccentricities are larger than the dispersion in eccentricities, the $latex \pm$ centroids obey a set of 4 autonomous ordinary differential equations. We show that these can be cast as a two-degree of freedom Hamiltonian system which is nonlinear, yet integrable. We study the linear instability of initially circular discs and derive a criterion for the counter-rotating instability. We then explore the rich nonlinear dynamics of counter-rotating discs, with focus on the variety of steadily precessing eccentric configurations that are allowed. The stability and properties of these configurations are studied as functions of parameters such as the disc mass ratios and angular momentum.

by Benacquista, Matthew J. and Downing, Jonathan M. B.
88 pages, 13 figures. Submitted update of Living Reviews article

Galactic globular clusters are old, dense star systems typically containing 10\super{4}–10\super{7} stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution that leads to relativistic binaries, and current and possible future observational evidence for this population. Our discussion of globular cluster evolution will focus on the processes that boost the production of hard binary systems and the subsequent interaction of these binaries that can alter the properties of both bodies and can lead to exotic objects. Direct {\it N}-body integrations and Fokker–Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.

by Dotti, M. and Sesana, A. and Decarli, R.
4 Figures. Accepted for publication in Advances in Astronomy

The study of the dynamical evolution of massive black hole pairs in mergers is crucial in the context of a hierarchical galaxy formation scenario. The timescales for the formation and the coalescence of black hole binaries are still poorly constrained, resulting in large uncertainties in the expected rate of massive black hole binaries detectable in the electromagnetic and gravitational wave spectra. Here we review the current theoretical understanding of the black hole pairing in galaxy mergers, with a particular attention to recent developments and open issues. We conclude with a review of the expected observational signatures of massive binaries, and of the candidates discussed in literature to date.

by Zubovas, Kastytis and Nayakshin, Sergei and Markoff, Sera
11 pages. MNRAS submitted

It is theoretically expected that a supermassive black hole (SMBH) in the centre of a typical nearby galaxy disrupts a Solar-type star every ~ 10^5 years, resulting in a bright flare lasting for months. Sgr A*, the resident SMBH of the Milky Way, produces (by comparison) tiny flares that last only hours but occur daily. Here we explore the possibility that these flares could be produced by disruption of smaller bodies – asteroids. We show that asteroids passing within an AU of Sgr A* could be split into smaller fragments which then vaporise by bodily friction with the tenuous quiescent gas accretion flow onto Sgr A*. The ensuing shocks and plasma instabilities may create a transient population of very hot electrons invoked in several currently popular models for Sgr A* flares, thus producing the required spectra. We estimate that asteroids larger than ~ 10 km in size are needed to power the observed flares, with the maximum possible luminosity of the order 10^39 erg s^-1. Assuming that the asteroid population per parent star in the central parsec of the Milky Way is not too dissimilar from that around stars in the Solar neighbourhood, we estimate the asteroid disruption rates, and the distribution of the expected luminosities, finding a reasonable agreement with the observations. We also note that planets may be tidally disrupted by Sgr A* as well, also very infrequently. We speculate that one such disruption may explain the putative increase in Sgr A* luminosity ~ 300 yr ago.

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 Alexander, R. D. and Smedley, S. L. and Nayakshin, S. and King, A. R.
7 pages, 3 figures. Accepted for publication in MNRAS

We study the dynamical evolution of stars and gas close to the centre of the Milky Way. Any plausible means of forming the young stars observed at the Galactic Centre leaves behind a residual gas disc at ~0.01pc radii. We show that the combined effects of viscous accretion and gravitational interactions with stars do not remove the residual gas efficiently, and that a substantial gas disc, interior to the stellar disc, persists for >10Myr after the stars form. Since no such disc is currently seen at the Galactic Centre we argue that it has been accreted by the super-massive black hole. This scenario offers an attractive connection between nuclear star formation and black hole feeding, and we suggest that the “missing” gas may have been used to power Sgr A*.

by Yusef-Zadeh, F. and Bushouse, H. and Wardle, M.
16 pages, 7 figures, ApJ, in press

We present HST/NICMOS data to study the surface brightness distribution of stellar light within the inner 10″ of Sgr A* at 1.4, 1.7 and 1.9 microns. We use these data to independently examine the surface brightness distribution that had been measured previously with NICMOS and to determine whether there is a drop in the surface density of stars very near Sgr A*. Our analysis confirms that a previously reported drop in the surface brightness within 0.8″ of Sgr A* is an artifact of bright and massive stars near that radius. We also show that the surface brightness profile within 5″ or ~0.2 pc of Sgr A* can be fitted with broken power laws. The power laws are consistent with previous measurements, in that the profile becomes shallower at small radii. For radii > 0.7″ the slope is beta=-0.34\pm0.04 where Sigma is proportional to r^beta and becomes flatter at smaller radii with beta=-0.13\pm0.04. Modeling of the surface brightness profile gives a stellar density that increases roughly as r^-1 within the inner 1″ of Sgr A*. This slope confirms earlier measurements in that it is not consistent with that expected from an old, dynamically-relaxed stellar cluster with a central supermassive black hole. Assuming that the diffuse emission is not contaminated by a faint population of young stars down to the 17.1 magnitude limit of our imaging data at 1.70$latex \mu$, the shallow cusp profile is not consistent with a decline in stellar density in the inner arcsecond. In addition, converting our measured diffuse light profile to a stellar mass profile, with the assumption that the light is dominated by K0 dwarfs, the enclosed stellar mass within radius r < 0.1 pc of Sgr A* is ~ 3.2×10^4 M_solar (r/0.1 {pc})^2.1.

by Gualandris, Alessia and Dotti, Massimo and Sesana, Alberto
5 pages, 5 figures, submitted to MNRAS

We study the evolution of the orientation of the orbital plane of massive black hole binaries (BHBs) in rotating stellar systems in which the total angular momentum of the stellar cusp is misaligned with respect to that of the binary. We compare results from direct summation N-body simulations with predictions from a simple theoretical model. We find that the same encounters between cusp stars and the BHB that are responsible for the hardening and eccentricity evolution of the binary, lead to a reorientation of the binary orbital plane. In particular, binaries whose angular momentum is initially misaligned with respect to that of the stellar cusp tend to realign their orbital planes with the angular momentum of the cusp on a timescale of a few hardening times. This is due to angular momentum exchange between stars and the BHB during close encounters, and may have important implications for the relative orientation of host galaxies and radio jets.

by Amaro-Seoane, Pau and Brem, Patrick and Cuadra, Jorge and Armitage, Philip J.
Submitted

Measurements of gravitational waves from the inspiral of a stellar-mass compact object into a massive black hole (MBH) are unique probes to test General Relativity (GR) and MBH properties, as well as the stellar distribution about these holes in galactic nuclei. Current data analysis techniques can provide us with parameter estimation with very narrow errors. However, an EMRI is not a two-body problem, since other stellar bodies orbiting nearby will influence the capture orbit. Any deviation from the isolated inspiral of the binary will induce a small, though observable deviation from the idealised waveform which could be misinterpreted as a failure of GR. Based on conservative analysis of mass segregation in a Milky Way like nucleus, we estimate that the possibility that a star has a semi-major axis comparable to that of the EMRI is non-negligible. This star introduces an observable perturbation in the orbit in the case in which we consider only loss of energy via gravitational radiation at periapsis. When considering the two first-order non-dissipative post-Newtonian contributions (the periapsis shift of the orbit) the evolution of the orbital elements of the EMRI turns out to be chaotic in nature. The implications of this study are twofold. From the one side, the application to testing GR and measuring MBHs parameters with the detection of EMRIs in galactic nuclei with a millihertz mission will be even more challenging than believed. From the other side, this behaviour could in principle be used as a signature of mass segregation in galactic nuclei.

by Konstantinidis, Symeon and Amaro-Seoane, Pau and Kokkotas, Kostas D.
Submitted

Contrary to supermassive and stellar-mass black holes (SBHs), the existence of intermediate-mass black holes (IMBHs) with masses ranging between 100 and 10,000 Msun has not yet been confirmed. The main problem in the detection is that the innermost stellar kinematics of globular clusters (GCs), the natural loci to IMBHs, are very difficult to resolve. However, if IMBHs reside in the center of GCs, a possibility is that they interact dynamically with their enviroment. A binary formed with the IMBH and a compact object of the GC would naturally lead to a prominent source of gravitational radiation, detectable with future observatories. We run for the first time direct-summation integrations of GCs with an IMBH including the dynamical evolution of the IMBH with the stellar system and relativistic effects, such as energy loss in gravitational waves (GWs) and periapsis shift, and gravitational recoil. We find in one of our models an intermediate-mass ratio inspiral (IMRI), which leads to a merger with a recoiling velocity higher than the escape velocity of the GC. The GWs emitted fall in the range of frequencies that a LISA-like observatory could detect, like the European eLISA or in mission options considered in the recent preliminary mission study conducted in China. The merger has an impact on the global dynamics of the cluster, as an important heating source is removed when the merged system leaves the GC. The detection of one IMRI would constitute a test of GR, as well as an irrefutable proof of the existence of IMBHs.

by Galaviz, Pablo
15 pages, 15 figures and 4 tables

We study the stability and chaos of three compact objects using post-Newtonian (PN) equations of motion derived from the Arnowitt-Deser-Misner-Hamiltonian formulation, where we include terms up to 2.5 PN order in the orbital part and the leading order in spin corrections. We perform numerical simulations of a hierarchical configuration of three compact bodies in which a binary system is perturbed by a third, lighter body initially far away from the binary. The relative importance of the different PN orders is examined. The basin boundary method and the computation of Lyapunov exponent are employed to analyze the stability and chaotic properties of the system. The 1 PN terms produce a small but noticeable change in the stability regions of the parameters considered. On the other hand, the inclusion of spin or gravitational radiation does not produce a significant change with respect to the inclusion of the 1 PN terms.

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 Antonini, Fabio and Merritt, David
28 pages, 23 figures

The density of stars in galactic bulges is often observed to be flat or slowly rising inside the influence radius of the supermassive black hole (SMBH). Chandrasekhar’s dynamical friction formula predicts little or no frictional force on a test body in such a core, regardless of its density, due to the absence of stars moving more slowly than the local circular velocity. We have tested this prediction using large-scale $latex N$-body experiments. The rate of orbital decay never drops precisely to zero, because stars moving faster than the test body also contribute to the frictional force. When the contribution from the fast-moving stars is included in the expression for the dynamical friction force, and the changes induced by the massive body on the stellar distribution are taken into account, Chandrasekhar’s theory is found to reproduce the rate of orbital decay remarkably well. However, this rate is still substantially smaller than the rate predicted by Chandrasekhar’s formula in its most widely-used forms, implying longer time scales for inspiral. Motivated by recent observations that suggest a parsec-scale core around the Galactic center SMBH, we investigate the evolution of a population of stellar-mass black holes (BHs) as they spiral in to the center of the Galaxy. After $latex \sim 10$ Gyr, we find that the density of BHs can remain substantially less than the density in stars at all radii; we conclude that it would be unjustified to assume that the spatial distribution of BHs at the Galactic center is well described by steady-state models. One consequence is that rates of capture of BHs by the SMBH at the Galactic center (EMRIs) may be much lower than in standard models. When capture occurs, inspiraling BHs often reach the gravitational-radiation-dominated regime while on orbits that are still highly eccentric.

by Brockamp, M. and Baumgardt, H. and Kroupa, P.
19 pages, 11 figures, accepted for publication in MNRAS

The disruption rate of stars by supermassive black holes (SMBHs) is calculated numerically with a modified version of Aarseth’s NBODY6 code. The initial stellar distribution around the SMBH follows a S\’{e}rsic n=4 profile representing bulges and early type galaxies. In order to infer relaxation driven effects and to increase the statistical significance, a very large set of N-body integrations with different particle numbers N, ranging from 10^{3} to 0.5 \cdot 10^{6} particles, is performed. Three different black hole capture radii are taken into account, enabling us to scale these results to a broad range of astrophysical systems with relaxation times shorter than one Hubble time, i.e. for SMBHs up to M_bh \approx 10^{7} M_sun. The computed number of disrupted stars are driven by diffusion in angular momentum space into the loss cone of the black hole and the rate scales with the total number of particles as dN/dt \propto N^{b}, where b is as large as 0.83. This is significantly steeper than the expected scaling dN/dt \propto ln(N) derived from simplest energy relaxation arguments. Only a relatively modest dependence of the tidal disruption rate on the mass of the SMBH is found and we discuss our results in the context of the M_bh/sigma relation. The number of disrupted stars contribute a significant part to the mass growth of black holes in the lower mass range as long as a significant part of the stellar mass becomes swallowed by the SMBH. This also bears direct consequences for the search and existence of IMBHs in globular clusters. For SMBHs similar to the galactic center black hole SgrA*, a tidal disruption rate of 55 \pm 27 events per Myr is deduced. Finally relaxation driven stellar feeding can not account for the masses of massive black holes M_bh \geq 10^{7} M_sun. (abridged)

by Gualandris, Alessia and Merritt, David
22 pages, 23 figures, submitted to ApJ

We simulate mergers between galaxies containing collisionally-relaxed nuclei around massive black holes (BHs). Our galaxies contain four mass groups, representative of old stellar populations; a primary goal is to understand the distribution of stellar-mass BHs after the merger. Mergers are followed using direct-summation N-body simulations, assuming a mass ratio of 1:3 and two different orbits. Evolution of the massive BH binary is followed until its separation has shrunk by a factor of 20 below the hard-binary separation. During the galaxy merger, large cores are carved out in the stellar distribution, with radii several times the influence radius of the massive BH. Much of the pre-existing mass segregation is erased during this phase. We follow the evolution of the merged galaxies for approximately three, central relaxation times after coalescence of the massive binary; both standard, and top-heavy, mass functions are considered. The cores that were formed in the stellar distribution persist, and the distribution of the stellar-mass black holes evolves against this essentially fixed background. Even after three central relaxation times, these models look very different from the relaxed, multi-mass models that are often assumed to describe the distribution of stars and stellar remnants near a massive BH; in particular, the density of stellar BHs is much smaller than in those models. We discuss the implications of our results for the EMRI problem and for the existence of Bahcall-Wolf cusps.

by Iorio, Lorenzo
LaTex2e, 21 pages, 4 tables, no figures

Empirically determining the averaged variations of the orbital parameters of the stars orbiting the Supermassive Black Hole (SBH) hosted by the Galactic Centre (GC) in Sgr A* is, in principle, a valuable tool to put on the test the General Theory of Relativity (GTR), in regimes far stronger than those tested so far, and certain key predictions of it like the no-hair theorems. We analytically work out the long-term variations of all the six osculating Keplerian orbital elements of a test particle orbiting a non-spherical, rotating body with quadrupole moment Q_2 and angular momentum S for a generic spatial orientation of its spin axis k. This choice is motivated by the fact that, basically, we do not know the position in the sky of the spin axis of the SBH in Sgr A* with sufficient accuracy. We apply our results to S2, which is the closest star discovered so far having an orbital period P_b = 15.98 yr, and to a hypothetical closer star X with P_b = 0.5 yr. Our calculations are quite general, not being related to any specific parameterization of k, and can be applied also to astrophysical binary systems, stellar planetary systems, and planetary satellite geodesy in which different reference frames, generally not aligned with the primary’s rotational axis, are routinely used.

by Sadeghian, Laleh and Will, Clifford M.
17 pages, 2 figures, submitted to Classical and Quantum Gravity

Observations of the precessing orbits of stars very near the massive black hole in the galactic center could provide measurements of the spin and quadrupole moment of the hole and thereby test the no-hair theorem of general relativity. Since the galactic center is likely to be populated by a distribution of stars and small black holes, their gravitational interactions will perturb the orbit of any given star. We estimate the effects of such perturbations using analytic orbital perturbation theory, and show that for a range of possible stellar distributions, and for an observed star sufficiently close to the black hole, the relativistic spin and quadrupole effects will be larger than the effects of stellar cluster perturbations. Our results are consistent those from recent numerical N-body simulations by Merritt et al.

by Bédorf, Jeroen and Gaburov, Evghenii and Zwart, Simon Portegies
Submitted to Journal of Computational Physics. 34 pages, 13 figures, single column

We present parallel algorithms for constructing and traversing sparse octrees on graphics processing units (GPUs). The algorithms are based on parallel-scan and sort methods. To test the performance and feasibility, we implemented them in CUDA in the form of a gravitational tree-code which completely runs on the GPU.(The code is publicly available at: http://castle.strw.leidenuniv.nl/software.html) The tree construction and traverse algorithms are portable to many-core devices which have support for CUDA or OpenCL programming languages. The gravitational tree-code outperforms tuned CPU code during the tree-construction and shows a performance improvement of more than a factor 20 overall, resulting in a processing rate of more than 2.8 million particles per second.

by Goswami, Sanghamitra and Umbreit, Stefan and Bierbaum, Matt and Rasio, Frederic A.

A promising mechanism to form intermediate-mass black holes (IMBHs) is the runaway merger in dense star clusters, where main-sequence stars collide and form a very massive star (VMS), which then collapses to a black hole. In this paper we study the effects of primordial mass segregation and the importance of the stellar initial mass function (IMF) on the runaway growth of VMSs using a dynamical Monte Carlo code for N-body systems with N as high as 10^6 stars. Our code now includes an explicit treatment of all stellar collisions. We place special emphasis on the possibility of top-heavy IMFs, as observed in some very young massive clusters. We find that both primordial mass segregation and the shape of the IMF affect the rate of core collapse of star clusters and thus the time of the runaway. When we include primordial mass segregation we generally see a decrease in core collapse time (tcc). Moreover, primordial mass segregation increases the average mass in the core, thus reducing the central relaxation time, which also decreases tcc. The final mass of the VMS formed is always close to \sim 10^-3 of the total cluster mass, in agreement with the previous studies and is reminiscent of the observed correlation between the central black hole mass and the bulge mass of the galaxies. As the degree of primordial mass segregation is increased, the mass of the VMS increases at most by a factor of 3. Flatter IMFs generally increase the average mass in the whole cluster, which increases tcc. For the range of IMFs investigated in this paper, this increase in tcc is to some degree balanced by stellar collisions, which accelerate core collapse. Thus there is no significant change in tcc for the somewhat flatter global IMFs observed in very young massive clusters.

by Valsecchi, Francesca and Farr, Will M. and Willems, Bart and Deloye, Christopher . J. and Kalogera, Vassiliki
21 pages, 7 figures, submitted to APJ

Galactic interacting double white dwarfs (DWD) are guaranteed gravitational wave (GW) sources for the GW detector LISA, with more than 10^4 binaries expected to be detected over the mission’s lifetime. While the majority of DWDs are expected to be circular, dynamical interactions in globular clusters can lead to a sub-population of eccentric DWDs detectable by LISA. Here we investigate the potential for constraining the white dwarf (WD) properties through apsidal precession in these binaries. We analyze the tidal, rotational, and general relativistic contributions to apsidal precession by using detailed He WD models, where the evolution of the star’s interior is followed throughout the cooling phase. In agreement with previous studies of zero-temperature WDs, we find that apsidal precession in eccentric DWDs can lead to a detectable shift in the emitted GW signal when binaries with cool (old) components are considered. This shift increases significantly for hot (young) WDs. We find that apsidal motion in hot (cool) DWDs is dominated by tides at orbital frequencies above ~10^(-4) Hz [10^(-3) Hz]. The analysis of apsidal precession in these sources while ignoring the tidal component would lead to an extreme bias in the mass determination, and could lead us to misidentify WDs as neutron stars or black holes. We use the detailed WD models to show that for older, cold WDs, there is a unique relationship that ties the radius and apsidal precession constant to the WD masses, therefore allowing tides to be used as a tool to constrain the source masses.

by Haas, Jaroslav and Subr, Ladislav and Vokrouhlicky, David
Accepted for publication in MNRAS; 11 pages, 6 figures

We investigate the orbital evolution of a system of N mutually interacting stars on initially circular orbits around the dominating central mass. We include perturbative influence of a distant axisymmetric source and an extended spherical potential. In particular, we focus on the case when the secular evolution of orbital eccentricities is suppressed by the spherical perturbation. By means of standard perturbation methods, we derive semi-analytic formulae for the evolution of normal vectors of the individual orbits. We find its two qualitatively different modes. Either the orbits interact strongly and, under such circumstances, they become dynamically coupled, precessing synchronously in the potential of the axisymmetric perturbation. Or, if their mutual interaction is weaker, the orbits precess independently, interchanging periodically their angular momentum, which leads to oscillations of inclinations. We argue that these processes may have been fundamental for the evolution of the disc of young stars orbiting the supermassive black hole in the centre of the Milky Way.

by Merritt, David
Talk presented at the “Chandrasekhar Centenary Conference” (2010)

Chandrasekhar’s most important contribution to stellar dynamics was the concept of dynamical friction. I briefly review that work, then discuss some implications of Chandrasekhar’s theory of gravitational encounters for motion in galactic nuclei.

by Hénon, Michel
Originally published in 1965. 7 pages, 5 figures

This paper is an English translation of Michel H\’enon’s article, “Sur l’\'evolution dynamique des amas globulaires. II- L’amas isol\’e” originally published in French in the Annales d’Astrophysique, Vol. 28, p.62 (1965). A translation of the first paper of this series (”Sur l’\'evolution dynamique des amas globulaires”, H\’enon 1961, Annales d’Astrophysique, Vol. 24, p.369) is also available.

by Hénon, Michel
Originally published in 1961. 44 pages, 23 figures

This paper is an English translation of Michel H\’enon’s thesis, “Sur l’\'evolution dynamique des amas globulaires” originally published in French in the Annales d’Astrophysique, Vol. 24, p.369 (1961).

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 Oshino, Shoichi and Funato, Yoko and Makino, Junichiro
22 pages, 15 figures

In this paper, we present a new hybrid algorithm for the time integration of collisional N-body systems. In this algorithm, gravitational force between two particles is divided into short-range and long-range terms, using a distance-dependent cutoff function. The long-range interaction is calculated using the tree algorithm and integrated with the constant-timestep leapfrog integrator. The short-range term is calculated directly and integrated with the high-order Hermite scheme. We can reduce the calculation cost per orbital period from O(N^2) to O(N log N), without significantly increasing the long-term integration error. The results of our test simulations show that close encounters are integrated accurately. Long-term errors of the total energy shows random-walk behaviour, because it is dominated by the error caused by tree approximation.

by McKernan, Barry and Ford, K. E. Saavik and Yaqoob, Tahir and Winter, Lisa M.
6 pages. MNRAS Letters (accepted)

Small and intermediate mass black holes should be expected in galactic nuclei as a result of stellar evolution, minor mergers and gravitational dynamical friction. If these minor black holes accrete as X-ray binaries or ultra-luminous X-ray sources, and are associated with star formation, they could account for observations of many low luminosity AGN or LINERs. Accreting and inspiralling intermediate mass black holes could provide a crucial electromagnetic counterpart to strong gravitational wave signatures, allowing tests of strong gravity. Here we discuss observational signatures of minor black holes in galactic nuclei and we demonstrate that optical line ratios observed in LINERs or transition-type objects can be produced by an ionizing radiation field from ULXs. We conclude by discussing constraints from existing observations as well as candidates for future study.

by Gürkan, M. Atakan
5 pages, 5 figures. Accepted for publication in MNRAS Letters

In this paper, we propose a method to study the nature of resonant relaxation in near-Keplerian systems. Our technique is based on measuring the fractal dimension of the angular momentum trails and we use it to analyze the outcome of N-body simulations. With our method, we can reliably determine the timescale for resonant relaxation, as well as the rate of change of angular momentum in this regime. We find that growth of angular momentum is more rapid than random walk, but slower than linear growth. We also determine the presence of long term correlations, arising from the bounds on angular momentum growth. We develop a toy model that reproduces all essential properties of angular momentum evolution.

by Haas, Jaroslav and Subr, Ladislav and Kroupa, Pavel
Accepted for publication in MNRAS; 9 pages, 4 figures, 1 table

The Galactic centre hosts, according to observations, a number of early-type stars. About one half of those which are orbiting the central supermassive black hole on orbits with projected radii $latex \gtrsim$ 0.03 pc form a coherently rotating disc. Observations further reveal a massive gaseous torus and a significant population of late-type stars. In this paper, we investigate, by means of numerical N-body computations, the orbital evolution of the stellar disc, which we consider to be initially thin. We include the gravitational influence of both the torus and the late-type stars, as well as the self-gravity of the disc. Our results show that, for a significant set of system parameters, the evolution of the disc leads, within the lifetime of the early-type stars, to a configuration compatible with the observations. In particular, the disc naturally reaches a specific – perpendicular – orientation with respect to the torus, which is indeed the configuration observed in the Galactic centre. We, therefore, suggest that all the early-type stars may have been born within a single gaseous disc.

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 Blecha, Laura and Cox, Thomas J. and Loeb, Abraham and Hernquist, Lars
29 pages, 18 figures. Submitted to MNRAS

Gravitational-wave (GW) recoil of merging supermassive black holes (SMBHs) may influence the co-evolution of SMBHs and their host galaxies. We examine this possibility using SPH/N-body simulations of gaseous galaxy mergers in which the merged BH receives a recoil kick. This enables us to follow recoiling BHs in self-consistent, evolving merger remnants. In contrast to recent studies on similar topics, we conduct a large parameter study, generating a suite of over 200 simulations with more than 60 merger models and a range of recoil velocities (vk). Our main results are as follows. (1) BHs kicked at nearly the central escape speed (vesc) may oscillate on large orbits for up to a Hubble time, but in gas-rich mergers, BHs kicked with up to ~ 0.7 vesc may be confined to the central few kpc of the galaxy, owing to gas drag and steep central potentials. (2) vesc in gas-rich mergers may increase rapidly during final coalescence, in which case trajectories may depend on the timing of the BH merger relative to the formation of the potential well. (3) Recoil events generally reduce the lifetimes of bright active galactic nuclei (AGN), but may actually extend AGN lifetimes at lower luminosities. (4) Kinematically-offset AGN (v > 800 km s^-1) may be observable for up to ~ 10 Myr either immediately after the recoil or during pericentric passages through a gas-rich remnant. (5) Spatially-offset AGN (R > 1 kpc) generally have low luminosities and lifetimes of ~ 1 – 100 Myr. (6) Rapidly-recoiling BHs may be up to ~ 5 times less massive than their stationary counterparts. This lowers the normalization of the M-sigma relation and contributes to both intrinsic and overall scatter. (7) Finally, the displacement of AGN feedback after a recoil event enhances central star formation rates, thereby extending the starburst phase of the merger and creating a denser stellar cusp. [Abridged.]

by Amaro-Seoane, Pau and Freitag, Marc Dewi
A small note of 5 pages, submitted to MNRAS letts

Two coalescing black holes (BHs) represent a conspicuous source of gravitational waves (GWs). The merger involves 17 parameters in the general case of Kerr BHs, so that a successful identification and parameter extraction of the information encoded in the waves will provide us with a detailed description of the physics of BHs. A search based on matched-filtering for characterization and parameter extraction requires the development of some $latex 10^{15}$ waveforms. If a third additional BH perturbed the system, the waveforms would not be applicable, and we would need to increase the number of templates required for a valid detection. In this letter, we calculate the probability that more than two BHs interact in the regime of strong relativity in a dense stellar cluster. We determine the physical properties necessary in a stellar system for three black holes to have a close encounter in this regime and also for an existing binary of two BHs to have a strong interaction with a third hole. In both cases the event rate is negligible. While dense stellar systems such as galactic nuclei, globular clusters and nuclear stellar clusters are the breeding grounds for the sources of gravitational waves that ground-based and space-borne detectors like Advanced LIGO and LISA will be exploring, the analysis of the waveforms in full general relativity needs only to evaluate the two-body problem. This reduces the number of templates of waveforms to create by orders of magnitude.

by Just, A. and Khan, F. M. and Berczik, P. and Ernst, A. and Spurzem, R.
22 pages, 28 figures, accepted by MNRAS

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 Chandrasekhar’s 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 scale-length 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 timescale 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.