by Alexander, Tal
Invited overview lecture in “The Galactic Center, a window to the nuclear environment of disk galaxies” (Shanghai 19-23/10/2009). To appear in ASP Conf. Proc. Ser. “Galactic center workshop 2009″ ed. Mark Morris (12 pp 5 fig)

I discuss four key questions about Galactic Center dynamics, their implications for understanding both the environment of the Galactic MBH and galactic nuclei in general, and the progress made in addressing them. The questions are (1) Is the stellar system around the MBH relaxed? (2) Is there a “dark cusp” around the MBH? (3) What is the origin of the stellar disk(s)?, and (4) What is the origin of the S-stars?

by Komorowski, P. G. and Valluri, S. R. and Houde, M.
48 pages, 7 figures, submitted to Classical and Quantum Gravity on March 2nd, 2010

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits; and develop an analysis that is independent of and complements radiation reaction models. For a Schwarzschild black hole, the polar orbits represent the abutment between the prograde and retrograde orbits at which Q is at its maximum value for given values of latus rectum (l) and eccentricity (e). The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or abutment, to be moved towards greater orbital inclination; thus it no longer cleanly separates prograde and retrograde orbits. To characterise the abutment of a Kerr black hole (KBH), we first investigated the last stable orbit (LSO) of a test-particle about a KBH, and then extended this work to general orbits. To develop a better understanding of the evolution of Q we developed analytical formulae for Q in terms of l, e, and S to describe elliptical orbits at the abutment, polar orbits, and last stable orbits (LSO). By knowing the analytical form of dQ/dl at the abutment, we were able to test a 2PN flux equation for Q. We also used these formulae to numerically calculate the di/dl of hypothetical circular orbits that evolve along the abutment. From these values we have determined that di/dl = -(122.7S – 36S^3)l^-11/2 -(63/2 S + 35/4 S^3) l^-9/2 -15/2 S l^-7/2 -9/2 S l^-5/2. Thus the abutment becomes an important analytical and numerical laboratory for studying the evolution of Q and i in Kerr spacetime and for testing current and future radiation back-reaction models for near-polar retrograde orbits.

by Thornburg, Jonathan
27 pages, 12 eps figures (10 of them color, but all are viewable ok in black-and-white), uses RevTeX 4.1

If a small “particle” of mass $latex \mu M$ (with $latex \mu \ll 1$) orbits a Schwarzschild or Kerr black hole of mass $latex M$, the particle is subject to an $latex \O(\mu)$ radiation-reaction “self-force”. Here I argue that it’s valuable to compute this self-force highly accurately (relative error of $latex \ltsim 10^{-6}$) and efficiently, and I describe techniques for doing this and for obtaining and validating error estimates for the computation. I use an adaptive-mesh-refinement (AMR) time-domain numerical integration of the perturbation equations in the Barack-Ori mode-sum regularization formalism; this is efficient, yet allows easy generalization to arbitrary particle orbits. I focus on the model problem of a scalar particle in a circular geodesic orbit in Schwarzschild spacetime.

The mode-sum formalism gives the self-force as an infinite sum of regularized spherical-harmonic modes $latex \sum_{\ell=0}^\infty F_{\ell,\reg}$, with $latex F_{\ell,\reg}$ (and an “internal” error estimate) computed numerically for $latex \ell \ltsim 30$ and estimated for larger~$latex \ell$ by fitting an asymptotic “tail” series. Here I validate the internal error estimates for the individual $latex F_{\ell,\reg}$ using a large set of numerical self-force computations of widely-varying accuracies. I present numerical evidence that the actual numerical errors in $latex F_{\ell,\reg}$ for different~$latex \ell$ are at most weakly correlated, so the usual statistical error estimates are valid for computing the self-force. I show that the tail fit is numerically ill-conditioned, but this can be mostly alleviated by renormalizing the basis functions to have similar magnitudes.

Using AMR, fixed mesh refinement, and extended-precision floating-point arithmetic, I obtain the (contravariant) radial component of the self-force for a particle in a circular geodesic orbit of areal radius $latex r = 10M$ to within $latex 1$~ppm relative error.

by Barack, Leor and Sago, Norichika
42 pages

We present a numerical code for calculating the local gravitational self-force acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenz-gauge metric perturbation equations (sourced by the delta-function particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical self-force along the orbit is then obtained via mode-sum regularization. The total self-force contains a dissipative piece as well as a conservative piece, and we describe a simple method for disentangling these two pieces in a time-domain framework. The dissipative component is responsible for the loss of orbital energy and angular momentum through gravitational radiation; as a test of our code we demonstrate that the work done by the dissipative component of the computed force is precisely balanced by the asymptotic fluxes of energy and angular momentum, which we extract independently from the wave-zone numerical solutions. The conservative piece of the self force does not affect the time-averaged rate of energy and angular-momentum loss, but it influences the evolution of the orbital phases; this piece is calculated here for the first time in eccentric strong-field orbits. As a first concrete application of our code we recently reported the value of the shift in the location and frequency of the innermost stable circular orbit due to the conservative self-force [Phys. Rev. Lett.\ {\bf 102}, 191101 (2009)]. Here we provide full details of this analysis, and discuss future applications.

by Sopuerta, Carlos F. and Yunes, Nicolas
3 pages. To appear in Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity, edited by Thibault Damour, Robert T Jantzen and Remo Ruffini, World Scientific, Singapore, 2010

The inspiral of stellar compact objects into massive black holes, usually known as extreme-mass-ratio inspirals (EMRIs), is one of the most important sources of gravitational-waves for the future Laser Interferometer Space Antenna (LISA). Intermediate-mass-ratio inspirals (IMRIs are also of interest to advance ground-based gravitational-wave observatories. We discuss here how modifications to the gravitational interaction can affect the signals emitted by these systems and their detectability by LISA. We concentrate in particular on Chern-Simons modified gravity, a theory that emerges in different quantum gravitational approaches.

by Canizares, Priscilla and Sopuerta, Carlos F.
3 pages. To appear in Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity, edited by Thibault Damour, Robert T Jantzen and Remo Ruffini, World Scientific, Singapore, 2010

We introduce a new time-domain method for computing the self-force acting on a scalar particle in a Schwarzschild geometry. The principal feature of our method consists in the division of the spatial domain into several subdomains and locating the particle at the interface betweem two them. In this way, we avoid the need of resolving a small length scale associated with the presence of a particle in the computational domain and, at the same time, we avoid numerical problems due to the low differentiability of solutions of equations with point-like singular behaviour.

by Khanna, Gaurav and McKennon, Justin
14 pages, 4 figures

In this work, we make use of the OpenCL framework to accelerate an EMRI modeling application using the hardware accelerators — Cell BE and Tesla CUDA GPU. We describe these compute technologies and our parallelization approach in detail, present our performance results, and then compare them with those from our previous implementations based on the native CUDA and Cell SDKs. The OpenCL framework allows us to execute identical source-code on both architectures and yet obtain strong performance gains that are comparable to what can be derived from the native SDKs.

by Field, Scott E. and Hesthaven, Jan S. and Lau, Stephen R.
Uses revtex4, 23 pages, 9 figures, 3 tables

In the context of metric perturbation theory for non-spinning black holes, extreme mass ratio binary (EMRB) systems are described by distributionally forced master wave equations. Numerical solution of a master wave equation as an initial boundary value problem requires initial data. However, because the correct initial data for generic-orbit systems is unknown, specification of trivial initial data is a common choice, despite being inconsistent and resulting in a solution which is initially discontinuous in time. As is well known, this choice leads to a “burst” of junk radiation which eventually propagates off the computational domain. We observe another unintended consequence of trivial initial data: development of a persistent spurious solution, here referred to as the Jost junk solution, which contaminates the physical solution for long times. This work studies the influence of both types of junk on metric perturbations, waveforms, and self-force measurements, and it demonstrates that smooth modified source terms mollify the Jost solution and reduce junk radiation.

by Hadar, Shahar and Kol, Barak
17 pages, 2 figures. v3: minor changes

An extreme mass ratio inspiral consists of two parts: adiabatic inspiral and plunge. The plunge trajectory from the innermost stable circular orbit (ISCO) is special (somewhat independent of initial conditions). We write an expression for its solution in closed-form and for the emitted waveform. In particular we extract an expression for the associated black-hole ringdown amplitudes, which reduces to solving certain ordinary (radial) differential equations in the Schwarzschild background.

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 Damour, Thibault
44 pages

We discuss various ways in which the computation of conservative Gravitational Self Force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the Effective One-Body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by comparing the EOB formalism to high-accuracy numerical relativity (NR) data on coalescing binary black holes. The information coming from GSF data helps to break the degeneracy (among some EOB parameters) which was left after using comparable-mass NR data to constrain the EOB formalism. We suggest various ways of obtaining more information from GSF computations: either by studying eccentric orbits, or by focussing on a special zero-binding zoom-whirl orbit. We show that logarithmic terms start entering the post-Newtonian expansions of various (EOB and GSF) functions at the fourth post-Newtonian (4PN) level, and we analytically compute the first logarithm entering a certain, gauge-invariant “redshift” GSF function (defined along the sequence of circular orbits).

by Lu, Youjun and Zhang, Fupeng and Yu, Qingjuan
7 pages, 5 figures

Hypervelocity stars (HVSs) escaping away from the Galactic halo are dynamical products of interactions of stars with the massive black hole(s) (MBH) in the Galactic Center (GC). They are mainly B-type stars with their progenitors unknown. OB stars are also populated in the GC, with many being hosted in a clockwise-rotating young stellar (CWS) disk within half a parsec from the MBH and their formation remaining puzzles. In this paper, we demonstrate that HVSs can well memorize the injecting directions of their progenitors using both analytical arguments and numerical simulations, i.e., the ejecting direction of an HVS is almost anti-parallel to the injecting direction of its progenitor. Therefore, the spatial distribution of HVSs maps the spatial distribution of the parent population of their progenitors directly. We also find that almost all the discovered HVSs are spatially consistent with being located on two thin disk planes. The orientation of one plane is consistent with that of the (inner) CWS disk, which suggests that most of the HVSs originate from the CWS disk or a previously existed disk-like stellar structure with an orientation similar to it. The rest of HVSs may be correlated with the plane of the northern arm of the mini-spiral in the GC or the plane defined by the outer warped part of the CWS disk. Our results not only support the GC origin of HVSs but also imply that the central disk (or the disk structure with a similar orientation) should persist or be frequently rejuvenated over the past 200 Myr, which adds a new challenge to the stellar disk formation and provides insights to the longstanding problem of gas fueling into massive black holes.

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 Spallicci, A. and Aoudia, S.
To be published on 21 Rencontres de Blois: Windows on the Universe, http://confs.obspm.fr/Blois2009/, 4 pages 1 figure

Through detection by low gravitational wave space interferometers, the capture of stars by supermassive black holes will constitute a giant step forward in the understanding of gravitation in strong field. The impact of the perturbations on the motion of the star is computed via the tail, the back-scattered part of the perturbations, or via a radiative Green function. In the former approach, the self-force acts upon the background geodesic, while in the latter, the geodesic is conceived in the total (background plus perturbations) field. Regularisations (mode-sum and Riemann-Hurwitz $latex \zeta$ function) intervene to cancel divergencies coming from the infinitesimal size of the particle. The non-adiabatic trajectories require the most sophisticated techniques for studying the evolution of the motion, like the self-consistent approach.

by Gvaramadze, V. V. and Gualandris, A. and Zwart, S. Portegies
4 pages, 2 figure, to appear in Star Clusters — Basic Galactic Building Blocks throughout Time and Space, Proceed. of the IAU Symp. 266, eds. R. de Grijs and J. Lepine

We performed numerical simulations of dynamical encounters between hard massive binaries and a very massive star (VMS; formed through runaway mergers of ordinary stars in the dense core of a young massive star cluster), in order to explore the hypothesis that this dynamical process could be responsible for the origin of high-velocity (\geq 200-400 km/s) early or late B-type stars. We estimated the typical velocities produced in encounters between very tight massive binaries and VMSs (of mass of \geq 200 Msun) and found that about 3-4 per cent of all encounters produce velocities of \geq 400 km/s, while in about 2 per cent of encounters the escapers attain velocities exceeding the Milky Ways’s escape velocity. We therefore argue that the origin of high-velocity (\geq 200-400 km/s) runaway stars and at least some so-called hypervelocity stars could be associated with dynamical encounters between the tightest massive binaries and VMSs formed in the cores of star clusters. We also simulated dynamical encounters between tight massive binaries and single ordinary 50-100 Msun stars. We found that from 1 to \simeq 4 per cent of these encounters can produce runaway stars with velocities of \geq 300-400 km/s (typical of the bound population of high-velocity halo B-type stars) and occasionally (in less than 1 per cent of encounters) produce hypervelocity (\geq 700 km/s) late B-type escapers.

by Yunes, Nicolas and Buonanno, Alessandra and Hughes, Scott A. and Miller, M. Coleman and Pan, Yi
4 pages, 3 figures, submitted to Phys. Rev. Letters

We present the first models of extreme-mass-ratio inspirals within the effective-one-body (EOB) formalism, focusing on quasi-circular orbits into non-rotating black holes. We show that the phase difference and (Newtonian normalized) amplitude difference between EOB and Teukolsky-based gravitational waveforms can be reduced to < 0.1 rads and < 0.002, respectively, after a 2-year evolution. The inclusion of post-Newtonian self-force terms in the EOB approach leads to a phase disagreement of ~6-27 rads after a 2-year evolution. Such inclusion could also allow for the EOB modeling of waveforms from intermediate-mass ratio, quasi-circular inspirals.

by Khanna, Gaurav and McKennon, Justin
8 pages, 4 figures, Accepted for publication in Parallel and Distributed Computing and Systems (PDCS 2009)

In this paper, we accelerate a gravitational physics numerical modelling application using hardware accelerators — Cell processor and Tesla CUDA GPU. We describe these new technologies and our approach in detail, and then present our final performance results. We obtain well over an order-of-magnitude performance gain in our application by making use of these many-core architectures.

by Antonini, Fabio and Faber, Joshua and Gualandris, Alessia and Merritt, David
15 pages, 10 figures

The tidal breakup of binary star systems by the supermassive black hole (SMBH) in the center of the galaxy has been suggested as the source of both the observed sample of hypervelocity stars (HVSs) in the halo of the Galaxy and the S-stars that remain in tight orbits around Sgr A*. Here, we use a post-Newtonian N-body code to study the dynamics of main-sequence binaries on highly elliptical bound orbits whose periapses lie close to the SMBH, determining the properties of ejected and bound stars as well as collision products. Unlike previous studies, we follow binaries that remain bound for several revolutions around the SMBH, finding that in the case of relatively large periapses and highly inclined binaries the Kozai resonance can lead to large periodic oscillations in the internal binary eccentricity and inclination. Collisions and mergers of the binary elements are found to increase significantly for multiple orbits around the SMBH, while HVSs are primarily produced during a binary’s first passage. This process can lead to stellar coalescence and eventually serve as an important source of young stars at the galactic center.

by Merritt, David
22 pages, 18 figures

Motivated by recent observations that suggest a low density of old stars around the Milky Way supermassive black hole, evolutionary models for the nuclear star cluster are considered that postulate a parsec-scale core as initial conditions. Gravitational encounters cause the core to shrink; a core of initial radius 1-1.5 pc evolves to a size of 0.5 pc after 10 Gyr, roughly the size of the observed core. The absence of a Bahcall-Wolf cusp is naturally explained. In these models, the time for a 10-Solar-mass black hole to spiral in to the Galactic center from an initial distance of 5 pc can be much greater than 10 Gyr. Assuming that the stellar black holes had the same phase-space distribution initially as the stars, their density after 5-10 Gyr is predicted to rise very steeply going into the stellar core, but to remain substantially below the densities inferred from steady-state models that include a steep density cusp in the stars. The implications of these models are discussed for the rates of gravitational wave inspiral events and of other physical processes that depend on a high density of stars or stellar mass black holes near Sagittarius A*.

by Comeau, Simon and Poisson, Eric
4 pages, 2 figures

The rates at which the mass and angular momentum of a small black hole change as a result of a tidal interaction with a much larger black hole are calculated to leading order in the small mass ratio. The small black hole is either rotating or nonrotating, and it moves on a circular orbit in the equatorial plane of the large Kerr black hole. The orbits are fully relativistic, and the rates are computed to all orders in the orbital velocity V < V_{isco}, which is limited only by the size of the innermost stable circular orbit. We show that as V \to V_{isco}, the rates take on a limiting value that depends only on V_{isco} and not on the spin parameter of the large black hole.

by Vega, Ian and Diener, Peter and Tichy, Wolfgang and Detweiler, Steven
23 pages, 13 figures

Prescriptions for numerical self-force calculations have traditionally been designed for frequency-domain or (1+1) time-domain codes which employ a mode decomposition to facilitate in carrying out a delicate regularization scheme. This has prevented self-force analyses from benefiting from the powerful suite of tools developed and used by numerical relativists for simulations of the evolution of comparable-mass black hole binaries. In this work, we revisit a previously-introduced (3+1) method for self-force calculations, and demonstrate its viability by applying it to the test case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. Two (3+1) codes originally developed for numerical relativity applications were independently employed, and in each we were able to compute the two independent components of the self-force and the energy flux correctly to within $latex < 1%$. We also demonstrate consistency between $latex t$-component of the self-force and the scalar energy flux. Our results constitute the first successful calculation of a self-force in a (3+1) framework, and thus open opportunities for the numerical relativity community in self-force analyses and the perturbative modeling of extreme-mass-ratio inspirals.

by Barack, Leor
Invited topical review for CQG; 61 pages, 4 eps figures; uses iopart.cls, iopart10.clo

This review is concerned with the gravitational self-force acting on a mass particle in orbit around a large black hole. Renewed interest in this old problem is driven by the prospects of detecting gravitational waves from strongly gravitating binaries with extreme mass ratios. We begin here with a summary of recent advances in the theory of gravitational self-interaction in curved spacetime, and proceed to survey some of the ideas and computational strategies devised for implementing this theory in the case of a particle orbiting a Kerr black hole. We review in detail two of these methods: (i) the standard mode-sum method, in which the metric perturbation is regularized mode-by-mode in a multipole decomposition, and (ii) $latex m$-mode regularization, whereby individual azimuthal modes of the metric perturbation are regularized in 2+1 dimensions. We discuss several practical issues that arise, including the choice of gauge, the numerical representation of the particle singularity, and how high-frequency contributions near the particle are dealt with in frequency-domain calculations. As an example of a full end-to-end implementation of the mode-sum method, we discuss the computation of the gravitational self-force for eccentric geodesic orbits in Schwarzschild, using a direct integration of the Lorenz-gauge perturbation equations in the time domain. With the computational framework now in place, researchers have recently turned to explore the physical consequences of the gravitational self force; we will describe some preliminary results in this area. An appendix to this review presents, for the first time, a detailed derivation of the regularization parameters necessary for implementing the mode-sum method in Kerr spacetime.

by Barausse, E. and Racine, E. and Buonanno, A.
17 pages

Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test-particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase-space algebra in the Newton-Wigner spin supplementary condition (SSC), suitably generalized to curved spacetime, and find that the phase-space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in Post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner (ADM) canonical Hamiltonian computed in PN theory in the test-particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type S_Kerr S (and S_Kerr^2) through 3PN order, S_Kerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test-particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order.

by Levin, Janna
7 pages

A spinning black hole with a much smaller black hole companion forms a fundamental gravitational system, like a colossal classical analog to an atom. In an appealing if imperfect analogy to atomic physics, this gravitational atom can be understood through a discrete spectrum of periodic orbits. Through a correspondence between the set of periodic orbits and the set of rational numbers, we are able to construct periodic tables of orbits and energy level diagrams of the accessible states around black holes. We also present a closed form expression for the rational q, thereby quantifying zoom-whirl behavior in terms of spin, energy, and angular momentum. The black hole atom is not just a theoretical construct, but corresponds to extant astrophysical systems detectable by future gravitational wave observatories.

by Capozziello, Salvatore and De Laurentis, Mariafelicia and Forte, Luca and Garufi, Fabio and Milano, Leopoldo
6 pages, 10 figures; Multifrequency Behaviour of High-Energy Cosmic Sources, Vulcano Workshop 2009

Corrections to the relativistic theory of orbits are discussed considering higher order approximations induced by gravitomagnetic effects. Beside the standard periastron effect of General Relativity (GR), a new nutation effect was found due to the $latex {\displaystyle c^{-3}}$ orbital correction. According to the presence of that new nutation effect we studied the gravitational waveforms emitted through the capture in a gravitational field of a massive black hole (MBH) of a compact object (neutron star (NS) or BH) via the quadrupole approximation. We made a numerical study to obtain the emitted gravitational wave (GW) amplitudes. We conclude that the effects we studied could be of interest for the future space laser interferometric GW antenna LISA.

by De Laurentis, M. and Capozziello, S.
6 pages, 3 figures; Multifrequency Behaviour of High-Energy Cosmic Sources, Vulcano Workshop 2009

The emission of gravitational waves from a system of massive objects interacting on elliptical, hyperbolic and parabolic orbits is studied in the quadrupole approximation. Analytical expressions are then derived for the gravitational wave luminosity, the total energy output and gravitational radiation amplitude. A crude estimate of the expected number of events towards peculiar targets (i.e. globular clusters) is also given. In particular, the rate of events per year is obtained for the dense stellar cluster at the Galactic Center.

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 Yagi, Kent and Tanaka, Takahiro
37 pages, 16 figures

We calculate how strong one can put constraints on the alternative theories of gravities such as Brans-Dicke and massive graviton theories with LISA. We consider the inspiral gravitational waves from NS/IMBH binaries in Brans-Dicke theory and SMBH/BH binaries in massive graviton theories. We use the 2PN waveforms including spins. We also take both precession and small eccentricity of the orbit into account. We neglect the spin of one of the binary object so that we can apply the so-called \textit{simple precession}. We perform the Monte Carlo simulations of $latex 10^4$ binaries, whose parameters include the Brans-Dicke parameter $latex \omega_{\mathrm{BD}}$ and the graviton Compton length $latex \lambda_g$. We find that including both the spin-spin coupling $latex \sigma$ and the small eccentricity into the binary parameters reduces the determination accuracy by an order of magnitude for the Brans-Dicke case, whilst it has less influence on massive graviton theories. On the other hand, including precession enhances the constraint on $latex \omega_{\mathrm{BD}}$ only 20% but it increases the constraint on $latex \lambda_g$ by several factors. For $latex (1.4+1000)M_{\odot}$ NS/BH binaries of SNR=10, one can put $latex \omega_{\mathrm{BD}}>7040$, whilst for $latex (10^7+10^6)M_{\odot}$ BH/BH binaries at 3Gpc, one can put $latex \lambda_g>4.24\times10^{21}$cm, on average. This is four orders of magnitude stronger than the one obtained from the solar system experiment. From these results, it is understood that the effects of precession and eccentricity cannot be neglected in the parameter estimation analysis.

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 Fujita, Ryuichi and Hikida, Wataru

We derive the analytical solutions of the bound timelike geodesic orbits in Kerr spacetime. The analytical solutions are expressed in terms of the elliptic integrals using Mino time $latex \lambda$ as the independent variable. Mino time decouples the radial and polar motion of a particle and hence leads to forms more useful to estimate three fundamental frequencies, radial, polar and azimuthal motion, for the bound timelike geodesics in Kerr spacetime. This paper gives the first derivation of the analytical expressions of the fundamental frequencies. This paper also gives the first derivation of the analytical expressions of all coordinates for the bound timelike geodesics using Mino time. These analytical expressions should be useful not only to investigate physical properties of Kerr geodesics but more importantly to applications related to the estimation of gravitational waves from the extreme mass ratio inspirals.

by Hopman, Clovis
Accepted to ApJ

We analyze the dynamical evolution of binary stars that interact with a static background of single stars in the environment of a massive black hole (MBH). All stars are considered to be single mass, Newtonian point particles. We follow the evolution of the energy E and angular momentum J of the center of mass of the binaries with respect to the MBH, as well as their internal semi-major axis a, using a Monte Carlo method. For a system like the Galactic center, the main conclusions are the following: (1) The binary fraction can be of the order of a few percent outside 0.1 pc, but decreases quickly closer to the MBH. (2) Within ~0.1 pc, binaries can only exist on eccentric orbits with apocenters much further away from the MBH. (3) Far away from the MBH, loss-cone effects are the dominant mechanism that disrupts binaries with internal velocities close to the velocity dispersion. Closer to the MBH, three-body encounters are more effective in disrupting binaries. (4) The rate at which hard binaries become tighter is usually less than the rate at which a binary diffuses to orbits that are more bound to the MBH. (5) Binaries are typically disrupted before they experience an exchange interaction; as a result, the number of exchanges is less than one would estimate from a simple “nv\sigma estimate”. We give applications of our results to the formation of X-ray binaries near MBHs and to the production rates of hyper-velocity stars by intermediate mass MBHs.

by Fujita, Ryuichi and Hikida, Wataru and Tagoshi, Hideyuki

We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can be evaluated by solving the Teukolsky equation with a point like source term, which is computed from the stress-energy tensor of a test particle moving on generic bound geodesic orbits. In our previous papers, we computed the homogeneous solutions of the Teukolsky equation using a formalism developed by Mano, Suzuki and Takasugi and showed that we could compute gravitational waves efficiently and very accurately in the case of circular orbits on the equatorial plane. Here, we apply this method to eccentric inclined orbits. The geodesics around a Kerr black hole have three constants of motion: energy, angular momentum and the Carter constant. We compute the rates of change of the Carter constant as well as those of energy and angular momentum. This is the first time that the rate of change of the Carter constant has been evaluated accurately. We also treat the case of highly eccentric orbits with $latex e=0.9$. To confirm the accuracy of our codes, several tests are performed. We find that the accuracy is only limited by the truncation of $latex \ell$-, $latex k$- and $latex n$-modes, where $latex \ell$ is the index of the spin-weighted spheroidal harmonics, and $latex n$ and $latex k$ are the harmonics of the radial and polar motion, respectively. When we set the maximum of $latex \ell$ to 20, we obtain a relative accuracy of $latex 10^{-5}$ even in the highly eccentric case of $latex e=0.9$. The accuracy is better for lower eccentricity. Our numerical code is expected to be useful for computing templates of the extreme mass ratio inspirals, which is one of the main targets of the Laser Interferometer Space Antenna (LISA).

by Sopuerta, Carlos F. and Yunes, Nicolas
24 pages, 8 figures, Revtex 4

[abridged] Chern-Simons (CS) modified gravity is a 4D effective theory that descends both from string theory and loop quantum gravity, and that corrects the Einstein-Hilbert action by adding the product of a scalar field and the parity-violating, Pontryagin density. In this theory, the gravitational field of spinning black holes is described by a modified Kerr geometry whose multipole moments deviate from the Kerr ones only at the fourth multipole, l = 4. We investigate possible signatures of this theory in the gravitational wave emission produced in the inspiral of stellar compact objects into massive black holes, both for intermediate- and extreme-mass ratios. We use the semi-relativistic approximation, where the trajectories are geodesics of the massive black hole geometry and the gravitational waveforms are obtained from a multipolar decomposition of the radiative field. The main CS corrections to the waveforms arise from modifications to the geodesic trajectories, due to changes to the massive black hole geometry, and manifest themselves as an accumulating dephasing relative to the general relativistic case. We also explore the propagation and the stress-energy tensor of gravitational waves in this theory. We find that, although this tensor has the same form as in General Relativity, the energy and angular momentum balance laws are indeed modified through the stress-energy tensor of the CS scalar field. These balance laws could be used to describe the inspiral through adiabatic changes in the orbital parameters, which in turn would enhance the dephasing effect. Gravitational-wave observations of intermediate- or extreme-mass ratio inspirals with advanced ground detectors or with LISA could use such dephasing to test the dynamical theory to unprecedented levels.

by Barack, Leor and Sago, Norichika
4 pages

The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass $latex M$ is located at $latex r_{\rm isco}=6M G/c^2$ (Schwarzschild coordinate radius). If the particle is endowed with mass $latex \mu(\ll M)$, it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts $latex \Delta r_{\rm isco}$ and $latex \Delta\Omega_{\rm isco}$ in the ISCO’s radius and frequency, at leading order in the mass ratio $latex \mu/M$. We obtain $latex \Delta r_{\rm isco}=-3.27 \mu G/c^2$ (in the Lorenz gauge) and $latex \Delta\Omega_{\rm isco}/\Omega_{\rm isco}=0.487 \mu/M$ (gauge invariant). We discuss the implications of our result within the context of extreme mass-ratio binary inspirals.

by O’Leary, Ryan M. and Kocsis, Bence and Loeb, Abraham
22 pages, 13 figures. MNRAS accepted, in press

Stellar mass black holes (BHs) are expected to segregate and form a steep density cusp around supermassive black holes (SMBHs) in galactic nuclei. We follow the evolution of a multi-mass system of BHs and stars by numerically integrating the Fokker-Planck energy diffusion equations for a variety of BH mass distributions. We find that the BHs “self-segregate”, and that the rarest, most massive BHs dominate the scattering rate closest to the SMBH (< 0.1 pc). BH–BH binaries form out of gravitational wave emission during BH encounters. We find that the expected rate of BH coalescence events detectable by Advanced LIGO is ~1 – 100/yr, depending on the initial mass function of stars in galactic nuclei and the mass of the most massive BHs. We find that the actual merger rate is likely ~10 times larger than this due to the intrinsic scatter of stellar densities in many different galaxies. The BH binaries that form this way in galactic nuclei have significant eccentricities as they enter the LIGO band (90% with e > 0.9), and are therefore distinguishable from other binaries, which circularise before becoming detectable. We also show that eccentric mergers can be detected to larger distances and greater BH masses than circular mergers, up to ~ 700 solar masses. Future ground-based gravitational wave observatories will be able to constrain both the mass function of BHs and stars in galactic nuclei.

by Canizares, Priscilla and Sopuerta, Carlos F.
15 pages, 9 figures, Revtex 4. Minor changes to match published version

The description of the inspiral of a stellar-mass compact object into a massive black hole sitting at a galactic centre is a problem of major relevance for the future space-based gravitational-wave observatory LISA (Laser Interferometer Space Antenna), as the signals from these systems will be buried in the data stream and accurate gravitational-wave templates will be needed to extract them. The main difficulty in describing these systems lies in the estimation of the gravitational effects of the stellar-mass compact object on his own trajectory around the massive black hole, which can be modeled as the action of a local force, the self-force. In this paper, we present a new time-domain numerical method for the computation of the self-force in a simplified model consisting of a charged scalar particle orbiting a nonrotating black hole. We use a multi-domain framework in such a way that the particle is located at the interface between two domains so that the presence of the particle and its physical effects appear only through appropriate boundary conditions. In this way we eliminate completely the presence of a small length scale associated with the need of resolving the particle. This technique also avoids the problems associated with the impact of a low differentiability of the solution in the accuracy of the numerical computations. The spatial discretization of the field equations is done by using the pseudospectral collocation method and the time evolution, based on the method of lines, uses a Runge-Kutta solver. We show how this special framework can provide very efficient and accurate computations in the time domain, which makes the technique amenable for the intensive computations required in the astrophysically-relevant scenarios for LISA.

by Miller, M. Coleman and Alexander, Tal and Amaro-Seoane, Pau and Barth, Aaron J. and Cutler, Curt and Gair, Jonathan R. and Hopman, Clovis and Merritt, David and Phinney, E. Sterl and Richstone, Douglas O.
8 pages, Science white paper for the Astro2010 Decadal Survey

Electromagnetic observations over the last 15 years have yielded a growing appreciation for the importance of supermassive black holes (SMBH) to the evolution of galaxies, and for the intricacies of dynamical interactions in our own Galactic center. Here we show that future low-frequency gravitational wave observations, alone or in combination with electromagnetic data, will open up unique windows to these processes. In particular, gravitational wave detections in the 10^{-5}-10^{-1} Hz range will yield SMBH masses and spins to unprecedented precision and will provide clues to the properties of the otherwise undetectable stellar remnants expected to populate the centers of galaxies. Such observations are therefore keys to understanding the interplay between SMBHs and their environments.

by Prince, T. A. and Team, for the LISA International Science
Science White Paper submitted to the Astro2010 Decadal Survey

This Astro2010 science white paper provides an overview of the opportunities in low-frequency gravitational-wave astronomy, a new field that is poised to make significant advances. While discussing the broad context of gravitational-wave astronomy, this paper concentrates on the low-frequency region (10^(-5) to 1 Hz), a frequency range abundantly populated in strong sources of gravitational waves including massive black hole mergers, ultra-compact stellar-mass galactic binaries, and capture of compact objects by massive black holes in the nuclei of galaxies.

by Phinney, E. S.
Science White Paper submitted to the Astro2010 Decadal Survey

The principal goal of this whitepaper is not so much to demonstrate that gravitational wave detectors like LIGO and LISA will help answer many central questions in astronomy and astrophysics, but to make the case that they can help answer a far greater range of questions if we prepare to make the (sometimes substantial) effort to identify electromagnetic counterparts to the gravitational wave sources.

by Babak, Stanislav and Gair, Jonathan R. and Porter, Edward K.
14 pages, 4 figures

The gravitational wave signal from a compact object spiralling toward a massive black hole (MBH) is thought to be one of the most difficult sources to detect in the LISA data stream. Due to the large parameter space of possible signals and many orbital cycles spent in the sensitivity band of LISA, it has been estimated previously that of the order of 10^{35} templates would be required for a fully coherent search with a template grid, which is computationally impossible. Here we describe an algorithm based on a constrained Metropolis-Hastings stochastic search which allows us to find and accurately estimate parameters of isolated EMRI signals buried in Gaussian instrumental noise. We illustrate the effectiveness of the algorithm with results from searches of the Mock LISA Data Challenge round 1B data sets.

by Field, Scott E. and Hesthaven, Jan S. and Lau, Stephen R.
27 pages, 7 figures, 3 tables. Uses revtex4

Gravitational wave emission from extreme-mass-ratio binaries (EMRBs) should be detectable by the joint NASA-ESU LISA project, spurring interest in analytical and numerical methods for investigating EMRBs. We describe a discontinuous Galerkin (dG) method for solving the distributionally forced 1+1 wave equations which arise when modeling EMRBs via the perturbation theory of Schwarzschild black holes. Despite the presence of jump discontinuities in the relevant polar and axial gravitational “master functions”, our dG method achieves global spectral accuracy, provided that we know the instantaneous position, velocity, and acceleration of the small particle. Here these variables are known, since we assume that the particle follows a timelike geodesic of the Schwarzschild geometry. We document the results of several numerical experiments testing our method, and discuss the possible incorporation of radiation reaction in the model.

by Hopman, Clovis
Accepted to CQG, special LISA issue

We study the rate at which stars spiral into a massive black hole (MBH) due to the emission of gravitational waves (GWs), as a function of the mass M of the MBH. In the context of our model, it is shown analytically that the rate approximately depends on the MBH mass as $latex M^{-1/4}$. Numerical simulations confirm this result, and show that for all MBH masses, the event rate is highest for stellar black holes, followed by white dwarfs, and lowest for neutron stars. The Laser Interferometer Space Antenna (LISA) is expected to see hundreds of these extreme mass ratio inspirals per year. Since the event rate derived here formally diverges as M->0, the model presented here cannot hold for MBHs of masses that are too low, and we discuss what the limitations of the model are.