by Sopuerta, Carlos F. and Yunes, Nicolas
10 pages, 3 figures. LaTeX, JPCS style. Submitted to the proceedings of the 9th Edoardo Amaldi Conference on Gravitational Waves, and the 2011 Numerical Relativity – Data Analysis (NRDA) meeting, held 10-15 July 2011 in Cardiff, Wales, UK, July 10-15 2011

We describe a new kludge scheme to model the dynamics of generic extreme-mass-ratio inspirals (EMRIs; stellar compact objects spiraling into a spinning supermassive black hole) and their gravitational-wave emission. The Chimera scheme is a hybrid method that combines tools from different approximation techniques in General Relativity: (i) A multipolar, post-Minkowskian expansion for the far-zone metric perturbation (the gravitational waveforms) and for the local prescription of the self-force; (ii) a post-Newtonian expansion for the computation of the multipole moments in terms of the trajectories; and (iii) a BH perturbation theory expansion when treating the trajectories as a sequence of self-adjusting Kerr geodesics. The EMRI trajectory is made out of Kerr geodesic fragments joined via the method of osculating elements as dictated by the multipolar post-Minkowskian radiation-reaction prescription. We implemented the proper coordinate mapping between Boyer-Lindquist coordinates, associated with the Kerr geodesics, and harmonic coordinates, associated with the multipolar post-Minkowskian decomposition. The Chimera scheme is thus a combination of approximations that can be used to model generic inspirals of systems with extreme to intermediate mass ratios, and hence, it can provide valuable information for future space-based gravitational-wave observatories, like LISA, and even for advanced ground detectors. The local character in time of our multipolar post-Minkowskian self-force makes this scheme amenable to study the possible appearance of transient resonances in generic inspirals.

by Haas, Roland and Shcherbakov, Roman V. and Bode, Tanja and Laguna, Pablo
15 pages, 17 figures, submitted to Astrophysical Journal

We present numerical relativity results of tidal disruptions of white dwarfs from ultra-close encounters with a spinning, intermediate mass black hole. These encounters require a full general relativistic treatment of gravity. We show that the disruption process and prompt accretion of the debris strongly depend on the magnitude and orientation of the black hole spin. However, the late-time accretion onto the black hole follows the same decay, $latex \dot{M}$ ~ t^{-5/3}, estimated from Newtonian gravity disruption studies. We compute the spectrum of the disk formed from the fallback material using a slim disk model. The disk spectrum peaks in the soft X-rays and sustains Eddington luminosity for 1-3 yrs after the disruption. For arbitrary black hole spin orientations, the disrupted material is scattered away from the orbital plane by relativistic frame dragging, which often leads to obscuration of the inner fallback disk by the outflowing debris. The disruption events also yield bursts of gravitational radiation with characteristic frequencies of ~3.2 Hz and strain amplitudes of ~10^{-18} for galactic intermediate mass black holes. The optimistic rate of considered ultra-close disruptions is consistent with no sources found in ROSAT all-sky survey. The future missions like Wide-Field X-ray Telescope (WFXT) could observe dozens of events.

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 Berger, E. and Zauderer, A. and Pooley, G. G. and Soderberg, A. M. and Sari, R. and Brunthaler, A. and Bietenholz, M. F.
Submitted to ApJ; 22 pages, 2 tables, 9 figures

We present continued radio observations of the tidal disruption event SwiftJ164449.3+573451 extending to \sim216 days after discovery. The data are part of a long-term program to monitor the expansion and energy scale of the relativistic outflow, and to trace the parsec-scale environment around a previously-dormant supermassive black hole (SMBH). The new observations reveal a significant change in the radio evolution starting at \sim1 month, with a brightening at all frequencies that requires an increase in the energy by about an order of magnitude, and an overall density profile around the SMBH of rho \propto r^{-3/2} (0.1-1.2 pc) with a significant flattening at r\sim0.4-0.6 pc. The increase in energy cannot be explained with continuous injection from an L \propto t^{-5/3} tail, which is observed in the X-rays. Instead, we conclude that the relativistic jet was launched with a wide range of Lorentz factors, obeying E(>Gamma) \propto Gamma^{-2.5}. The similar ratio of duration to dynamical timescale for Sw1644+57 and GRBs suggests that this result may be applicable to GRBs as well. The radial density profile may be indicative of Bondi accretion, with the inferred flattening at r\sim0.5 pc in good agreement with the Bondi radius for a \sim10^6 M_sun black hole. The density at \sim0.5 pc is about a factor of 30 times lower than inferred for the Milky Way galactic center, potentially due to a smaller number of mass-shedding massive stars. From our latest observations (\sim216 d) we find that the jet energy is E_{iso}\sim5×10^{53} erg (E_j\sim2.4×10^{51} erg for theta_j=0.1), the radius is r\sim1.2 pc, the Lorentz factor is Gamma\sim2.2, the ambient density is n\sim0.2 cm^{-3}, and the projected size is r_{proj}\sim25 microarcsec. Assuming no future changes in the observed evolution we predict that the radio emission from Sw1644+57 should be detectable with the EVLA for several decades, and will be resolvable with VLBI in a few years.

by Warburton, Niels and Akcay, Sarp and Barack, Leor and Gair, Jonathan R. and Sago, Norichika
4.3 pages, 3 figures

We present results from calculations of the orbital evolution in eccentric binaries of nonrotating black holes with extreme mass-ratios. Our inspiral model is based on the method of osculating geodesics, and is the first to incorporate the full gravitational self-force (GSF) effect, including conservative corrections. The GSF information is encapsulated in an analytic interpolation formula based on numerical GSF data for over a thousand sample geodesic orbits. We assess the importance of including conservative GSF corrections in waveform models for gravitational-wave searches.

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 Gair, Jonathan R and Yunes, Nicolas and Bender, Carl M
12 pages, 3 figures, submitted to JMP

An expected source of gravitational waves for future detectors in space are the inspirals of small compact objects into much more massive black holes. These sources have the potential to provide a wealth of information about astronomy and fundamental physics. On short timescales the orbit of the small object is approximately geodesic. Generic geodesics for a Kerr black hole spacetime have a complete set of integrals and can be characterized by three frequencies of the motion. Over the course of an inspiral, a typical system will pass through resonances where two of these frequencies become commensurate. The effect of the resonance will be to alter significantly the rate of inspiral for the duration of the resonance. Understanding the impact of these resonances on gravitational wave phasing is important to detect and exploit these signals for astrophysics and fundamental physics. Two differential equations that might describe the passage of an inspiral through such a resonance are investigated. These differ depending on whether it is the phase or the frequency components of a Fourier expansion of the motion that are taken to be continuous through the resonance. Asymptotic and hyperasymptotic analysis are used to find the late-time analytic behavior of the solution for a system that has passed through a resonance. Linearly growing (weak resonances) or linearly decaying (strong resonances) solutions are found depending on the strength of the resonance. In the weak-resonance case, frequency resonances leave an imprint (a resonant memory) on the gravitational frequency evolution. The transition between weak and strong resonances is characterized by a square-root singularity, and as one approaches this transition from above, the solutions to the frequency resonance equation bunch up into families exponentially fast.

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 Blandford, Roger D.
10 pages, 10 figures, to be submitted to MNRAS

In this paper we consider Roche accretion in an Extreme Mass-Ratio Inspiral (EMRI) binary system formed by a star orbiting a massive black hole. The ultimate goal is to detect the mass and spin of the black hole and provide a test of general relativity in the strong-field regime from the resultant quasi-periodic signals. Before accretion starts, the stellar orbit is presumed to be circular and equatorial, and shrinks due to gravitational radiation. New fitting formulae are presented for the inspiral time and the radiation-reaction torque in the relativistic regime. If the inspiralling star fills its Roche lobe outside the Innermost Stable Circular Orbit (ISCO) of the hole, gas will flow through the inner Lagrange point (L1) to the hole. We give new relativistic interpolation formulae for the volume enclosed by the Roche lobe. If this mass-transfer happens on a time scale faster than the thermal time scale but slower than the dynamical time scale, the star will evolve adiabatically, and, in most cases, will recede from the hole while filling its Roche lobe. We calculate how the stellar orbital period and mass-transfer rate will change through the “Roche evolution” for various types of stars in the relativistic regime. We envisage that the mass stream eventually hits the accretion disc, where it forms a hot spot orbiting the hole and may ultimately modulate the luminosity with the stellar orbital frequency. The observability of such a modulation is discussed along with a possible interpretation of an intermittent 1 hour period in the X-ray emission of RE J1034+396.

by Harada, Tomohiro and Kimura, Masashi
17 pages, no figure

An inspiralling object of mass $latex \mu$ around a Kerr black hole of mass $latex M (\gg \mu)$ experiences a continuous transition near the innermost stable circular orbit from adiabatic inspiral to plunge into the horizon as gravitational radiation extracts its energy and angular momentum. We investigate the collision of such an object with a generic counterpart around a Kerr black hole. We find that the angular momentum of the object is fine-tuned through gravitational radiation and that the high-velocity collision of the object with a generic counterpart naturally occurs around a nearly maximally rotating black hole. We also find that the centre-of-mass energy can be far beyond the Planck energy for dark matter particles colliding around a stellar mass black hole and as high as $latex 10^{58}$ erg for stellar mass compact objects colliding around a supermassive black hole, where the present transition formalism is well justified. Therefore, rapidly rotating black holes can accelerate objects inspiralling around them to energy high enough to be of great physical interest.

by Sopuerta, Carlos F. and Yunes, Nicolás
RevTeX 4.1. 35 pages, 10 Figures, 3 Tables

We introduce the Chimera scheme, a new framework to model the dynamics of generic extreme mass-ratio inspirals (stellar compact objects spiraling into a spinning super-massive black hole) and to produce the gravitational waveforms that describe the gravitational wave emission of these systems. The Chimera scheme combines techniques from black hole perturbation theory and post-Minkowskian theory. The orbital evolution is approximated as a sequence of osculating geodesics that shrink due to the stellar compact object’s self-acceleration. Lacking a general prescription for this self-force, we here approximate it locally in time via a post-Minkowskian expansion. The orbital evolution is thus equivalent to evolving the geodesic equations with time-dependent orbital elements, as dictated by this post-Minkowskian radiation-reaction prescription. Gravitational radiation is modeled via a multipolar expansion in post-Minkowskian theory, here taken up to mass hexadecapole and current octopole order. To complete the scheme, both the orbital evolution and wave generation require to map the Boyer-Lindquist coordinates of the orbits to the harmonic coordinates in which the different post-Minkowskian quantities have been derived, a mapping that we provide explicitly in this paper. The Chimera scheme is thus a combination of approximations that can be used to model generic inspirals of systems with extreme mass ratios to systems with more moderate mass ratios, and hence can provide valuable information for future space-based gravitational-wave observatories like the Laser Interferometer Space Antenna and even for advanced ground detectors. Finally, due to the local character in time of our post-Minkowskian self-force, the Chimera scheme can be used to perform studies of the possible appearance of transient resonances in generic inspirals.

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 Zenginoğlu, Anıl and Khanna, Gaurav
12 pages, 7 figures

We describe the hyperboloidal compactification for Teukolsky equations in Kerr spacetime. We include null infinity on the numerical grid by attaching a hyperboloidal layer to a compact domain surrounding the rotating black hole and the orbit of an inspiralling point particle. This technique allows us to study, for the first time, gravitational waveforms from large- and extreme-mass-ratio inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons of our results with previous calculations establish the accuracy and efficiency of the hyperboloidal layer method.

by Grossman, Rebecca and Levin, Janna and Perez-Giz, Gabe
30 pages, 7 figures. Submitted to Phys. Rev. D

Motivated by the prohibitive computational cost of producing adiabatic extreme mass ratio inspirals, we explain how a judicious use of resonant orbits can dramatically expedite both that calculation and the generation of snapshot gravitational waves from geodesic sources. In the course of our argument, we clarify the resolution of a lingering debate on the appropriate adiabatic averaging prescription in favor of torus averaging over time averaging.

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 Galley, Chad R.
For Part 1 of this series, see arXiv:1012.4488. 20 pages, 7 figures

The motion of a small compact object (SCO) in a background spacetime is investigated further in a class of model nonlinear scalar field theories having a perturbative structure analogous to the General Relativistic description of extreme mass ratio inspirals (EMRIs). We derive regular expressions for the scalar perturbations generated by the SCO’s motion valid through third order in $latex \epsilon$, the size of the SCO to the background curvature length scale. Our expressions are compared to those calculated through second order in $latex \epsilon$ by Rosenthal in [E. Rosenthal, CQG 22, S859 (2005)] and found to agree but our procedure for regularizing the scalar perturbations is considerably simpler. Following the Detweiler-Whiting (DW) scheme, we use our regular expressions for the field and derive the regular self-force corrections through third order. We find agreement with our previous derivation based on a variational principle of an effective action for the worldline associated with the SCO thus demonstrating the internal consistency of our formalism. This also explicitly demonstrates that the DW decomposition of Green’s functions is a valid and practical method of self force computation at higher orders in perturbation theory and, as we show in an appendix, at all orders in perturbation theory. Finally, we identify a master source from which all other physically relevant quantities are derivable. Knowing the master source perturbatively allows one to construct the waveform measured by an observer, the regular part of the field on the worldline, the regular part of the self force, and orbital quantities such as shifts of the innermost stable circular orbit, etc. The existence of a master source together with the regularization methods implemented in this series should be indispensable for derivations of higher-order gravitational self force corrections.

by Dolan, Sam R. and Wardell, Barry and Barack, Leor
30 pages, 5 figures, 3 tables

This is the second in a series of papers aimed at developing a practical time-domain method for self-force calculations in Kerr spacetime. The key elements of the method are (i) removal of a singular part of the perturbation field with a suitable analytic “puncture” based on the Detweiler–Whiting decomposition, (ii) decomposition of the perturbation equations in azimuthal ($latex m$-)modes, taking advantage of the axial symmetry of the Kerr background, (iii) numerical evolution of the individual $latex m$-modes in 2+1-dimensions with a finite difference scheme, and (iv) reconstruction of the physical self-force from the mode sum. Here we report an implementation of the method to compute the scalar-field self-force along circular equatorial geodesic orbits around a Kerr black hole. This constitutes a first time-domain computation of the self force in Kerr geometry. Our time-domain code reproduces the results of a recent frequency-domain calculation by Warburton and Barack, but has the added advantage of being readily adaptable to include the back-reaction from the self force in a self-consistent manner. In a forthcoming paper—the third in the series—we apply our method to the gravitational self-force (in the Lorenz gauge).

by Amaro-Seoane, Pau and Miller, M. Coleman and Kennedy, Gareth F.
Submitted to MNRAS

Several galaxies have exhibited X-ray flares that are consistent with the tidal disruption of a star by a central supermassive black hole. In theoretical treatments of this process it is usually assumed that the star was initially on a nearly parabolic orbit relative to the black hole. Such an assumption leads in the simplest approximation to a $latex t^{-5/3}$ decay of the bolometric luminosity and this is indeed consistent with the relatively poorly sampled light curves of such flares. We point out that there is another regime in which the decay would be different: if a binary is tidally separated and the star that remains close to the hole is eventually tidally disrupted from a moderate eccentricity orbit, the decay is slower, typically $latex \sim t^{-1.2}$. As a result, careful sampling of the light curves of such flares could distinguish between these processes and yield insight into the dynamics of binaries as well as single stars in galactic centres. We explore this process using three-body simulations and analytic treatments and discuss the consequences for present-day X-ray detections and future gravitational wave observations.

by Krolik, Julian H. and Piran, Tsvi

We propose that the remarkable object Swift J1644+57, in which multiple recurring hard X-ray flares were seen over a span of several days, is a system in which a white dwarf was tidally disrupted by an intermediate mass black hole. Disruption of a white dwarf rather than a main sequence star offers a number of advantages in understanding the multiple, and short, timescales seen in the light curve of this system. In particular, the short internal dynamical timescale of a white dwarf offers a more natural way of understanding the short rise times (~100s) observed. The relatively long intervals between flares (~5 x 10^4 s) may also be readily understood as the period between successive pericenter passages of the remnant white dwarf. In addition, the expected jet power is larger when a white dwarf is disrupted. If this model is correct, the black hole responsible must have mass < 10^5 M_{odot}.

by Zhang, Fupeng and Lu, Youjun and Yu, Qingjuan
19 pages, 16 figures

Hypervelocity stars (HVSs) found in the Galactic halo are probably the dynamical products of interactions between (binary) stars and the massive black hole(s) (MBH) in the Galactic center (GC). It has been shown that the detected HVSs are spatially consistent with being located on two thin disks (Lu et al.), one of which has the same orientation as the clockwise-rotating stellar disk in the GC. Here we perform a large number of three-body experiments of the interactions between the MBH and binary stars bound to it, and find that the probability of ejecting HVSs is substantially enhanced by multiple encounters between the MBH and binary stars at distances substantially larger than the initial tidal breakup radii. Assuming that the HVS progenitors are originated from the two disks, the inclination distribution of the HVSs relative to the disk planes can be reproduced by either the mechanism of tidal breakup of binary stars or the mechanism of ejecting HVSs by a hypothetical binary black hole (BBH) in the GC. However, an isotropical origination of HVS progenitors is inconsistent with the observed inclination distribution. Assuming that the HVSs were ejected out by the tidal breakup mechanism, its velocity distribution can be reproduced if their progenitors diffuse onto low angular momentum orbits slowly and most of the progenitors were broken up at relatively large distances due to multiple encounters. Assuming that the HVSs were ejected out by a BBH within the allowed parameter space in the GC, our simulations produce relatively flatter velocity spectra compared to the observed ones; however, the BBH mechanism cannot be statistically ruled out, yet. Future surveys of HVSs and better statistics of their spatial and velocity distributions should enable to distinguish the ejection mechanisms of HVSs and shed new light on the dynamical environment of the MBH.(abridged)

by Fujita, Ryuichi
4 pages, 2 figures

We derive gravitational waveforms needed to compute the 14th post-Newtonian (14PN) order energy flux, i.e. $latex v^{28}$ beyond Newtonian approximation where $latex v$ is the orbital velocity of a test particle, in a circular orbit around a Schwarzschild black hole. We exhibit clearly the convergence of the energy flux in the PN expansion and suggest the fitting formula which can be used for more general case. The phase difference between the 14PN waveforms and numerical waveforms after two years inspiral becomes about $latex 10^{-7}$ for $latex \mu/M=10^{-4}$ and $latex 10^{-3}$ for $latex \mu/M=10^{-5}$ where $latex \mu$ and $latex M$ are the masses of a compact object and a supermassive black hole at the centers of galaxies respectively. The 14PN expressions will lead to the parameter estimation comparable to numerical waveforms for extreme mass ratio inspirals, which are one of the main targets of Laser Interferometer Space Antenna.

by Kocsis, Bence and Yunes, Nicolas and Loeb, Abraham
42 pages, 8 figures, 3 tables, submitted to Phys. Rev. D

We examine the electromagnetic (EM) and gravitational wave (GW) signatures of stellar-mass compact objects (COs) spiraling into a supermassive black hole (extreme mass-ratio inspirals or EMRIs), embedded in a thin, radiation-pressure dominated, accretion disk. At large separations, the tidal effect of the secondary CO clears a gap. We show that the gap refills during the late GW-driven phase of the inspiral, leading to a sudden EM brightening of the source. The accretion disk leaves an imprint on the GW through its angular momentum exchange with the binary, the mass increase of the binary members due to accretion, and its gravity. We compute the disk-modified GWs both in an analytical Newtonian approximation and in a numerical effective-one-body approach. We find that disk-induced migration provides the dominant perturbation to the inspiral, with weaker effects from the mass accretion onto the CO and hydrodynamic drag. Depending on whether a gap is present, the perturbation of the GW phase is between 10 and 1000 radians per year, detectable with the future Laser Interferometer Space Antenna (LISA) at high significance. The Fourier transform of the disk-modified GW in the stationary phase approximation is sensitive to disk parameters with a frequency trend different from post-Newtonian vacuum corrections. Our results suggest that observations of EMRIs may place new sensitive constraints on the physics of accretion disks.

by Pani, Paolo and Cardoso, Vitor and Gualtieri, Leonardo
RevTex4, 18 pages, 7 figures, 1 table

Dynamical Chern-Simons gravity is an interesting extension of General Relativity, which finds its way in many different contexts, including string theory, cosmological settings and loop quantum gravity. In this theory, the gravitational field is coupled to a scalar field by a parity-violating term, which gives rise to characteristic signatures. Here we investigate how Chern-Simons gravity would affect the quasi-circular inspiralling of a small, stellar-mass object into a large non-rotating supermassive black hole, and the accompanying emission of gravitational and scalar waves. We find the relevant equations describing the perturbation induced by the small object, and we solve them through the use of Green’s function techniques. Our results show that for a wide range of coupling parameters, the Chern-Simons coupling gives rise to an increase in total energy flux, which translates into a fewer number of gravitational-wave cycles over a certain bandwidth. For space-based gravitational-wave detectors such as LISA, this effect can be used to constrain the coupling parameter effectively.

by Zhang, Zhongyang and Yunes, Nicolas and Berti, Emanuele
9 pages, 8 figures

We study the effect of black hole spin on the accuracy of the post-Newtonian approximation. We focus on the gravitational energy flux for the quasicircular, equatorial, extreme mass-ratio inspiral of a compact object into a Kerr black hole of mass M and spin J. For a given dimensionless spin a=J/M^2 (in geometrical units), the energy flux depends only on the orbital velocity v or (equivalently) on the Boyer-Lindquist orbital radius r. We investigate the formal region of validity of the Taylor post-Newtonian expansion of the energy flux (which is known up to order v^8 beyond the quadrupole formula), generalizing previous work by two of us. The “error function” used to determine the region of validity of the post-Newtonian expansion can have two qualitatively different kinds of behavior, and we deal with these two cases separately. We find that, at any fixed post-Newtonian order, the edge of the region of validity (as measured by v/v_{ISCO}, where v_{ISCO} is the orbital velocity at the innermost stable circular orbit) is only weakly dependent on a. Unlike in the nonspinning case, the lack of sufficiently high order terms does not allow us to determine if there is a convergent to divergent transition at order v^6. Independently of a, the inclusion of angular multipoles up to and including l=5 in the numerical flux is necessary to achieve the level of accuracy of the best-known (N=8) PN expansion of the energy flux.

by Koekoek, G. and van Holten, J. W.

The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and Zerilli-Moncrief equations, which describe the propagation of gravitational waves emitted by a compact massive object moving in the Schwarzschild background space-time. The wave equations are solved numerically to provide the asymptotic form of the wave at large distances for a series of non-circular bound orbits with periastron distances up to the ISCO radius, and the power emitted in gravitational waves by the extreme-mass ratio binary system is computed. The results compare well with those of purely numerical approaches.

by Canizares, Priscilla and Sopuerta, Carlos F.
4 pages, 2 figures, JPCS latex style. Submitted to JPCS (special issue for the proceedings of the Spanish Relativity Meeting (ERE2010))

When a stellar-mass compact object is captured by a supermassive black hole located in a galactic centre, the system losses energy and angular momentum by the emission of gravitational waves. Subsequently, the stellar compact object evolves inspiraling until plunging onto the massive black hole. These EMRI systems are expected to be one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna (LISA). However, the detection of EMRI signals will require of very accurate theoretical templates taking into account the gravitational self-force, which is the responsible of the stellar-compact object inspiral. Due to its potential applicability on EMRIs, the obtention of an efficient method to compute the scalar self-force acting on a point-like particle orbiting around a massive black hole is being object of increasing interest. We present here a review of our time-domain numerical technique to compute the self-force acting on a point-like particle and we show its suitability to deal with both circular and eccentric orbits.

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 Aoudia, Sofiane and Spallicci, Alessandro D. A. M.
12 pages, 13 figures (additional figures and text revised in v2 arXiv)

Perturbations of Schwarzschild-Droste black holes in the Regge-Wheeler gauge benefit from the availability of a wave equation and from the gauge invariance of the wave function, but lack smoothness. Nevertheless, the even perturbations belong to the C\textsuperscript{0} continuity class, if the wave function and its derivatives satisfy specific conditions on the discontinuities, known as jump conditions, at the particle position. These conditions suggest a new way for dealing with finite element integration in time domain. The forward time value in the upper node of the $latex (t, r^*$) grid cell is obtained by the linear combination of the three preceding node values and of analytic expressions based on the jump conditions. The numerical integration does not deal directly with the source term, the associated singularities and the potential. This amounts to an indirect integration of the wave equation. The known wave forms at infinity are recovered and the wave function at the particle position is shown. In this series of papers, the radial trajectory is dealt with first, being this method of integration applicable to generic orbits of EMRI (Extreme Mass Ratio Inspiral).

by Harada, Tomohiro and Kimura, Masashi
21 pages, 3 figures, submitted to PRD

We obtain an explicit expression for the center-of-mass (CM) energy of two colliding general geodesic massive and massless particles at any spacetime point around a Kerr black hole. Applying this, we show that the CM energy can be arbitrarily high only in the limit to the horizon and then derive a formula for the CM energy of two general geodesic particles colliding near the horizon in terms of the conserved quantities of each particle and the polar angle. We present the necessary and sufficient condition for the CM energy to be arbitrarily high in terms of the conserved quantities of each particle. To have an arbitrarily high CM energy, the angular momentum of either of the two particles must be fine-tuned to the critical value $latex L_{i}=\Omega_{H}^{-1}E_{i}$, where $latex \Omega_{H}$ is the angular velocity of the horizon and $latex E_{i}$ and $latex L_{i}$ are the energy and angular momentum of particle $latex i$ ($latex =1,2$), respectively. We show that, in the direct collision scenario, the collision with an arbitrarily high CM energy can occur near the horizon of maximally rotating black holes not only at the equator but also on a belt centered at the equator. If the critical particle is massless, this belt lies between latitudes $latex \pm acos(\sqrt{3}-1)\simeq \pm 42.94^{\circ}$. If the critical particle is massive, the highest absolute value of the latitude depends on the specific energy of the critical particle but rises up to the same value as the specific energy is increased to infinity. This is also true in the scenario through the collision of a last stable orbit particle.

by Yagi, Kent and Tanahashi, Norihiro and Tanaka, Takahiro
19 pages, 10 figures; submitted to PRD

In Randall-Sundrum II (RS-II) braneworld model, it has been conjectured according to the AdS/CFT correspondence that brane-localized black hole (BH) larger than the bulk AdS curvature scale $latex \ell$ cannot be static, and it is dual to a four dimensional BH emitting the Hawking radiation through some quantum fields. In this scenario, the number of the quantum field species is so large that this radiation changes the orbital evolution of a BH binary. We derived the correction to the gravitational waveform phase due to this effect and estimated the upper bounds on $latex \ell$ by performing Fisher analyses. We found that DECIGO/BBO can put a stronger constraint than the current table-top result by detecting gravitational waves from small mass BH/BH and BH/neutron star (NS) binaries. Furthermore, DECIGO/BBO is expected to detect 10$latex ^5$ BH/NS binaries per year. Taking this advantage, we found that DECIGO/BBO can actually measure $latex \ell$ down to $latex \ell=0.33 \mu$m for 5 year observation if we know that binaries are circular a priori. This is about 40 times smaller than the upper bound obtained from the table-top experiment. On the other hand, when we take eccentricities into binary parameters, the detection limit weakens to $latex \ell=1.5 \mu$m due to strong degeneracies between $latex \ell$ and eccentricities. We also derived the upper bound on $latex \ell$ from the expected detection number of extreme mass ratio inspirals (EMRIs) with LISA and BH/NS binaries with DECIGO/BBO, extending the discussion made recently by McWilliams. We found that these less robust constraints are weaker than the ones from phase differences.

by Kesden, Michael
9 pages, 6 figures, submitted to PRD

A test particle of mass mu on a bound geodesic of a Kerr black hole of mass M >> mu will slowly inspiral as gravitational radiation extracts energy and angular momentum from its orbit. This inspiral can be considered adiabatic when the orbital period is much shorter than the timescale on which energy is radiated, and quasi-circular when the radial velocity is much less than the azimuthal velocity. Although the inspiral always remains adiabatic provided mu << M, the quasi-circular approximation breaks down as the particle approaches the innermost stable circular orbit (ISCO). In this paper, we relax the quasi-circular approximation and solve the radial equation of motion explicitly near the ISCO. We use the requirement that the test particle's 4-velocity remain properly normalized to calculate a new contribution to the difference between its energy and angular momentum. This difference determines how a black hole's spin changes following a test-particle merger, and can be extrapolated to help predict the mass and spin of the final black hole produced in finite-mass-ratio black-hole mergers. Our new contribution is particularly important for nearly maximally spinning black holes, as it can affect whether a merger produces a naked singularity.

by Barack, Leor and Sago, Norichika
29 pages, 4 eps figures

We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle’s mass $latex \mu$ is much smaller than the black hole mass $latex M$, and explore post-geodesic corrections of $latex O(\mu/M)$. Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the $latex O(\mu/M)$ conservative correction to the periastron advance of the orbit, as a function of the (gauge dependent) semi-latus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler’s circular-orbit “red shift” invariant. We compute the $latex O(\mu/M)$ conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly-gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations.

by Canizares, Priscilla and Sopuerta, Carlos F.
IOP LaTeX style. 11 pages, 4 pages. Contribution to the NRDA/CAPRA 2010 Conference

The computation of the self-force constitutes one of the main challenges for the construction of precise theoretical waveform templates in order to detect and analyze extreme-mass-ratio inspirals with the future space-based gravitational-wave observatory LISA. Since the number of templates required is quite high, it is important to develop fast algorithms both for the computation of the self-force and the production of waveforms. In this article we show how to tune a recent time-domain technique for the computation of the self-force, what we call the Particle without Particle scheme, in order to make it very precise and at the same time very efficient. We also extend this technique in order to allow for highly eccentric orbits.

by Bernuzzi, Sebastiano and Nagar, Alessandro and Zenginoglu, Anil

We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses $latex \mu$ and $latex M$ in the extreme-mass-ratio limit, $latex \mu/M=\nu\ll 1$. We focus on the transition from quasicircular inspiral to plunge, merger and ringdown.We compare the EOB waveform to a Regge-Wheeler-Zerilli (RWZ) waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by leading-order $latex {\cal O}(\nu)$ analytically–resummed radiation reaction. The EOB and the RWZ waveforms have an initial dephasing of about $latex 5\times 10^{-4}$ rad and maintain then a remarkably accurate phase coherence during the long inspiral ($latex \sim 33$ orbits), accumulating only about $latex -2\times 10^{-3}$ rad until the last stable orbit, i.e. $latex \Delta\phi/\phi\sim -5.95\times 10^{-6}$. We obtain such accuracy without calibrating the analytically-resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for LISA-oriented studies. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasi-circular corrections both in the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasi-circular parameters by requiring compatibility between EOB and RWZ waveforms at the light-ring. The resulting phase difference around merger time is as small as $latex \pm 0.015$ rad, with a fractional amplitude agreement of $latex 2.5%$. This suggest that next-to-quasi-circular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical relativity waveforms.

by Mitsou, Ermis
15 pages, 7 figures

The computation of the gravitational radiation emitted by a particle falling into a Schwarzschild black hole is a classic problem studied already in the 1970s. Here we present a detailed numerical analysis of the case of radial infall starting at infinity with no initial velocity. We compute the radiated waveforms, spectra and energies for multipoles up to l = 6, improving significantly on the numerical accuracy of existing results. This is done by integrating the Zerilli equation in the frequency domain using the Green’s function method. The resulting wave exhibits a “ring-down” phase whose dominant contribution is a superposition of the quasi-normal modes of the black hole. The numerical accuracy allows us to recover the frequencies of these modes through a fit of that part of the wave. Comparing with direct computations of the quasi-normal modes we reach a \sim 10^{-4} to \sim 10^{-2} accuracy for the first two overtones of each multipole. Our numerical accuracy also allows us to display the power-law tail that the wave develops after the ring-down has been exponentially cut-off. The amplitude of this contribution is \sim 10^2 to \sim 10^3 times smaller than the typical scale of the wave.

by Gair, Jonathan R. and Flanagan, Eanna E. and Drasco, Steve and Hinderer, Tanja and Babak, Stanislav
27 pages, 2 figures, submitted to Phys. Rev. D

We present two methods for integrating forced geodesic equations in the Kerr spacetime, which can accommodate arbitrary forces. As a test case, we compute inspirals under a simple drag force, mimicking the presence of gas. We verify that both methods give the same results for this simple force. We find that drag generally causes eccentricity to increase throughout the inspiral. This is a relativistic effect qualitatively opposite to what is seen in gravitational-radiation-driven inspirals, and similar to what is observed in hydrodynamic simulations of gaseous binaries. We provide an analytic explanation by deriving the leading order relativistic correction to the Newtonian dynamics. If observed, an increasing eccentricity would provide clear evidence that the inspiral was occurring in a non-vacuum environment. Our two methods are especially useful for evolving orbits in the adiabatic regime. Both use the method of osculating orbits, in which each point on the orbit is characterized by the parameters of the geodesic with the same instantaneous position and velocity. Both methods describe the orbit in terms of the geodesic energy, axial angular momentum, Carter constant, azimuthal phase, and two angular variables that increase monotonically and are relativistic generalizations of the eccentric anomaly. The two methods differ in their treatment of the orbital phases and the representation of the force. In one method the geodesic phase and phase constant are evolved together as a single orbital phase parameter, and the force is expressed in terms of its components on the Kinnersley orthonormal tetrad. In the second method, the phase constants of the geodesic motion are evolved separately and the force is expressed in terms of its Boyer-Lindquist components. This second approach is a generalization of earlier work by Pound and Poisson for planar forces in a Schwarzschild background.

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 Jiang, Yanfei and Goodman, Jeremy
34 pages, 8 figures. Submitted to ApJ

Using a version of the ZEUS code, we carry out two-dimensional simulations of self-gravitating shearing sheets, with application to QSO accretion disks at a few thousand Schwarzschild radii, corresponding to a few hundredths of a parsec for a 10^8 solar-mass black hole. Radiation pressure and optically thick radiative cooling are implemented via vertical averages. We determine dimensionless versions of the maximum surface density, accretion rate, and effective viscosity that can be sustained by density-wave turbulence without fragmentation. Where fragments do form, we study the final masses that result. The maximum Shakura-Sunyaev viscosity parameter is approximately 0.4. Fragmentation occurs when the cooling time is less than about twice the shearing time, as found by Gammie and others, but can also occur at very long cooling times in sheets that are strongly radiation-pressure dominated. For accretion at the Eddington rate onto a 10^8 solar-mass black hole, fragmentation occurs beyond four thousand Schwarzschild radii, r_s. Near this radius, initial fragment masses are several hundred suns, consistent with estimates from linear stability; final masses after merging increase with the size of the sheet, reaching several thousand suns in our largest simulations. With increasing black-hole mass at a fixed Eddington ratio, self-gravity prevails to smaller multiples of r_s, where radiation pressure is more important and the cooling time is longer compared to the dynamical time; nevertheless, fragmentation can occur and produces larger initial fragment masses. We also find energy conservation is likely to be a challenge for all eulerian codes in self-gravitating regimes where radiation pressure dominates.

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 Favata, Marc
17 pages, 2 figures, 1 table

The innermost stable circular orbit (ISCO) delimits the transition from circular orbits to those that plunge into a black hole. In the test-mass limit, well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes. In the finite-mass case, there are a large variety of ways to define an ISCO in a post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCO condition of Blanchet & Iyer (2003) to the case of spinning (non-precessing) binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpected properties: (1) it exactly reproduces the Schwarzschild ISCO in the test-mass limit, and (2) it accurately approximates the recently-calculated shift in the Schwarzschild ISCO frequency due to the conservative-piece of the gravitational self-force [Barack & Sago (2009)]. The generalization of this ISCO condition to spinning binaries has the property that it also exactly reproduces the Kerr ISCO in the test-mass limit (up to the order at which PN spin corrections are currently known). The shift in the ISCO due to the spin of the test-particle is also calculated. Remarkably, the gauge-invariant PN ISCO condition exactly reproduces the ISCO shift predicted by the Papapetrou equations for a fully-relativistic spinning particle. It is surprising that an analysis of the stability of the standard PN equations of motion is able (without any form of “resummation”) to accurately describe strong-field effects of the Kerr spacetime. The ISCO frequency shift due to the conservative self-force in Kerr is also calculated from this new ISCO condition, as well as from the effective-one-body Hamiltonian of Barausse & Buonanno (2010). These results serve as a useful point-of-comparison for future gravitational self-force calculations in the Kerr spacetime.

by Sopuerta, Carlos F. and Yunes, Nicolas
10 pages, 2 figures, Springer Verlag LaTeX style. To appear in the proceedings of Cosmology, the Quantum Vacuum, and Zeta Functions: A workshop with a celebration of Emilio Elizalde’s sixtieth birthday, Bellaterra, Barcelona, Spain, 8-10 Mar 2010. Eds. S. D. Odintsov, D. Saez-Gomez, and S. Xambo

The emergent area of gravitational wave astronomy promises to provide revolutionary discoveries in the areas of astrophysics, cosmology, and fundamental physics. One of the most exciting possibilities is to use gravitational-wave observations to test alternative theories of gravity. In this contribution we describe how to use observations of extreme-mass-ratio inspirals by the future Laser Interferometer Space Antenna to test a particular class of theories: Chern-Simons modified gravity.

by Yunes, Nicolas and Miller, M. Coleman and Thornburg, Jonathan
9 pages, 3 figures, submitted to Phys. Rev. D

Extreme mass ratio inspirals, in which a stellar-mass object merges with a supermassive black hole, are prime sources for space-based gravitational wave detectors because they will facilitate tests of strong gravity and probe the spacetime around rotating compact objects. In the last few years of such inspirals, the total phase is in the millions of radians and details of the waveforms are sensitive to small perturbations. We show that one potentially detectable perturbation is the presence of a second supermassive black hole within a few tenths of a parsec. The acceleration produced by the perturber on the extreme mass-ratio system produces a steady drift that causes the waveform to deviate systematically from that of an isolated system. If the perturber is a few tenths of a parsec from the extreme-mass ratio system (plausible in as many as a few percent of cases) higher derivatives of motion might also be detectable. In that case, the mass and distance of the perturber can be derived independently, which would allow a new probe of merger dynamics.

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 Gair, Jonathan R and Sesana, Alberto and Berti, Emanuele and Volonteri, Marta
11 pages, 3 figures, submitted to Class. Quantum Grav. for proceedings of 8th LISA Symposium

LISA should detect gravitational waves from tens to hundreds of systems containing black holes with mass in the range from 10 thousand to 10 million solar masses. Black holes in this mass range are not well constrained by current electromagnetic observations, so LISA could significantly enhance our understanding of the astrophysics of such systems. In this paper, we describe a framework for combining LISA observations to make statements about massive black hole populations. We summarise the constraints that LISA observations of extreme-mass-ratio inspirals might be able to place on the mass function of black holes in the LISA range. We also describe how LISA observations can be used to choose between different models for the hierarchical growth of structure in the early Universe. We consider four models that differ in their prescription for the initial mass distribution of black hole seeds, and in the efficiency of accretion onto the black holes. We show that with as little as 3 months of LISA data we can clearly distinguish between these models, even under relatively pessimistic assumptions about the performance of the detector and our knowledge of the gravitational waveforms.

by Canizares, Priscilla and Sopuerta, Carlos F.
6 pages, 7 figures, submitted to proceedings of the 8th International LISA Symposium, Stanford, June 28 – July 2, 2010

The gravitational-wave signals emitted by Extreme-Mass-Ratio Inspirals will be hidden in the instrumental LISA noise and the foreground noise produced by galactic binaries in the LISA band. Then, we need accurate gravitational-wave templates to extract these signals from the noise and obtain the relevant physical parameters. This means that in the modeling of these systems we have to take into account how the orbit of the stellar-mass compact object is modified by the action of its own gravitational field. This effect can be described as the action of a local force, the self-force. We present a time-domain technique to compute the self-force for geodesic eccentric orbits around a non-rotating massive black hole. To illustrate the method we have applied it to a testbed model consisting of scalar charged particle orbiting a non-dynamical black hole. A key feature of our method is that it does not introduce a small scale associated with the stellar-mass compact object. This is achieved by using a multidomain framework where the particle is located at the interface between two subdomains. In this way, we just have to evolve homogeneous wave-like equations with smooth solutions that have to be communicated across the subdomain boundaries using appropriate junction conditions. The numerical technique that we use to implement this scheme is the pseudospectral collocation method. We show the suitability of this technique for the modeling of Extreme-Mass-Ratio Inspirals and show that it can provide accurate results for the self-force.

by Yunes, Nicolas and Buonanno, Alessandra and Hughes, Scott A. and Pan, Yi and Barausse, Enrico and Miller, M. Coleman and Throwe, William
21 pages, 8 figures, submitted to Phys. Rev. D

We construct effective-one-body waveform models suitable for data analysis with LISA for extreme-mass ratio inspirals in quasi-circular, equatorial orbits about a spinning supermassive black hole. The accuracy of our model is established through comparisons against frequency-domain, Teukolsky-based waveforms in the radiative approximation. The calibration of eight high-order post-Newtonian parameters in the energy flux suffices to obtain a phase and fractional amplitude agreement of better than 1 radian and 1 % respectively over a period between 2 and 6 months depending on the system considered. This agreement translates into matches higher than 97 % over a period between 4 and 9 months, depending on the system. Better agreements can be obtained if a larger number of calibration parameters are included. Higher-order mass ratio terms in the effective-one-body Hamiltonian and radiation-reaction introduce phase corrections of at most 30 radians in a one year evolution. These corrections are usually one order of magnitude larger than those introduced by the spin of the small object in a one year evolution. These results suggest that the effective-one-body approach for extreme mass ratio inspirals is a good compromise between accuracy and computational price for LISA data analysis purposes.

by Huerta, E. A. and Gair, Jonathan R
6 pages, 1 figure, submitted to proceedings of the 8th International LISA Symposium, Stanford, June 28 – July 2, 2010

It is not currently clear how important it will be to include conservative self-force (SF) corrections in the models for extreme-mass-ratio inspiral (EMRI) waveforms that will be used to detect such signals in LISA (Laser Interferometer Space Antenna) data. These proceedings will address this issue for circular-equatorial inspirals using an approximate EMRI model that includes conservative corrections at leading post-Newtonian order. We will present estimates of the magnitude of the parameter estimation errors that would result from omitting conservative corrections, and compare these to the errors that will arise from noise fluctuations in the detector. We will also use this model to explore the relative importance of the second-order radiative piece of the SF, which is not presently known.

by Flanagan, Eanna E. and Hinderer, Tanja
5 pages, 1 figure

We show that transient resonances occur in the two body problem in general relativity, in the highly relativistic, extreme mass-ratio regime for spinning black holes. These resonances occur when the ratio of polar and radial orbital frequencies, which is slowly evolving under the influence of gravitational radiation reaction, passes through a low order rational number. At such points, the adiabatic approximation to the orbital evolution breaks down, and there is a brief but order unity correction to the inspiral rate. Corrections to the gravitational wave signal’s phase due to resonance effects scale as the square root of the inverse of mass of the small body, and thus become large in the extreme-mass-ratio limit, dominating over all other post-adiabatic effects. The resonances make orbits more sensitive to changes in initial data (though not quite chaotic), and are genuine non-perturbative effects that are not seen at any order in a standard post-Newtonian expansion. Our results apply to an important potential source of gravitational waves, the gradual inspiral of white dwarfs, neutron stars, or black holes into much more massive black holes. It is hoped to exploit observations of these sources to map the spacetime geometry of black holes. However, such mapping will require accurate models of binary dynamics, which is a computational challenge whose difficulty is significantly increased by resonance effects. We estimate that the resonance phase shifts will be of order a few tens of cycles for mass ratios $latex \sim 10^{-6}$, by numerically evolving fully relativistic orbital dynamics supplemented with an approximate, post-Newtonian self-force.

by Lousto, Carlos O. and Zlochower, Yosef
4 pages, 4 figures, 3 tables

We perform the first fully nonlinear numerical simulations of black-hole binaries with mass ratios 100:1. Our technique for evolving such extreme mass ratios is based on the moving puncture approach with a new gauge condition and an optimal choice of the mesh refinement (plus large computational resources). We achieve a convergent set of results for simulations starting with a small nonspinning black hole just outside the ISCO that then performs over two orbits before plunging into the 100 times more massive black hole. We compute the gravitational energy and momenta radiated as well as the final remnant parameters and compare these quantities with the corresponding perturbative estimates. The results show a close agreement. We briefly discuss the relevance of this simulations for Advanced LIGO, third-generation ground based detectors, and LISA observations, and self-force computations.