Retaining Black Holes with Very Large Recoil Velocities

Recent numerical simulations of binary black hole mergers show the possibility of producing very large recoil velocities (> 3000 km/s). Kicks of this magnitude should be sufficient to eject the final black hole from virtually any galactic potential. This result has been seen as a potential contradiction with observations of supermassive black holes residing in the centers of most galaxies in the local universe. Using an extremely simplified merger tree model, we show that, even in the limit of very large ejection probability, after a small number of merger generations there should still be an appreciable fraction (>50%) of galaxies with supermassive black holes today. We go on to argue that the inclusion of more realistic physics ingredients in the merger model should systematically increase this retention fraction, helping to resolve a potential conflict between theory and observation. Lastly, we develop a more realistic Monte Carlo model to confirm the qualitative arguments and estimate occupation fractions as a function of the central galactic velocity dispersion.Comment: 6 pages, 3 figures; Comments welcom

Electromagnetic Chirps from Neutron Star-Black Hole Mergers

We calculate the electromagnetic signal of a gamma-ray flare coming from the surface of a neutron star shortly before merger with a black hole companion. Using a new version of the Monte Carlo radiation transport code Pandurata that incorporates dynamic spacetimes, we integrate photon geodesics from the neutron star surface until they reach a distant observer or are captured by the black hole. The gamma-ray light curve is modulated by a number of relativistic effects, including Doppler beaming and gravitational lensing. Because the photons originate from the inspiraling neutron star, the light curve closely resembles the corresponding gravitational waveform: a chirp signal characterized by a steadily increasing frequency and amplitude. We propose to search for these electromagnetic chirps using matched filtering algorithms similar to those used in LIGO data analysis.Comment: 13 pages, 5 figures, submitted to Ap

Interpreting the High Frequency QPO Power Spectra of Accreting Black Holes

In the context of a relativistic hot spot model, we investigate different physical mechanisms to explain the behavior of quasi-periodic oscillations (QPOs) from accreting black holes. The locations and amplitudes of the QPO peaks are determined by the ray-tracing calculations presented in Schnittman & Bertschinger (2004a): the black hole mass and angular momentum give the geodesic coordinate frequencies, while the disk inclination and the hot spot size, shape, and overbrightness give the amplitudes of the different peaks. In this paper additional features are added to the existing model to explain the broadening of the QPO peaks as well as the damping of higher frequency harmonics in the power spectrum. We present a number of analytic results that closely agree with more detailed numerical calculations. Four primary pieces are developed: the addition of multiple hot spots with random phases, a finite width in the distribution of geodesic orbits, Poisson sampling of the detected photons, and the scattering of photons from the hot spot through a corona of hot electrons around the black hole. Finally, the complete model is used to fit the observed power spectra of both type A and type B QPOs seen in XTE J1550-564, giving confidence limits on each of the model parameters.Comment: 30 pages, 5 figures, submitted to Ap

The Infrared Afterglow of Supermassive Black Hole Mergers

We model the spectra and light curves of circumbinary accretion disks during the time after the central black holes merge. The most immediate effect of this merger is the dissipation of energy in the outer regions of the disk due to the gravitational wave energy and linear momentum flux released at merger. This has the effect of perturbing the gas in the disk, which then radiates the dissipated energy over a cooling timescale, giving a characteristic infrared signal for tens of thousands of years when the total black hole mass is M~10^8 M_sun. On the basis of a simple cosmological merger model in which a typical supermassive black hole undergoes a few major mergers during its lifetime, we predict that ~10^4-10^5 of these IR sources should be observable today and discuss the possibility of identifying them with multi-wavelength surveys such as SWIRE/XMM-LSS/XBootes and COSMOS.Comment: v2: expanded discussion of optical depth calculations; ApJ in pres

Anatomy of the binary black hole recoil: A multipolar analysis

We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within ~2%) and that only a few dominant modes contribute significantly to it (within ~5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an ``effective Newtonian'' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulae with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes (QNMs). Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of ``anti-kick'' for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes.Comment: 28 pages, 20 figures, submitted to PRD; v2: minor revisions from referee repor

Gravitational-wave memory revisited: memory from the merger and recoil of binary black holes

Gravitational-wave memory refers to the permanent displacement of the test masses in an idealized (freely-falling) gravitational-wave interferometer. Inspiraling binaries produce a particularly interesting form of memory--the Christodoulou memory. Although it originates from nonlinear interactions at 2.5 post-Newtonian order, the Christodoulou memory affects the gravitational-wave amplitude at leading (Newtonian) order. Previous calculations have computed this non-oscillatory amplitude correction during the inspiral phase of binary coalescence. Using an "effective-one-body" description calibrated with the results of numerical relativity simulations, the evolution of the memory during the inspiral, merger, and ringdown phases, as well as the memory's final saturation value, are calculated. Using this model for the memory, the prospects for its detection are examined, particularly for supermassive black hole binary coalescences that LISA will detect with high signal-to-noise ratios. Coalescing binary black holes also experience center-of-mass recoil due to the anisotropic emission of gravitational radiation. These recoils can manifest themselves in the gravitational-wave signal in the form of a "linear" memory and a Doppler shift of the quasi-normal-mode frequencies. The prospects for observing these effects are also discussed.Comment: 6 pages, 2 figures; accepted to the proceedings of the 7th International LISA Symposium; v2: updated figures and signal-to-noise ratios, several minor changes to the tex

Self Organization and a Dynamical Transition in Traffic Flow Models

A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed.Comment: 6 pages, 4 figure

Ruling Out Chaos in Compact Binary Systems

We investigate the orbits of compact binary systems during the final inspiral period before coalescence by integrating numerically the second-order post-Newtonian equations of motion. We include spin-orbit and spin-spin coupling terms, which, according to a recent study by Levin [J. Levin, Phys. Rev. Lett. 84, 3515 (2000)], may cause the orbits to become chaotic. To examine this claim, we study the divergence of initially nearby phase-space trajectories and attempt to measure the Lyapunov exponent gamma. Even for systems with maximally spinning objects and large spin-orbit misalignment angles, we find no chaotic behavior. For all the systems we consider, we can place a strict lower limit on the divergence time t_L=1/gamma that is many times greater than the typical inspiral time, suggesting that chaos should not adversely affect the detection of inspiral events by upcoming gravitational-wave detectors.Comment: 8 pages, 4 figures, submitted to Phys. Rev. Let