Resonant recoil in extreme mass ratio binary black hole mergers

The inspiral and merger of a binary black hole system generally leads to an asymmetric distribution of emitted radiation, and hence a recoil of the remnant black hole directed opposite to the net linear momentum radiated. The recoil velocity is generally largest for comparable mass black holes and particular spin configurations, and approaches zero in the extreme mass ratio limit. It is generally believed that for extreme mass ratios eta<<1, the scaling of the recoil velocity is V {\propto} eta^2, where the proportionality coefficient depends on the spin of the larger hole and the geometry of the system (e.g. orbital inclination). Here we show that for low but nonzero inclination prograde orbits and very rapidly spinning large holes (spin parameter a*>0.9678) the inspiralling binary can pass through resonances where the orbit-averaged radiation-reaction force is nonzero. These resonance crossings lead to a new contribution to the kick, V {\propto} eta^{3/2}. For these configurations and sufficiently extreme mass ratios, this resonant recoil is dominant. While it seems doubtful that the resonant recoil will be astrophysically significant, its existence suggests caution when extrapolating the results of numerical kick results to extreme mass ratios and near-maximal spins.Comment: fixed references; matches PRD accepted version (minor revision); 9 pages, 2 figure

Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis

Building up on previous work, we present a new calculation of the gravitational wave (GW) emission generated during the transition from quasi-circular inspiral to plunge, merger and ringdown by a binary system of nonspinning black holes, of masses $m_1$ and $m_2$, in the extreme mass ratio limit, $m_1 m_2\ll(m_1+m_2)^2$. The relative dynamics of the system is computed {\it without making any adiabatic approximation} by using an effective one body (EOB) description, namely by representing the binary by an effective particle of mass $\mu=m_1 m_2/(m_1+m_2)$ moving in a (quasi-)Schwarzschild background of mass $M=m_1+m_2$ and submitted to an \O(\nu) 5PN-resummed analytical radiation reaction force, with $\nu=\mu/M$. The gravitational wave emission is calculated via a multipolar Regge-Wheeler-Zerilli type perturbative approach (valid in the limit $\nu\ll 1$). We consider three mass ratios, $\nu={10^{-2},10^{-3},10^{-4}}$,and we compute the multipolar waveform up to $\ell=8$. We estimate energy and angular momentum losses during the quasi-universal and quasi-geodesic part of the plunge phase and we analyze the structure of the ringdown. We calculate the gravitational recoil, or "kick", imparted to the merger remnant by the gravitational wave emission and we emphasize the importance of higher multipoles to get a final value of the recoil $v/(c\nu^2)=0.0446$. We finally show that there is an {\it excellent fractional agreement} ($\sim 10^{-3}$) (even during the plunge) between the 5PN EOB analytically-resummed radiation reaction flux and the numerically computed gravitational wave angular momentum flux. This is a further confirmation of the aptitude of the EOB formalism to accurately model extreme-mass-ratio inspirals, as needed for the future space-based LISA gravitational wave detector.Comment: 20 pages, 12 figures. Version published in Phys. Rev.

Four-Body Effects in Globular Cluster Black Hole Coalescence

In the high density cores of globular clusters, multibody interactions are expected to be common, with the result that black holes in binaries are hardened by interactions. It was shown by Sigurdsson & Hernquist (1993) and others that 10 solar mass black holes interacting exclusively by three-body encounters do not merge in the clusters themselves, because recoil kicks the binaries out of the clusters before the binaries are tight enough to merge. Here we consider a new mechanism, involving four-body encounters. Numerical simulations by a number of authors suggest that roughly 20-50% of binary-binary encounters will eject one star but leave behind a stable hierarchical triple. If the orbital plane of the inner binary is strongly tilted with respect to the orbital plane of the outer object, a secular Kozai resonance, first investigated in the context of asteroids in the Solar System, can increase the eccentricity of the inner body significantly. We show that in a substantial fraction of cases the eccentricity is driven to a high enough value that the inner binary will merge by gravitational radiation, without a strong accompanying kick. Thus the merged object remains in the cluster; depending on the binary fraction of black holes and the inclination distribution of newly-formed hierarchical triples, this mechanism may allow massive black holes to accumulate through successive mergers in the cores of globular clusters. It may also increase the likelihood that stellar-mass black holes in globular clusters will be detectable by their gravitational radiation.Comment: Submitted to ApJ Letters (includes emulateapj.sty

Recoil velocity at 2PN order for spinning black hole binaries

We compute the flux of linear momentum carried by gravitational waves emitted from spinning binary black holes at 2PN order for generic orbits. In particular we provide explicit expressions of three new types of terms, namely next-to-leading order spin-orbit terms at 1.5 PN order, spin-orbit tail terms at 2PN order, and spin-spin terms at 2PN order. Restricting ourselves to quasi-circular orbits, we integrate the linear momentum flux over time to obtain the recoil velocity as function of orbital frequency. We find that in the so-called superkick configuration the higher-order spin corrections can increase the recoil velocity up to about a factor 3 with respect to the leading-order PN prediction. Furthermore, we provide expressions valid for generic orbits, and accurate at 2PN order, for the energy and angular momentum carried by gravitational waves emitted from spinning binary black holes. Specializing to quasi-circular orbits we compute the spin-spin terms at 2PN order in the expression for the evolution of the orbital frequency and found agreement with Mik\'oczi, Vas\'uth and Gergely. We also verified that in the limit of extreme mass ratio our expressions for the energy and angular momentum fluxes match the ones of Tagoshi, Shibata, Tanaka and Sasaki obtained in the context of black hole perturbation theory.Comment: 28 pages (PRD format), 1 figure, reference added, version published in PRD, except that the PRD version contains a sign error: the sign of the RHS of Eqs.(4.26) and (4.27) is wrong; it has been corrected in this replacemen

Recoiling Black Holes in Quasars

Recent simulations of merging black holes with spin give recoil velocities from gravitational radiation up to several thousand km/s. A recoiling supermassive black hole can retain the inner part of its accretion disk, providing fuel for a continuing QSO phase lasting millions of years as the hole moves away from the galactic nucleus. One possible observational manifestation of a recoiling accretion disk is in QSO emission lines shifted in velocity from the host galaxy. We have examined QSOs from the Sloan Digital Sky Survey with broad emission lines substantially shifted relative to the narrow lines. We find no convincing evidence for recoiling black holes carrying accretion disks. We place an upper limit on the incidence of recoiling black holes in QSOs of 4% for kicks greater than 500 km/s and 0.35% for kicks greater than 1000 km/s line-of-sight velocity.Comment: 4 pages, 4 figures, uses emulateapj, Submitted to ApJ Letter

Rates and Characteristics of Intermediate Mass Ratio Inspirals Detectable by Advanced LIGO

Gravitational waves (GWs) from the inspiral of a neutron star (NS) or stellar-mass black hole (BH) into an intermediate-mass black hole (IMBH) with mass between ~50 and ~350 solar masses may be detectable by the planned advanced generation of ground-based GW interferometers. Such intermediate mass ratio inspirals (IMRIs) are most likely to be found in globular clusters. We analyze four possible IMRI formation mechanisms: (1) hardening of an NS-IMBH or BH-IMBH binary via three-body interactions, (2) hardening via Kozai resonance in a hierarchical triple system, (3) direct capture, and (4) inspiral of a compact object from a tidally captured main-sequence star; we also discuss tidal effects when the inspiraling object is an NS. For each mechanism we predict the typical eccentricities of the resulting IMRIs. We find that IMRIs will have largely circularized by the time they enter the sensitivity band of ground-based detectors. Hardening of a binary via three-body interactions, which is likely to be the dominant mechanism for IMRI formation, yields eccentricities under 10^-4 when the GW frequency reaches 10 Hz. Even among IMRIs formed via direct captures, which can have the highest eccentricities, around 90% will circularize to eccentricities under 0.1 before the GW frequency reaches 10 Hz. We estimate the rate of IMRI coalescences in globular clusters and the sensitivity of a network of three Advanced LIGO detectors to the resulting GWs. We show that this detector network may see up to tens of IMRIs per year, although rates of one to a few per year may be more plausible. We also estimate the loss in signal-to-noise ratio that will result from using circular IMRI templates for data analysis and find that, for the eccentricities we expect, this loss is negligible.Comment: Accepted for publication in ApJ; revised version reflects changes made to the article during the acceptance proces

Binary black hole merger gravitational waves and recoil in the large mass ratio limit

Spectacular breakthroughs in numerical relativity now make it possible to compute spacetime dynamics in almost complete generality, allowing us to model the coalescence and merger of binary black holes with essentially no approximations. The primary limitation of these calculations is now computational. In particular, it is difficult to model systems with large mass ratio and large spins, since one must accurately resolve the multiple lengthscales which play a role in such systems. Perturbation theory can play an important role in extending the reach of computational modeling for binary systems. In this paper, we present first results of a code which allows us to model the gravitational waves generated by the inspiral, merger, and ringdown of a binary system in which one member of the binary is much more massive than the other. This allows us to accurately calibrate binary dynamics in the large mass ratio regime. We focus in this analysis on the recoil imparted to the merged remnant by these waves. We closely examine the "antikick", an anti-phase cancellation of the recoil arising from the plunge and ringdown waves, described in detail by Schnittman et al. We find that, for orbits aligned with the black hole spin, the antikick grows as a function of spin. The total recoil is smallest for prograde coalescence into a rapidly rotating black hole, and largest for retrograde coalescence. Amusingly, this completely reverses the predicted trend for kick versus spin from analyses that only include inspiral information.Comment: 15 pages, 5 figures. Submitted to Phys. Rev.

Gravitational Radiation from Intermediate-Mass Black Holes

Recent X-ray observations of galaxies with ROSAT, ASCA, and Chandra have revealed numerous bright off-center point sources which, if isotropic emitters, are likely to be intermediate-mass black holes, with hundreds to thousands of solar masses. The origin of these objects is under debate, but observations suggest that a significant number of them currently reside in young high-density stellar clusters. There is also growing evidence that some Galactic globular clusters harbor black holes of similar mass, from observations of stellar kinematics. In such high-density stellar environments, the interactions of intermediate-mass black holes are promising sources of gravitational waves for ground-based and space-based detectors. Here we explore the signal strengths of binaries containing intermediate-mass black holes or stellar-mass black holes in dense stellar clusters. We estimate that a few to tens per year of these objects will be detectable during the last phase of their inspiral with the advanced LIGO detector, and up to tens per year will be seen during merger, depending on the spins of the black holes. We also find that if these objects reside in globular clusters then tens of sources will be detectable with LISA from the Galactic globular system in a five year integration, and similar numbers will be detectable from more distant galaxies. The signal strength depends on the eccentricity distribution, but we show that there is promise for strong detection of pericenter precession and Lense-Thirring precession of the orbital plane. We conclude by discussing what could be learned about binaries, dense stellar systems, and strong gravity if such signals are detected.Comment: Minor changes, accepted by ApJ (December 10, 2002

Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach

Using the Effective One Body approach, that includes nonperturbative resummed estimates for the damping and conservative parts of the compact binary dynamics, we compute the recoil during the late inspiral and the subsequent plunge of non-spinning black holes of comparable masses moving in quasi-circular orbits. Further, using a prescription that smoothly connects the plunge phase to a perturbed single black hole, we obtain an estimate for the total recoil associated with the binary black hole coalescence. We show that the crucial physical feature which determines the magnitude of the terminal recoil is the presence of a ``burst'' of linear momentum flux emitted slightly before coalescence. When using the most natural expression for the linear momentum flux during the plunge, together with a Taylor-expanded $(v/c)^4$ correction factor, we find that the maximum value of the terminal recoil is $\sim 74$ km/s and occurs for a mass ratio $m_2/m_1 \simeq 0.38$. We comment, however, on the fact that the above `best bet estimate' is subject to strong uncertainties because the location and amplitude of the crucial peak of linear momentum flux happens at a moment during the plunge where most of the simplifying analytical assumptions underlying the Effective One Body approach are no longer justified. Changing the analytical way of estimating the linear momentum flux, we find maximum recoils that range between 49 and 172 km/s. (Abridged)Comment: 46 pages, new figures and discussions, to appear in PR

Redshifts in the Southern Abell Redshift Survey Clusters. I. The Data

The Southern Abell Redshift Survey contains 39 clusters of galaxies with redshifts in the range 0.0 < z < 0.31 and a median redshift depth of z = 0.0845. SARS covers the region 0 21h (while avoiding the LMC and SMC) with b > 40. Cluster locations were chosen from the Abell and Abell-Corwin-Olowin catalogs while galaxy positions were selected from the Automatic Plate Measuring Facility galaxy catalog with extinction-corrected magnitudes in the range 15 <= b_j < 19. SARS utilized the Las Campanas 2.5 m duPont telescope, observing either 65 or 128 objects concurrently over a 1.5 sq deg field. New redshifts for 3440 galaxies are reported in the fields of these 39 clusters of galaxies.Comment: 20 pages, 5 figures, accepted for publication in the Astronomical Journal, Table 2 can be downloaded in its entirety from http://trotsky.arc.nasa.gov/~mway/SARS1/sars1-table2.cs