We estimate the expected signal-to-noise ratios ͑SNRs͒ from the three phases ͑inspiral, merger, and ringdown͒ of coalescing binary black holes ͑BBHs͒ for initial and advanced ground-based interferometers ͑LIGO-VIRGO͒ and for the space-based interferometer LISA. Ground-based interferometers can do moderate SNR ͑a few tens͒, moderate accuracy studies of BBH coalescences in the mass range of a few to about 2000 solar masses; LISA can do high SNR ͑of order 10 4 ͒, high accuracy studies in the mass range of about 10 5 -10 8 solar masses. BBHs might well be the first sources detected by LIGO-VIRGO: they are visible to much larger distances-up to 500 Mpc by initial interferometers-than coalescing neutron star binaries ͑heretofore regarded as the ''bread and butter'' workhorse source for LIGO-VIRGO, visible to about 30 Mpc by initial interferometers͒. Low-mass BBHs ͑up to 50M ᭪ for initial LIGO interferometers, 100M ᭪ for advanced, 10 6 M ᭪ for LISA͒ are best searched for via their well-understood inspiral waves; higher mass BBHs must be searched for via their poorly understood merger waves and/or their well-understood ringdown waves. A matched filtering search for massive BBHs based on ringdown waves should be capable of finding BBHs in the mass range of about 100M ᭪ -700M ᭪ out to ϳ200 Mpc for initial LIGO interferometers, and in the mass range of ϳ200M ᭪ to ϳ3000M ᭪ out to about zϭ1 for advanced interferometers. The required number of templates is of the order of 6000 or less. Searches based on merger waves could increase the number of detected massive BBHs by a factor of the order of 10 over those found from inspiral and ringdown waves, without detailed knowledge of the waveform shapes, using a noise monitoring search algorithm which we describe. A full set of merger templates from numerical relativity simulations could further increase the number of detected BBHs by an additional factor of up to ϳ4. ͓S0556-2821͑98͒06508-4͔ PACS number͑s͒: 04.80. Nn, 04.25.Dm, 04.30.Db, 95.55.Ym

Gravitational waves (GWs) from supermassive binary black hole (BBH) inspirals are potentially powerful standard sirens (the GW analog to standard candles) (Schutz 1986(Schutz , 2002. Because these systems are well-modeled, the space-based GW observatory LISA will be able to measure the luminosity distance (but not the redshift) to some distant massive BBH systems with 1-10% accuracy. This accuracy is largely limited by pointing error: GW sources generally are poorly localized on the sky. Localizing the binary independently (e.g., through association with an electromagnetic counterpart) greatly reduces this positional error. An electromagnetic counterpart may also allow determination of the event's redshift. In this case, BBH coalescence would constitute an extremely precise (better than 1%) standard candle visible to high redshift. In practice, gravitational lensing degrades this precision, though the candle remains precise enough to provide useful information about the distance-redshift relation. Even if very rare, these GW standard sirens would complement, and increase confidence in, other standard candles.

Recent observations support the hypothesis that a large fraction of "short-hard" gamma-ray bursts (SHBs) are associated with the inspiral and merger of compact binaries. Since gravitational-wave (GW) measurements of well-localized inspiraling binaries can measure absolute source distances, simultaneous observation of a binary's GWs and SHB would allow us to directly and independently determine both the binary's luminosity distance and its redshift. Such a "standard siren" (the GW analog of a standard candle) would provide an excellent probe of the nearby (z 0.3) universe's expansion, independent of the cosmological distance ladder, thereby complementing other standard candles. Previous work explored this idea using a simplified formalism to study measurement by advanced GW detector networks, incorporating a high signal-to-noise ratio limit to describe the probability distribution for measured parameters. In this paper we eliminate this simplification, constructing distributions with a Markov-Chain Monte-Carlo technique. We assume that each SHB observation gives source sky position and time of coalescence, and we take non-spinning binary neutron star and black hole-neutron star coalescences as plausible SHB progenitors. We examine how well parameters (particularly distance) can be measured from GW observations of SHBs by a range of ground-based detector networks. We find that earlier estimates overstate how well distances can be measured, even at fairly large signal-to-noise ratio. The fundamental limitation to determining distance proves to be a degeneracy between distance and source inclination. Overcoming this limitation requires that we either break this degeneracy, or measure enough sources to broadly sample the inclination distribution.

We present a new approximate method for constructing gravitational radiation driven inspirals of test bodies orbiting Kerr black holes. Such orbits can be fully described by a semilatus rectum p, an eccentricity e, and an inclination angle , or, by an energy E, an angular momentum component L z , and a third constant Q. Our scheme uses expressions that are exact ͑within an adiabatic approximation͒ for the rates of change (ṗ ,ė ,) as linear combinations of the fluxes (Ė ,L z ,Q ), but uses quadrupole-order formulas for these fluxes. This scheme thus encodes the exact orbital dynamics, augmenting it with an approximate radiation reaction. Comparing inspiral trajectories, we find that this approximation agrees well with numerical results for the special cases of eccentric equatorial and circular inclined orbits, far more accurate than corresponding weak-field formulas for (ṗ ,ė ,). We use this technique to study the inspiral of a test body in inclined, eccentric Kerr orbits. Our results should be useful tools for constructing approximate waveforms that can be used to study data analysis problems for the future Laser Interferometer Space Antenna gravitational-wave observatory, in lieu of waveforms from more rigorous techniques that are currently under development. I. BACKGROUND AND MOTIVATIONThe capture of stellar-mass compact objects by massive black holes residing in galactic nuclei is expected to be one of the most important sources of gravitational radiation for the future Laser Interferometer Space Antenna ͑LISA͒ spacebased detector ͓1,2͔. Observing such events will provide information about stellar dynamics in galactic nuclei, and should make possible precise measurements of black hole masses and spins. Indeed, the waves generated by such a capture will encode a detailed description of the black hole's spacetime, making it possible to test whether the ''large object'' in the galactic nucleus is indeed a Kerr black hole as predicted by general relativity, or is some exotic massive compact object ͓3,4͔.Extracting such information will require accurate modeling of the gravitational waveform. The smallness of the system's mass ratio ͑typically, /M ϳ10 Ϫ4 Ϫ10 Ϫ6 , where and M are the masses for the captured body and the central hole, respectively͒ allows one to treat the small body as a ''test particle'' moving in the gravitational field of the black hole. In the absence of radiation, the small body moves on a geodesic orbit of the black hole ͓5͔. These orbits have three integrals of motion ͑apart from ): energy E; angular momentum projected on the hole's spin axis, L z ; and Carter's third constant Q, related to the square of the angular momentum projected onto the equatorial plane. A body in a generic ͑eccentric and inclined͒ Kerr orbit traces an open ellipse precessing about the black hole's spin axis, resulting in a complicated overall motion. Astrophysical captured bodies will move in such complicated orbits.The integrals of the motion are not constant in the presence of gravitational radiation-they evolve as...

Coalescing binary black holes experience an impulsive kick from anisotropic emission of gravitational waves. Recoil velocities are sufficient to eject most coalescing black holes from dwarf galaxies and globular clusters, which may explain the apparent absence of massive black holes in these systems. Ejection from giant elliptical galaxies would be rare, but coalescing black holes are displaced from the center and fall back on a timescale of order the half-mass crossing time. Displacement of the black holes transfers energy to the stars in the nucleus and can convert a steep density cusp into a core. Radiation recoil calls into question models that grow supermassive black holes from hierarchical mergers of stellar-mass precursors. Subject headings: black hole physics -galaxies: nuclei -gravitation -gravitational waves 1. KICK AMPLITUDE In a companion paper (Favata, Hughes, & Holz 2004, hereafter Paper I), the amplitude of the recoil velocity resulting from anisotropic emission of gravitational waves during coalescence of a binary black hole (BH) is computed. Here we explore some of the consequences of the kicks. Unless otherwise indicated, notation is the same as in Paper I.For in-spiral from a circular orbit, the kick velocity is a function of the binary mass ratio , the BH spinsq p m /m ≤ 1 aand , and the initial angle i between the spin of the larger BH a 2 and the orbital angular momentum of the binary. Following Paper I, the spin of the smaller BH is ignored. Although Paper I only considers the cases and , the recoil for arbitrary i p 0 i p 180 inclination is likely to be bounded between these extreme values. Also, the detailed inclination dependence is unimportant in comparison with the large uncertainty already present in the contribution to the recoil from the final plunge and coalescence. We will therefore assume that the restriction to equatorial-prograde/ retrograde orbits ( ) considered in Paper I encom-passes the characteristic range of recoil velocities.Figure 2b of Paper I shows upper and lower limit estimates of the recoil velocity as a function of the effective spin parameter for a reduced mass ratio .is well fitted in the range Ϫ h ! 0.1 0.9 ≤ by the following fifth-order polynomial: We convert these expressions into estimates of the bounds on as follows. First, as discussed in Paper I, there is an V kick ambiguity in how one translates the physical spin parameter of the larger hole into the effective spin parameter ofã a 2 equations (1) and (2). Here we adopt the Damour (2001) relation . Second, Fitchett's scaling Ϫ2ã p (1 ϩ 3q/4)(1 ϩ q) a 2 function assumes that both bodies are nonspinning and vanishes when . In fact, when , significant recoil would q p 1 a ( 0 occur even for as a result of spin-orbit coupling. We q p 1 can guess the approximate form of a new scaling function by examining the spin-orbit corrections (Kidder 1995) to Fitchett's recoil formula. For equatorial orbits, equation (4) of Paper I suggests that should be multiplied by the factor kick esc tional potential o...