Binary Black Holes: Spin Dynamics and Gravitational Recoil

We present a study of spinning black hole binaries focusing on the spin dynamics of the individual black holes as well as on the gravitational recoil acquired by the black hole produced by the merger. We consider two series of initial spin orientations away from the binary orbital plane. In one of the series, the spins are anti-aligned; for the second series, one of the spins points away from the binary along the line separating the black holes. We find a remarkable agreement between the spin dynamics predicted at 2nd post-Newtonian order and those from numerical relativity. For each configuration, we compute the kick of the final black hole. We use the kick estimates from the series with anti-aligned spins to fit the parameters in the \KKF{,} and verify that the recoil along the direction of the orbital angular momentum is $\propto \sin\theta$ and on the orbital plane $\propto \cos\theta$, with $\theta$ the angle between the spin directions and the orbital angular momentum. We also find that the black hole spins can be well estimated by evaluating the isolated horizon spin on spheres of constant coordinate radius.Comment: 15 pages, 10 figures, replaced with version accepted for publication in PR

Supermassive recoil velocities for binary black-hole mergers with antialigned spins

Recent calculations of the recoil velocity in binary black hole mergers have found the kick velocity to be of the order of a few hundred km/s in the case of non-spinning binaries and about $500$km/s in the case of spinning configurations, and have lead to predictions of a maximum kick of up to $1300$km/s. We test these predictions and demonstrate that kick velocities of at least $2500$km/s are possible for equal-mass binaries with anti-aligned spins in the orbital plane. Kicks of that magnitude are likely to have significant repercussions for models of black-hole formation, the population of intergalactic black holes and the structure of host galaxies.Comment: Final version, published by Phys. Rev. Lett.; title changed according to suggestion of PRL; note added after preparation of manuscrip

Gravitational recoil from spinning binary black hole mergers

The inspiral and merger of binary black holes will likely involve black holes with both unequal masses and arbitrary spins. The gravitational radiation emitted by these binaries will carry angular as well as linear momentum. A net flux of emitted linear momentum implies that the black hole produced by the merger will experience a recoil or kick. Previous studies have focused on the recoil velocity from unequal mass, non-spinning binaries. We present results from simulations of equal mass but spinning black hole binaries and show how a significant gravitational recoil can also be obtained in these situations. We consider the case of black holes with opposite spins of magnitude $a$ aligned/anti-aligned with the orbital angular momentum, with $a$ the dimensionless spin parameters of the individual holes. For the initial setups under consideration, we find a recoil velocity of V = 475 \KMS a. Supermassive black hole mergers producing kicks of this magnitude could result in the ejection from the cores of dwarf galaxies of the final hole produced by the collision.Comment: 8 pages, 8 figures, replaced with version accepted for publication in Ap

How black holes get their kicks: Gravitational radiation recoil revisited

Gravitational waves from the coalescence of binary black holes carry away linear momentum, causing center of mass recoil. This "radiation rocket" effect has important implications for systems with escape speeds of order the recoil velocity. We revisit this problem using black hole perturbation theory, treating the binary as a test mass spiraling into a spinning hole. For extreme mass ratios (q = m1/m2 << 1) we compute the recoil for the slow inspiral epoch of binary coalescence very accurately; these results can be extrapolated to q ~ 0.4 with modest accuracy. Although the recoil from the final plunge contributes significantly to the final recoil, we are only able to make crude estimates of its magnitude. We find that the recoil can easily reach ~ 100-200 km/s, but most likely does not exceed ~ 500 km/s. Though much lower than previous estimates, this recoil is large enough to have important astrophysical consequences. These include the ejection of black holes from globular clusters, dwarf galaxies, and high-redshift dark matter halos.Comment: 4 pages, 2 figures, emulateapj style; minor changes made; accepted to ApJ Letter

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.

Construction and testing of a low-cost device for the collection of rainfall samples destined for stable isotope analysis

Oxygen- and hydrogen-isotope ratios in rainfall provide important hydroclimatic information, yet despite a global network of rainfall isotope measurements, significant geographical gaps exist in data coverage, with only three long-term stations spanning the southern African region. Project-based, ad hoc collections of rainfall for isotope analysis can improve this coverage. However, all rainfall samples that are destined for stable isotope analysis must be collected in such a way to avoid evaporation and resultant isotope fractionation. While such rainwater collectors are available commercially, both the product and shipping are prohibitively costly. We describe the construction of a simple rainfall collector using a design from the literature and materials that are readily available in South African hardware stores. Our rainwater collector can be constructed for the much lower cost of just under ZAR820 in comparison with the cost of ZAR9300 inclusive of shipping from commercial outlets (2022 prices). Our design modifications have the added advantage of portability, with the rainwater collector housed in a bucket with a handle. The device was tested by comparing its performance, in terms of evaporative water loss and isotopic fractionation, with that of an open bottle, using tap water in both cases. Testing confirmed that the collector prevented evaporation over a one-week period, indicating that it is suitable for weekly or more frequent sampling of rainfall. Although the design described was based on materials procured in South Africa, it could easily be adapted for construction elsewhere

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

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to non-reflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black-hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have been appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the non-axisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.Comment: 9 pages, 6 figures, final version to appear in PR