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.

Gravitational Radiation from Plunging Orbits - Perturbative Study -

Numerical relativity has recently yielded a plethora of results about kicks from spinning mergers which has, in turn, vastly increased our knowledge about the spin interactions of black hole systems. In this work we use black hole perturbation theory to calculate accurately the gravitational waves emanating from the end of the plunging stage of an extreme mass ratio merger in order to further understand this phenomenon. This study focuses primarily on spin induced effects with emphasis on the maximally spinning limit and the identification of possible causes of generic behavior. We find that gravitational waves emitted during the plunging phase exhibit damped oscillatory behavior, corresponding to a coherent excitation of quasi-normal modes by the test particle. This feature is universal in the sense that the frequencies and damping time do not depend on the orbital parameters of the plunging particle. Furthermore, the observed frequencies are distinct from those associated with the usual free quasi-normal ringing. Our calculation suggests that a maximum in radiated energy and momentum occurs at spin parameters equal to $a/M=0.86$ and $a/M=0.81$, respectively for the plunge stage of a polar orbit. The dependence of linear momentum emission on the angle at which a polar orbit impacts the horizon is quantified. One of the advantages of the perturbation approach adopted here is that insight into the actual mechanism of radiation emission and its relationship to black hole ringing is obtained by carefully identifying the dominant terms in the expansions used

The effect of gravitational-wave recoil on the demography of massive black holes

The coalescence of massive black hole (MBH) binaries following galaxy mergers is one of the main sources of low-frequency gravitational radiation. A higher-order relativistic phenomenon, the recoil as a result of the non-zero net linear momentum carried away by gravitational waves, may have interesting consequences for the demography of MBHs at the centers of galaxies. We study the dynamics of recoiling MBHs and its observational consequences. The ``gravitational rocket'' may: i) deplete MBHs from late-type spirals, dwarf galaxies, and stellar clusters; ii) produce off-nuclear quasars, including unusual radio morphologies during the recoil of a radio-loud source; and iii) give rise to a population of interstellar and intergalactic MBHs.Comment: emulateapj, 5 pages, 2 figures, to appear in the ApJ Letter

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

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

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

Using graphic novels to teach economics content to high school students with extensive support needs.

The purpose of social studies instruction in school is to facilitate the growth of competent citizens (National Council for the Social Studies [NCSS], 2013). Despite the recognized benefit of social studies instruction, emphasis on this subject has decreased over time, and has ultimately been termed a “dispensable subject” (Fitchett & Haefner, 2010). Social studies is an even more marginalized subject area for students with disabilities (Zakas et al., 2013). Expanding the research in this area is not only necessary to improving social studies academic content acquisition but is also likely to facilitate greater independence for students post-school – and by extension, improve their quality of life (White et al., 2018). Graphic novels are a popular independent reading choice for both children and adults; however, only recently have graphic novels started appearing as instructional materials in classrooms. Students gravitating to GNs for independent reading prompted the beginning of their use in the mainstream English language arts (ELA) classroom (Barter-Storm & Wik, 2020). The purpose of this study was to investigate any potential differences in student outcomes (i.e., social studies content acquisition and student engagement) when using graphic novels (GN) or traditional adapted informational text (TAIT) to teach economics concepts to high school students with ESN. Another purpose of this study was to understand both classroom teachers’ and students’ perceptions of the use of graphic novels to teach social studies content. While this study did not demonstrate clear and consistent separation of the two conditions, there were points at which GNs appear to be associated with higher engagement and content acquisition. Another finding of this study, although not addressed as a specific research question, was that text preference appeared to predict both engagement and content acquisition

The reactivity of [Pt₂(μ-S)₂(PPh₃)₄] towards difunctional chloroacetamide alkylating agents: Formation of cyclized or bridged products

The reactions of [Pt₂(μ-S)₂(PPh₃)₄] towards some bis(chloroacetamide) alkylating agents have been investigated. Reaction with one mole equivalent of the hydrazine-derived compound ClCH₂C(O)NHNHC(O)CH₂Cl led to the cyclized product [Pt₂{SCH₂C(O)NHNHC(O)CH₂S}(PPh₃)₄]²⁺ which showed two different PPh₃ environments in the ³¹P{1H} NMR spectrum, as a result of non-fluxional behavior of the dithiolate ligand in solution. Reactions of [Pt₂(μ-S)₂(PPh₃)₄] with the ortho and para isomers of the phenylenediamine-derived bis(chloroacetamides) ClCH2C(O)NHC6H4NHC(O)CH2Cl gave tetrametallic complexes containing two {Pt₂S₂} moieties spanned by the CH₂C(O)NHC₆H₄NHC(O)CH₂ group. Both the ortho and para isomers were crystallographically characterized; in the ortho isomer there is intramolecular CO=H–N and S•••H–N hydrogen bonding involving the two amide groups