Table Of Content

Boosting jet power in black hole spacetimes David Neilsen1,2, Luis Lehner2,3,4, Carlos Palenzuela5,6, Eric W. Hirschmann1, Steven L. Liebling7, Patrick M. Motl8, Travis Garrett2,6 1Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA, 2Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5, Canada, 3Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada, 4CIFAR, Cosmology & Gravity Program, Canada, 5Canadian Institute for Theoretical Astrophysics, Toronto, Ontario M5S 3H8, Canada, 6Department of Physics & Astronomy, Louisiana State University, Baton Rouge, LA 70802, USA, 7Department of Physics, Long Island University, New York 11548, USA, 8Department of Science, Mathematics and Informatics, Indiana University Kokomo, Kokomo, IN 46904-9003, USA (Dated: January 13, 2011) 1 1 The extraction of rotational energy from a spinning black hole via the Blandford-Znajek mecha- 0 nismhaslongbeenunderstoodasanimportantcomponentinmodelstoexplainenergeticjetsfrom 2 compact astrophysical sources. Here we show more generally that the kinetic energy of the black n hole, both rotational and translational, can be tapped, thereby producing even more luminous jets a powered by the interaction of the black hole with its surrounding plasma. We study the resulting J Poyntingjetthatarisesfromsingleboostedblackholesandbinaryblackholesystems. Inthelatter 2 case, we find that increasing the orbital angular momenta of the system and/or the spins of the 1 individual black holes results in an enhanced Poynting flux. ] E I. INTRODUCTION independentoftheirinclination, astrophysicaljetsmight H be powered by the efficient extraction of both rotational . and translational kinetic energy of black holes, and in- h Enormously powerful events illuminate the universe ducing even more powerful jets than the standard BZ p that challenge our understanding of the cosmos. Indeed, mechanism would suggest. - intenseelectromagneticemissionsoforder(cid:38)1051ergs[1– o 3] have been routinely observed in supernovae, gamma Galactic mergers provide a likely scenario for the pro- r t ray bursts (GRBs), and active galactic nuclei (AGNs), duction of the binary black hole systems considered s a forexample. However,despiteimportanttheoreticaland here [12, 13]. In such a merger, the supermassive black [ observational advances, we still lack a thorough under- holes associated with each galaxy will ultimately form a standingofthesesystems(e.g.[4]). Intenseobservational binary in the merged galaxy. A variety of interactions 2 v and theoretical efforts are ongoing in order to unravel will tighten the black hole binary. Eventually the dy- 1 these fascinating phenomena. While the full details re- namics of the system will be governed by gravitational 6 main elusive, one of the natural ingredients in theoreti- radiationreactionwhichdrivesthebinarytomerge. The 6 cal models is the inclusion of a rotating black hole which circumbinary disk will likely be magnetized and thereby 5 serves to convert binding and rotational energy of the anchor magnetic field lines, some of which will traverse 2. system to electromagnetic radiation in a highly efficient the central region containing the binary. Preliminary 1 manner. The starting point for these theoretical mod- observational evidence for supermassive black hole bi- 0 els can be traced back to ideas laid out by Penrose [5] naries resulting from galactic mergers has already been 1 and Blandford and Znajek (BZ) [6], which explain the presented [14]. : v extraction of energy from a rotating black hole. These An ambient magnetic field threading a spinning black i seminal studies, along with subsequent work (see refer- hole populates a low density plasma surrounding the X ences in e.g. [7–9]), have provided a basic understanding black hole as explained by BZ [6]. Even for black holes r a of highly energetic emissions from single black hole sys- with no spin, it was recently shown that the orbiting bi- tems interacting with their surroundings. nary interacting with the surrounding plasma can lead to a collimated Poynting flux [10]. In this work, we Recent work has indicated that related systems can consider this basic paradigm of energy extraction from also tap kinetic energy and lead to powerful jets [10]. black holes with the additional complexity of intrinsic Thisworkconcentratedonnon-spinningblackholesmov- black hole spin. Binaries consisting of spinning black ing through a plasma and highlighted that relative black holes demonstrate similar, albeit energetically enhanced, hole motion alone (with respect to a stationary electro- phenomenology. Furthermore, we investigate the depen- magnetic field topology at far distances from it) can in- dence of the energy flux on the black hole velocity and duce the production of jets. Furthermore, subsequent highlight a resulting strong boost in the emitted power. work [11] demonstrated that even black holes with mis- aligned spins with respect to the asymptotic magnetic In addition to exquisite and powerful electromagnetic field direction induce strong emissions with power com- detectors, soon gravitational waves will be added to the parabletothealignedcase. Thesestudiessuggestedthat, arsenal of phenomena employed to understand our cos- 2 mos. These studies suggest excellent prospects for the sothat∆t =0.4∆x oneachrefinementlevel(cid:96). Intests (cid:96) (cid:96) coincidentdetectionofbothelectromagneticandgravita- performedhereforthecoupledsystem(andinourprevi- tional signals from binary black hole systems. Certainly, ousworksfortheforce-freeMaxwellequations),thecode dualdetectionofelectromagneticandgravitationalwave demonstrates convergence while maintaining small con- signals would transform our understanding of these sys- straint residuals for orbiting black holes. Furthermore, tems and lead to the refinement of theoretical models we obtain for orbiting black hole evolutions agreemend (e.g [15–18]). with runs from other codes for the same initial data. In the remainder of this paper, we elucidate the ba- To extract physical information, we monitor the sic phenomenology arising from the interaction of bi- Newman-Penroseelectromagnetic(Φ )andgravitational 2 nary black hole systems immersed within a plasma en- (Ψ ) radiative scalars [27]. These scalars are computed 4 vironment. We focus in particular on understanding bycontractingtheMaxwellandtheWeyltensorsrespec- the Poynting flux emissions from such binaries as well tively, with a suitably defined null tetrad (as discussed as single, possibly spinning, black holes moving through in [28]), plasma. Wedescribeourequationsandassumptionsem- Φ =F nam¯b, Ψ =C nam¯bncm¯d, (1) ployedtogetherwithsomeofthedetailsofournumerical 2 ab 4 abcd implementation in Sec. II. Sec. III describes our results andtheyallowustoaccountfortheenergycarriedoffby for both single and binary black holes and we provide outgoingwavesatinfinity. ThescalarΦ (essentiallythe 2 concluding comments in Sec. IV. radialcomponentofthePoyntingvector)providesamea- sure of the electromagnetic radiation at large distances fromanisolatedsystem. However, asthesystemstudied here has a ubiquitous magnetic field, special care must II. IMPLEMENTATION DETAILS betakentocomputetheenergyflux. Weaccountforthis difficulty by subtracting the scalar Φ =−F lamb from The combined gravitational and electromagnetic sys- 0 ab Φ . Hence,fromhereforward,byΦ wemeanthediffer- tems that we consider consist of black hole spacetimes 2 2 ence Φ →Φ −Φ . The luminosities in electromagnetic in which the black holes can be regarded as immersed 2 2 0 and gravitational waves are given by the integrals of the in an external magnetic field. Such fields, as mentioned fluxes above, will be anchored to a disk. We consider this disk tobeoutsideourcomputationaldomainbutitsinfluence dEEM (cid:90) L = = lim r2|Φ |2dΩ , (2) is realized through the imposition of suitable boundary EM dt r→∞ 2 cfireoegnldadsridtoiotnnostthhoeenbmtohaugenndceaotrorirseepsshpoeofrneodauinrrogudnoelmdecatthirneic[b1al0an,cdk11mh]o.algeWsn,eiwttihce LGW = dEdGtW =rl→im∞(cid:90) 1r62π (cid:12)(cid:12)(cid:12)(cid:12)(cid:90)∞tΨ4dt(cid:48)(cid:12)(cid:12)(cid:12)(cid:12)2dΩ . (3) assumethattheenergydensityofthemagneticfielddom- We assume that the black holes are immersed in an inatesoveritstenuousdensitysuchthattheinertiaofthe initially constant magnetic field, such as one produced plasmacanbeneglected. Themagnetosphereistherefore by a distant disk surrounding the black hole system. For treated within the force-free approximation [6, 19]. We the binary systems we consider, the orbital plane of the note that the contribution of the energy density of the evolution is assumed to be aligned with that of the cir- plasma to the dynamics of the spacetime is negligible cumbinary disk. The magnetic field is anchored in the and we can ignore its back reaction on the spacetime. diskwithitsassociatedmagneticdipolealignedwiththe We use the BSSN formulation [20, 21] of the Ein- orbital angular momentum (chosen along the zˆ direc- stein equations and the force-free equations as described tion). Initially, the magnetic field is set to be perpen- in[10,11]. Wediscretizetheequationsusingfinitediffer- dicular to the velocity of the black holes and the electric encetechniquesonaregularCartesiangridanduseadap- field is set to zero. Because the electromagnetic field is tive mesh refinement (AMR) to ensure that sufficient affected by the spacetime curvature, it will be dynami- resolutionisavailablewhererequiredinanefficientman- callydistortedfromitsinitialconfigurationandgenerate ner. Weusethehadcomputationalinfrastructure,which a transient burst of both gravitational and electromag- provides distributed, Berger-Oliger style AMR [22, 23] netic waves as it settles into a physically relevant and with full sub-cycling in time, together with an improved dynamical configuration. treatment of artificial boundaries [24]. Refinement re- The initial magnitude of the magnetic field B is cho- 0 gions are determined using truncation error estimation sen to be consistent with astrophysically relevant val- provided by a shadow hierarchy [25], which adapts dy- ues [29, 30]. We present our results for a field strength namically to ensure the estimated error is bounded by which is bounded by the the Eddington magnetic field a pre-specified tolerance. Typically our adopted values strength B (cid:39) 6×104(M/108M )−1/2 G [31]. As noted (cid:12) result in a grid hierarchy yielding a resolution such that above, for these values the plasma’s energy is several or- 40 grid points in each direction cover each black hole. ders of magnitude smaller than that of the gravitational Weuseafourthorderaccuratespatialdiscretizationand field. Thus, although the plasma is profoundly affected a third order accurate in time Runge-Kutta integration by the black holes, it has a negligible influence on their scheme [26]. We adopt a Courant parameter of λ = 0.4 dynamics. 3 collimated luminosity achieved once the system reaches a quasi-stationary state (in other words, after the initial transient stage) for the spinning and non-spinning cases in Fig. 2. Several key observations are evident from the figure. For v = 0, the electromagnetic energy luminosity does not vanish for the spinning black hole, while it does vanish for the non-spinning black hole. This is expected, as the spinning black hole interacts with a surrounding plasma and radiates by the Blandford-Znajek mechanism [6]. This luminosity results from the plasma’s FIG.1: Zoom-inoftheelectromagneticemission|rΦ |2 from ability to extract rotational energy from the black hole 2 a boosted black hole (with p(cid:126)=0.15xˆ). The left frame shows and power a jet with an energy luminosity scaling as the non-spinning black hole case (a = 0), while the right L ≈ Ω2 B2 [11, 32] (with Ω ≡ a/(2R ) the rota- BZ H H H frame shows the spinning case (a = 0.6). The color scale is tion frequency associated with the black hole). the same for both frames and the black hole is boosted to For v (cid:54)= 0, both the spinning and non-spinning black the right. The stronger emission in the vertically collimated holes have a non-trivial associated energy flux. In the region of the right frame is apparent. latter case this flux arises solely from the ability of the systemtotaptranslationalkineticenergyfromtheblack hole,whiletheformerresultsfromtheextractionofboth III. RESULTS translational and rotational kinetic energies. The non-spinning black hole shows the expected v2 Here we discuss our results for both boosted and dependence in the electromagnetic energy luminosity binary black hole systems. For simplicity we introduce (see Fig. 2) consistent with the membrane picture of the notation L = 1043 ergs/s and compute dimension- 43 a black hole as a conductor. Indeed, as was already ful quantities with respect to a representative system indicatedinthespinlesscase[10,11,33,34],ablackhole with total mass 108M immersed in a magnetic field (cid:12) moving (with speed v) through an ambient magnetic with strength 104 G. We explicitly provide proportion- field acquires an induced charge separation (∝ v). The ality factors for calculations for other configurations. membrane paradigm [35] of a black hole explains this Quantities in geometric units are calculated by setting induced charge by regarding the black hole as a con- G=c=1. ductor moving through a magnetic field, and hence the induced charge is analogous to the classical Hall effect. Single black holes With this observation and the induction equation, it is For single, boosted black holes, we adopt a computa- straightforward to conclude an electromagnetic energy tional domain defined by [−320mb,320mb]3 and assume flux will be produced with magnitude ∝ v2B2. Such a fixed “bare” mass of the black hole (the mass it would a quadratic dependence on speed is apparent in the have if it were static and in isolation) of mb = 1 in geo- figure. These results are also consistent with the work metric units. We set the initial linear momentum of the of [36] which studied the Poynting flux associated with a black hole to p(cid:126) = 0.05 nî (with n an integer that we moving conductor in a magnetized plasma, in particular vary between 0 and 4), and we set the intrinsic angular the motion of artificial satellites in orbit. They found momentum parameter (cid:126)a ≡ J(cid:126)/M2 to be 0 or 0.6kˆ. For that this flux obeys L ≈ (v/v )2B2 [36] where v , v alf alf these parameters we study the resulting electromagnetic the propagation speed of the Alfvén modes, is the speed collimated flux energy and its dependence on both boost of light in a force-free environment. Furthermore, a velocity and black hole spin. misalignment is expected between the collimated energy Fig. 1 illustrates the qualitative features of the elec- flux and the original magnetic field orientation such tromagnetic emission for a boosted black hole with and that tan(α) = v/v . With the cautionary note that alf without spin. A collimated emission is clearly induced measuring this angle is a delicate enterprise within Gen- along the asymptotic magnetic field direction. Signifi- eral Relativity, especially in the strongly curved region cantly,anevenstrongeremissionisobtainedforthespin- around the black hole, such a relation is manifested ning case as expected. in our results. For instance, for a = 0, p = 0.10 the x Toachieveamorequantitativeunderstanding,wecom- measured angle obeys tan(α) = 0.07 instead of the pute a measure of the collimated electromagnetic lumi- predicted 0.08 [36]. nosity,L ,byintegratingthefluxovera15◦ cone collimated of a spherical surface centered along the moving black Theluminosityforthespinningblackholealsodemon- hole with a radius r = 20m (roughly equivalent to strates the same quadratic dependence in velocity, with b 40R ,whereR istheSchwarzschildradiusoftheblack the additional component from the spin. Notice that H H hole). Wepresentourresultswithrespecttov (themea- the difference between the obtained luminosities in the sured coordinate velocity of the black hole) and plot the spinning and spinless cases remains fairly constant for 4 the different values of v. Thus, to a reasonably good Case (p ,p ) a M J x y i ADM ADM approximation, we can express the luminosity obtained 0/0 (0.00208,−0.11235) 0 1.0 0.108 as a sum of a spin dependent component and a speed u/d (0.00208,−0.11235) ±0.515 1.1 0.108 dependent one, L (cid:39) L + L , the latter collimated spin speed scaling as L = L v2 . A fit to the case a = 0 u/u (0.00208,−0.11235) 0.515 1.1 0.349 speed 2 gives L = 127 (M B )2L . Next, using this value for 2 8 4 43 the case a = 0.6, we obtain the fit for L = L = spin 1 TABLE I: Binary black hole configurations considered here. 0.87 (M8B4)2L43. We can then provide an estimate of All begin with no momentum in the z direction. the associated luminosity for general cases as follows. The spin component for the general case can be ex- pressed in terms of its dependence on the the black hole a computational domain of [−638m ,638m ]3 and con- b b spin as L = L (Ω (a)/Ω (a = 0.6))2. The boost sider configurations with individual spins either vanish- spin 1 H H component takes the already mentioned quadratic form ingorintheup(+z)ordown(−z)orientationwithspin L =L v2. magnitude|a|=0.515. Theseconfigurationsaresumma- speed 2 Therefore, we have for the estimate rized in Table I. Before discussing these configurations, we describe Lcollimated = Lspin+Lspeed, our numerical measurements which enable a quantita- (cid:18) Ω | (cid:19)2 tive comparison between the evolutions. First, we com- = L H a +L v2, 1 Ω | 2 pare the luminosities as functions of gravitational wave H 0.6 (cid:34) (cid:18) Ω | (cid:19)2 (cid:35) frequency, asthisisanobservableandallowsforadirect = 0.87 H a +127v2 L . (4) comparison of the different cases. We obtain frequencies Ω | 43 H 0.6 from the l=2,m=2 gravitational mode. Second, we compute three different luminosities for Notice that for a = 0.6, the non-rotational contribution each case: (i) the collimated luminosity L ob- collimated L to the emitted power becomes larger than the speed tainedbyintegratingtheelectromagneticfluxoveracone rotational one for speeds approximately v >0.08c. This of points within 15◦ from the center of mass of the sys- relationship, for example, would predict a luminosity for tem; (ii) the non-collimated, or “isotropic,” luminosity ana=0.95,v =0.5cblackholetobe(cid:39)36L (M B )2. 43 8 4 L obtained from the integral over an encompass- isotropic ThisphenomenologystronglysuggeststhatthePoynting ingsphereminusthecollimatedluminosityof(i);(iii)the flux can tap both rotational and translational kinetic gravitational wave luminosity, L . These different lu- GW energies from the black hole and that faster and more minosities are displayed for the three binary configura- rapidly spinning black holes have a stronger associated tions in Fig. 3. power output. Consider first the 0/0 and u/d configurations which have essentially the same total angular momentum. Ex- tensive numerical simulations (see for instance [37]) and simple estimates [38] indicate that both binaries will merge into a final black hole with essentially the same spin (a (cid:39) 0.67), and, so for late times after-merger, the expected jet structure should be quite similar, dictated by the standard BZ mechanism. The binary with individual spins aligned reaches a higher orbital velocity before merger than the previous two cases; thus, the expected maximum power should be higher. Moreover, the resulting final black hole spins faster (a (cid:39) 0.8) and thus its BZ associated power will FIG. 2: Collimated luminosity as a function of the boost ve- be higher than that of the previous cases. Fig. 3 illus- locityoftheblackholefortwodifferentspinmagnitudes. The tratesthisexpectedbehaviorbypresentingthePoynting dashed lines are obtained from a quadratic fit of the form fluxenergyvs. gravitationalwavefrequencyforthethree L = L +L v2 where L and L are two con- cases. collimated spin 2 spin 2 stants. The constant L2 is the same for both fits, supporting As evident from the figure, at low frequencies where the argument that the luminosity does contain two different theorbitaldynamicsarethesameinallcases,bothspin- components, one for spin and one for boost. ning cases have a higher output than the non-spinning one and the difference is provided by the spin contri- Binary black holes bution to the jet emission. Furthermore, both spinning We turn our attention now to the orbiting binary black cases have equal collimated power output because the hole case. We consider equal-mass configurations in spin contribution to the luminosity depends only on the which each bare black hole has mass m = 0.483 and spin magnitude. b thepairisseparatedbyadistanceD ≈16m . Weadopt We can further examine the basic relation explaining b 5 the observed flux by comparing the three cases studied. We estimate the black hole coordinate velocities v and (collimated)luminositiesatthreerepresentativefrequen- cies Ω = {1;1.5;2}10−5 [Hz/M ] (i = 1..3) before the i 8 strong non-linear interaction starts. Since for these frequencies the measured speeds for the 0/0 and u/d cases areessentiallythesame,wenoticethatthefluxofenergy contributedbythespinningblackholescanbeestimated to be: Lest(Ω)(cid:39)L (Ω)−L (Ω); (5) BZ u/d 0/0 thus, Ω (L ;L )(M B )2L Lest(M B )2L 0/0 u/d 8 4 43 BZ 8 4 43 1 (1.08; 1.62) 0.54 2 (1.83; 2.30) 0.47 3 (2.30; 2.80) 0.50 FIG. 3: Luminosity as a function of the orbital frequency for the binary black hole configurations described in Table I, Notice that the Lest remains fairly constant through assuming M = 108M and B = 104 G. Top left: the colli- BZ (cid:12) thesefrequencieswhichisevidentalsointheFig.3. With mated luminosity associated with the jets. Top right: the this value one can estimate the luminosity for the u/u isotropicluminosityrepresentingelectromagneticfluxnotas- case as: sociated with the jets. Bottom: the gravitational wave output. (cid:18)v (Ω)(cid:19)2 Lest (Ω)(cid:39)L (Ω) u/u +Lest(Ω). (6) u/u 0/0 v (Ω) BZ 0/0 wide applicability to general black hole binaries. More- Applying such expression to our representative values over,astheplasmagenerallyhasanegligibleeffectonthe we obtain, dynamicsoftheblackholes,thenoneneedsonlytoknow the dynamics of the black holes, say by numerical solu- Ω (v ;v ) (L ;Lest )(M B )2L u/u 0/0 u/u u/u 8 4 43 tion or other approximate methods, in order to estimate 1 (0.192; 0.174) (1.64; 1.85) theexpectedelectromagneticluminosity. Arecentexam- ple is the work of [39] which uses the expected (cid:39) B2v2 2 (0.206; 0.186) (2.52; 2.71) scalingfornon-spinningblackholebinariescoupledwith 3 (0.211; 0.187) (3.26; 3.42) the known distance dependence in time to obtain excel- thus the estimates are within (cid:39) 10% of the measured lentagreementwiththeobtainedluminosityfromsucha valueswhiletheblackholesaresufficientlyseparatedthat system. their jets do not strongly interact. Notice that at higher Naturally, spinning black holes produce stronger jets, frequencies the aligned (u/u) case indeed has a higher and these jets, as shown earlier [11], will be aligned with associated power. theasymptoticmagneticfielddirection[42]. Thus,there- Inallcases,asignificantnon-collimatedemissionisin- sultingelectromagneticluminositycanbeestimatedtobe duced (illustrated in the top right plot of Fig. 3) during LEM (cid:39)L +L , which can be significant andhave col spin speed themergerphase. Clearly,thesimplemindedpictureofa associatedtime-variabilitiestiedtothedynamicalbehav- jetproducedbythesuperpositionoftheorbitalandspin- ior of the system. In particular, the luminosity tied to ning effect can not fully capture the complete behavior the motion can result significantly higher than that tied at the merger epoch, although it serves to understand to the spin. In addition, eccentric orbits and spin-orbit the main qualitative features and provides a means to interactions driving orbital plane precessions can induce estimate the power of the electromagnetic emission. important variabilities that can aid in the detection of these systems. Furthermore, a significant pulse of nearly isotropic radiation is emitted during merger, thereby al- IV. FINAL COMMENTS lowing observations of the system along directions not aligned with the jet. We have studied the impact of black hole motion Consequently, binary black hole interactions with sur- through a plasma and indicated how the interaction can rounding plasmas can yield powerful electromagnetic induce powerful electromagnetic emissions even for non- outputs and allow for observing these systems through spinning black holes. Despite having examined a very both gravitational and electromagnetic radiation. Grav- small subset of the binary black hole parameter space, itational waves from these systems corresponding to the the results presented both here and in [10, 11] suggest a last year before the merger could be observed to large 6 distances with LISA (up to redshifts of 5-10 [40]) for masses (cid:39) 104−7M or earlier in the orbiting phase (cid:12) (and possibly through merger) via Pulsar Timing Ar- ray observations [41], targeting binaries with masses in M (cid:39)107−10M . Aswehaveindicatedhere,bothscenar- (cid:12) ioscanhavestrongassociatedelectromagneticemissions. Our inferred luminosities of several 1043(M B )2 ergs/s 8 4 correspondstoanisotropicbolometricfluxofF (cid:39)10−15 x erg(M B )2 /(cm2 s)thatcouldbedetectedtoredshifts 8 4 of z ≈1 and even further depending on anisotropies, depending on the efficiency of processes taping this avail- able energy and producing observable signals. FIG. 4: Electromagnetic flux corresponding to the 0/0 (top row) and u/d (bottom row) cases at times (−16.7,−2.5) hrsM and (−10.5,3.6) hrsM (with respect to the merger 8 8 timeasmarkedbythepeakinstrengthofgravitationalwave emission) respectively. The orbiting stage leaves its imprint as twisted tubes. Acknowledgments It is a pleasure to thank J. Aarons, P. Chang, B. MacNamara, K. Menou, E. Quataert and C. Thompson as well as our long time collaborators Matthew Ander- son, Miguel Megevand and Oscar Reula for useful dis- cussions and comments. We acknowledge support from NSF grants PHY-0803629 to Louisiana State Univer- sity, PHY-0969811 to Brigham Young University, PHY- FIG.5: Electromagneticfluxcorrespondingtotheu/ucaseat times (−2.5,11.6,40,68) hrsM (with respect to the merger 0969827 to Long Island University, as well as NSERC 8 timeasmarkedbythepeakinstrengthofgravitationalwave throughaDiscoveryGrant. ResearchatPerimeterInsti- emission). The orbiting behavior leaves a clear imprint in tute is supported through Industry Canada and by the theresultingfluxofenergyand,asthemergerproceedsemis- Province of Ontario through the Ministry of Research sion along all directions is evident. At late times, the system & Innovation. Computations were performed at LONI, settles to a single jet as dictated by the BZ mechanism. Teragrid and Scinet. 7 [1] M. Hamuy (2003), astro-ph/0301006. [20] T. W. Baumgarte and S. L. Shapiro, Phys. Rev. D59, [2] S. E. Woosley and J. S. Bloom, Ann. Rev. Astron. As- 024007 (1999), gr-qc/9810065. trophys. 44, 507 (2006), astro-ph/0609142. [21] M. Shibata and T. Nakamura, Phys. Rev. D52, 5428 [3] B. R. McNamara, M. W. Wise, P. E. J. Nulsen, L. P. (1995). David,C.L.Carilli,C.L.Sarazin,C.P.O’Dea,J.Houck, [22] Http://www.had.liu.edu/. M. Donahue, S. Baum, et al., Ap. J. Letters 562, L149 [23] S. L. Liebling, Phys. Rev. D66, 041703 (2002). (2001), arXiv:astro-ph/0110554. [24] L. Lehner, S. L. Liebling, and O. Reula, Class. Quant. [4] R. Fender, E. Gallo, and D. Russell (2010), 1003.5516. Grav. 23, S421 (2006). [5] R. Penrose, Riv. Nuovo Cim. 1, 252 (1969). [25] F. Pretorius, Ph.D. thesis, The University of British [6] R. D. Blandford and R. L. Znajek, Mon. Not. Roy. As- Columbia (2002). tron. Soc. 179, 433 (1977). [26] M. Anderson et al., Phys. Rev. D77, 024006 (2008). [7] H.K.Lee,R.A.M.J.Wijers,andG.E.Brown,Physics [27] E.NewmanandR.Penrose,J.Math.Phys.3,566(1962). Reports 325, 83 (2000), arXiv:astro-ph/9906213. [28] L. Lehner and O. M. Moreschi, Phys. Rev. D76, 124040 [8] R. D. Blandford, in Lighthouses of the Universe: The (2007), 0706.1319. MostLuminousCelestialObjectsandTheirUseforCos- [29] M.MassiandM.Kaufman,AstronomyandAstrophysics mology,editedbyM.Gilfanov,R.Sunyeav,&E.Chura- 477, 1 (2008). zov (2002), pp. 381–+. [30] G. B. Field and R. D. Rogers, Astrophys. J. 403, 94 [9] B. Punsly, ed., Black Hole Gravitohydromagnetics, vol. (1993). 355 of Astrophysics and Space Science Library (2008). [31] C.D.Dermer,J.D.Finke,andG.Menon,ArXive-prints [10] C.Palenzuela,L.Lehner,andS.L.Liebling,Science329, (2008), 0810.1055. 927 (2010), 1005.1067. [32] A. Tchekhovskoy, R. Narayan, and J. C. McKinney, As- [11] C.Palenzuela,T.Garrett,L.Lehner,andS.L.Liebling, trophys. J. 711, 50 (2010), 0911.2228. Phys. Rev. D82, 044045 (2010), 1007.1198. [33] C. Palenzuela, M. Anderson, L. Lehner, S. L. Liebling, [12] M. C. Begelman, R. D. Blandford, and M. J. Rees, Na- and D. Neilsen, Phys. Rev. Lett. 103, 081101 (2009), ture (London) 287, 307 (1980). 0905.1121. [13] M. Milosavljevic and E. S. Phinney, Astrophys. J. 622, [34] C. Palenzuela, L. Lehner, and S. Yoshida, Phys. Rev. L93 (2005). D81, 084007 (2010), 0911.3889. [14] J. M. Comerford et al., Astrophys. J. 698, 956 (2009), [35] K. S. Thorne, R. H. Price, and D. A. MacDonald, Black 0810.3235. holes: The membrane paradigm (1986). [15] B. F. Schutz, in Lighthouses of the Universe: The Most [36] S. D. Drell, H. M. Foley, and M. A. Ruderman, Journal Luminous Celestial Objects and Their Use for Cosmol- of Geophysical Research 70, 3131 (1965). ogy, edited by M. Gilfanov, R. Sunyeav, & E. Churazov [37] M. Hannam et al., Phys. Rev. D79, 084025 (2009), (2002), pp. 207–+. 0901.2437. [16] J. Sylvestre, Astrophys. J. 591, 1152 (2003), [38] A. Buonanno, L. E. Kidder, and L. Lehner, Phys. Rev. arXiv:astro-ph/0303512. D77, 026004 (2008). [17] J. S. Bloom, D. E. Holz, S. A. Hughes, K. Menou, [39] S. T. McWilliams (2010), 1012.2872. A. Adams, S. F. Anderson, A. Becker, G. C. Bower, [40] A. Vecchio, Phys. Rev. D70, 042001 (2004), astro- N. Brandt, B. Cobb, et al., ArXiv e-prints (2009), ph/0304051. 0902.1527. [41] P. Demorest, J. Lazio, A. Lommen, and NANOGRAV [18] E. S. Phinney, in astro2010: The Astronomy and Astro- collaboration (2009), 0902.2968. physics Decadal Survey (2009), vol. 2010 of Astronomy, [42] ThemagnitudeoftheBZ-associatedemissiondiminishes pp. 235–+. for non-aligned cases but it is nevertheless significant: [19] P. Goldreich and W. H. Julian, Astrophys. J. 157, 869 theorthogonalcaseisonlyhalfaspowerfulasthealigned (1969). case.