Large Merger Recoils and Spin Flips from Generic Black-Hole Binaries Manuela Campanelli Rochester Institute of Technology

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3-5-2007 Large Merger Recoils and Spin Flips from Generic Black-Hole Binaries Manuela Campanelli Rochester Institute of Technology

Carlos O. Lousto Rochester Institute of Technology

Yosef Zlochower Rochester Institute of Technology

David Merritt Rochester Institute of Technology

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Recommended Citation Manuela Campanelli et al 2007 ApJ 659 L5 https://doi.org/10.1086/516712

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For more information, please contact [email protected]. arXiv:gr-qc/0701164v3 2 Mar 2007 obMmra rv,Rcetr e ok14623 York New Rochester, Drive, Memorial Lomb obMmra rv,Rcetr e ok14623 Technolo York New of Rochester, Institute Drive, Rochester Memorial Lomb Sciences, Mathematical of hsc n srnm,TeUiest fTxsa Brownsvil at Texas of 78520 University Texas The Brownsville, Astronomy, and Physics a togeeto h egrtm n energy- and time merger the on effect strong momentum) aligned angular a either orbital shown case has that the was (in with it spin counter-aligned where the or of (2006c) direction al. the et that Campanelli intro were in binaries duced black-hole highly-spinning of lations optd npriua,teacrt calculations wi ratio was accurate binaries, re- mass quasi-circular maximum remnant non-spinning the the of that velocity post-merger indicate particular, coil (2006) the al. In González et where of of (2006), velocity al. computed. González (2006), et recoil and al. et (2006e) the Herrmann al. were (2005), et holes Baker Campanelli black in al. mass et with unequal studied Baker Non-spinning 2006; were theory al. et 2006c,d). separations post-Newtonian (Buonanno agreement initial good to gener- very large waveforms matched with and successfully binaries 2006) radiation, from (Pretorius gravitational ated motion al. et the elliptical including Baker of on 2006b; effects detail, al. 18 et the in un- (Campanelli past 2006b), orbits our studied few the last in were the Within achieved binaries Non-spinning been equal-mass mergers. black-hole-binary has realized. this of progress derstanding 2006a) being al. rapid finally et months Baker the is 2006a; With al. goal et galaxy. Campanelli (Pretorius host techniques 2005; the numerical in from that breakthroughs remnant recoils recent the merger eject large lin for can of responsible radiation momentum the gravita- including ear the in emitted, of is is most It radiation where tional ringdown. regime bina- and merger black-hole non-linear merger this generic through inspiral of from evolution ries accurate the been 2 3 1 n ftemjrgaso ueia eaiiyhas relativity numerical of goals major the of One rpittpstuigL using 2008 typeset Preprint 6, February version Draft etrfrGaiainlWv srnm,Dprmn of Department Astronomy, Wave Gravitational for Center eateto hsc,RcetrIsiueo Technology, of Institute Rochester Physics, of Department etrfrCmuainlRltvt n rvtto,Scho Gravitation, and Relativity Computational for Center ffteobtlpae hsvlesae onal 00k s km 4000 nearly to scales value This plane. orbital the off ag eolvlct pn h osblt htamre bi merged headings: a galaxy.Subject that host massive possibility a the of opens velocity recoil large ihat-lge spins, anti-aligned with hntiea ag stemxmmkc rmnnsinn bin non-spinning from kick maximum the 103 by as flipped large as twice than n egrfor merger and 0 ossso niiilynnsinn oeobtn large a configur orbiting hole Our non-spinning spins. initially misaligned an with of consists holes black mass unequal . 8) ihtesi ieto oriented direction spin the with 885), AG EGRRCISADSI LP RMGNRCBLACK-HOLE GENERIC FROM FLIPS SPIN AND RECOILS MERGER LARGE erpr h rtrslsfo vltoso eei black- generic of evolutions from results first the report We q = m aul Campanelli Manuela 1 1. /m A INTRODUCTION T ◦ 2 E tl mltajv 12/01/06 v. emulateapj style X ihrsett h nta pndrcino h agrhole larger the of direction spin initial the to respect with ∼ ≈ lc oepyis–glxe:nce rvttoa waves gravitational – nuclei galaxies: – physics hole black risadfidta h enn eevsasbtnilkick substantial a receives remnant the that find and orbits 2 1 / ,is 3, a/m ∼ = 7 ms km 175 1 alsLousto Carlos , ± 0 . yn nteobtlpaeta rdcsakc of kick a produces that plane orbital the in lying 5 rf eso eray6 2008 6, February version Draft − 1 − Simu- . 45 y 78 gy, ◦ ABSTRACT ihrsett h ria ln.W rc h inspiral the track We plane. orbital the to respect with th le, 85 ol - - 2,1 oe Zlochower Yosef , iee ee ihms lc oe ihaseicspin specific a with hole, black a of high-mass con- evolve a scenario and here, the design In sidered now binary. black-hole can prototypical we truly simulations calculation, gained recoil knowledge these the the from With of entirely. case neglected were the spins in and gen of mergers, coupling) binary spin-orbit proper- recoil, precession, astrophysical (e.g. important ties some suppressed which magni- same the having direction). spins and individual tude momen- angular with orbital (but the tum indi- with aligned with and not binaries spins precession state. equal-mass vidual spin corotating for effects (2006e) a studied tidal were into al. spin-flips et binary non-linear Campanelli al. a the in et drive Campanelli Finally to that weak In found too were was infinity. it to (2006d) radiated momentum 97 ln ihthe with along 1997) larger alone. magnitude unequal-masses to of to due order due recoil an recoil the maximum than the more that simulations than show be The letter can this spin kick. the in recoil report hori- the significant we individual of a that initial flip and the spin spin, to significant zon respect a with axis, 45 spin points spin manifest remnant hole will the configuration larger of This the precession of plane. orbital spin the the below that such is ration ftetohlsi 1 is holes ratio mass two The the spin. negligible of having hole smaller a with rd ffie ieaearne bu h coordinate the about arranged ‘moving are refined a approach size this provide fixed In of to refinement. grids driver mesh the al. style refinement et 1987; boxes’ (Schnetter Shapiro mesh Carpet al. using and the et Baumgarte 2004) (Nakamura use We BSSN sets 1995; formulation). 2006a) 1999) the evolve Nakamura on al. data and et We Shibata based (Campanelli is binary approach (which puncture data. hole moving initial compute black LazEv to these thorn 2004) l h rvossmltoscnandsymmetries contained simulations previous the All euetepntr prah(rntadBrügmann and (Brandt approach puncture the use We a/m ,rpdysinn oe(pcfi spin (specific hole spinning rapidly r, aycnb jce vnfo h nucleus the from even ejected be can nary − 0 = 1 Zohwre l 05 mlmnaino the of implementation 2005) al. et (Zlochower to,wihhsams ai f2:1, : 2 of ratio mass a has which ation, o aial pnighls uha Such holes. spinning maximally for oebnre,ie iaycontaining binary a i.e. binaries, hole . re.Termatsi ieto is direction spin remnant The aries. 8 telretcniee hsfr,merges far), thus considered largest (the 885 2,1 epromdascn run second a performed We . ai Merritt David , 2. . 9 n h nta iayconfigu- binary initial the and 99, TECHNIQUES eaiiy–gravitation – relativity – TwoPunctures f44k s km 454 of ∼ BINARIES 80k s km 1830 1,3 − 1 a/m more , Asr tal. et (Ansorg − = 1 eric ◦ 2

500 TABLE 1 Vx Vy Initial data parameters for the SP6 (top) and SP2 Vz (bottom) configurations. mp is the puncture mass 300 V parameter of the two holes. SP6 has spins S~1 = (0,S, −S) ) −1 and S~2 = (0, 0, 0), momenta P~ = ±(Pr,P⊥, 0), puncture positions ~x1 = (x+, d, d) and ~x2 = (x−, d, d), and masses m1 100 and m2. While SP2 has spins S~1 = −S~2 = (0,S, 0), puncture Vrecoil (km s positions ~x1 = −~x2 = (x, 0, 0), and momenta −100 P~1 = −P~2 = (0,P, 0).

mp/M 0.3185 d/M 0.0012817 m1/M 0.6680 −300 x+/M 2.68773 Pr/M −0.0013947 m2/M 0.3355 100 150 200 250 300 2 t/M x−/M −5.20295 P⊥/M 0.10695 S/M 0.27941 2 mp/M 0.430213 x/M 3.28413 S/M 0.12871 Fig. 1.— The recoil velocities for the SP6 configurations as P/M 0.13355 m/M 0.5066 measured for an observed at r = 30M. centers of both holes. The Carpet code then moves these fine grids about the computational domain by following for calculating the spin direction is reasonably accurate the trajectories of the two black holes. We measure for our choice of coordinates. The final horizon spin is the horizon spin (magnitude and direction) using the flipped by 103◦ with respect to the initial spin of the techniques detailed in Campanelli et al. (2006e). larger individual horizon and 33◦ with respect to the initial orbital angular momentum. 3. RESULTS The remnant hole acquires a significant recoil velocity −1 The initial data parameters for our SP6 configuration of V~recoil = (−208 ± 30, −48 ± 7, 424 ± 10)km s (see (i.e. generic binary configuration), which were obtained Fig. 1), which makes an angle of 27◦ with respect to the using the 3PN equations of motion, are given in Table 1. initial orbital angular momentum and 135◦ with respect Note that the binary has a small inward radial velocity to the initial spin. We measured this kick by calculating (that we obtain from the post-Newtonian inspiral.) The the radiated linear momentum (Campanelli and Lousto initial orbital plane coincides with the xy plane. 1999) based on the ℓ = 2 through ℓ = 4 modes of ψ4. We tested our code with mesh refinement by evolving We extracted these modes at r = 25M, 30M, 35M, 40M the SP3 configuration of Campanelli et al. (2006e). For and then extrapolated the radiated momenta calculated this test we evolved SP3 with three different grid con- at these radii to r = ∞ using a linear (least-squares) fit figuration with finest resolutions of M/32, M/40, M/52 (we excluded the initial data burst from this momentum respectively, and 6 levels of refinement. We placed the calculation). The quoted errors in V~recoil are the differ- refinement boundaries at the same coordinate distance ences between the linear extrapolation and a quadratic from the punctures for each configuration. We confirmed extrapolation. This recoil velocity of 454 ± 25kms−1 is that the waveforms converge to fourth order and agree more than double the maximum recoil velocity found for with our unigrid SP3 evolution. non-spinning holes (González et al. 2006) even including We ran the SP6 run with 7 levels of refinement, with a small eccentricity effects (Sopuerta et al. 2006). Further- finest resolution of M/43.6. The outer boundaries were more, the spin-induced recoil in the xy plane might be placed at 250M. We tracked the individual horizon spins offset by the mass-difference-induced recoil, potentially throughout the evolution and found no significant spin- implying that a rotation of the spin about the z-axis may up of the smaller (initially non-spinning) hole (the value lead to a significantly larger in-plane component of the of a/m at merger was ∼ 10−4). The larger black hole, on ◦ recoil velocity. Further study will be needed to determine the other hand, showed a significant 45 angle of spin- if the mass-difference-induced recoil is (partially) aligned ~merger 2 precession, with final spin (at merger) S1 /M = or counter-aligned with the spin-induced recoil. (−0.262, 0.189, −0.214). During the evolution the binary performed ∼ 1.8 orbits prior to the formation of the com- 4. DISCUSSION mon apparent horizon (CAH). The first common horizon We studied, for the first time using fully non-linear nu- was detected at tCAH/M = 197.96 ± 0.07. The common merical relativity, a realistic astrophysical configuration horizon had mass MH/M = 0.9781 ± 0.0001 indicating of unequal mass, spinning black holes starting from a that (2.19 ± 0.01)% of the mass was converted into grav- slightly elliptical orbit, with radial inward velocity as pre- itational radiation. The spin of the remnant horizon was dicted by post-Newtonian theory, for large initial separa- ~ 2 Srem/M = (−0.0397 ± 0.0005, 0.242 ± 0.002, 0.4097 ± tions. Our main new result is that the spin component to 0.0002). The ADM angular momentum for this system is the recoil velocity may produce the leading contribution. 2 J~ADM/M = (0, 0.27941, 0.56447), thus we predict that This is suggested by the fact that the z-component of 2 the radiated angular momentum is J~rad/M = (0.0397 ± the recoil velocity, which is not present for non-spinning 0.0005, 0.037±0.002, 0.1548±0.0002). The measured ra- binaries, is the dominant component. This also can be diated mass and angular momentum, based on the ℓ =2 seen from the 2nd post-Newtonian expressions for the through ℓ = 4 modes of ψ4 were Erad/M = 0.0218 ± radiated linear momentum (Kidder 1995) ~ 0.0004 and Jrad = (0.04 ± 0.01, 0.04 ± 0.01, 0.16 ± 0.01), ˙ 8 µ2m which agree well with the remnant horizon parameters. P~ = − 4r ˙(~v × ∆)~ − 2v2(ˆn × ∆)~ 15 r5 Note that the agreement in J~ between the horizon n rad ~ ~ spin and radiation calculation indicates that our method − (ˆn × v) 3r ˙(ˆn · ∆) + 2(~v · ∆) , (1) h io 3 where ~x ≡ ~x1 − ~x2, r ≡ |~x|, ~v = d~x/dt,n ˆ ≡ ~x/r, µ ≡ 5. ASTROPHYSICAL IMPLICATIONS ~ ~ ~ m1m2/m, m = m1 + m2, ∆ ≡ m(S2/m2 − S1/m1), and A number of arguments (Shapiro 2005; Gammie et al. an overdot denotes d/dt. 2004) suggest that spins of supermassive black holes Based on this expression we can predict that the maxi- (SMBHs) are close to maximal, a/m ∼> 0.8, and per- mum recoil velocity is reached for equal mass black holes haps as great as 0.99 (Reynolds et al. 2005). Mass ratios with opposite (and maximal) spins lying on the orbital of binary SMBHs are poorly constrained observation- plane since all four terms add constructively to the ra- ally, but the luminous galaxies known to harbor SMBHs diated momentum. We performed one additional run, are believed to have experienced a few to several major denoted by SP2, with anti-aligned spins of magnitude mergers (mass ratios 0.3 ∼< q ∼< 1) over their lifetimes a/m ± 0.5 lying initially along the y-axis as reported in (Haehnelt and Kauffmann 2002; Merritt 2006); mergers ~ −1 Table 1. We obtain a Vrecoil = (0, 0, 1830 ± 30)km s . with q ≈ 1 were more common in the past. Together By rescaling this to maximal spins we obtain essentially with the results discussed above, these arguments sug- double those values raising the maximum recoil of spin- gest that recoil velocities for binary SMBHs in galactic −1 ning holes to almost 4000 km s . nuclei are often of order ∼ 103 km s−1. Here, we consider Equation (1) also allows us to propose an empirical some consequences of such large recoil velocities. formula for the total recoil velocities 4 Ejection: Central escape velocities from giant ellipti- −1 < ~ cal galaxies and spiral galaxy bulges are 450 km s ∼ Vrecoil(q, ~α)= vm eˆ1 + v⊥(cos ξ eˆ1 + sin ξ eˆ2)+ vk eˆz, −1 −1 ve < 2000 km s , dropping to < 300 km s in 2 ∼ ∼ q (1 − q) q dwarf elliptical (dE) and dwarf spheroidal (dSph) galax- vm = A 1+ B , (1 + q)5 (1 + q)2 ies (Merritt et al. 2004). Recoil velocities as large as −1 q2 103 km s would easily eject SMBHs from dE and dSph v = H αk − qαk , ⊥ (1 + q)5 2 1 galaxies, and in fact there is little evidence for SMBHs in these galaxies. However, we note that the mass de- q2 2 v = K cos(Θ − Θ ) α⊥ − qα⊥ , (2) pendence of spin-dominated kicks, Vrecoil ∼ q , implies k 0 (1 + q)5 2 1 that recoil velocities might only infrequently be as large as in the equal-mass case. If the tight empirical relations ~ 2 between SMBH mass and luminous galaxy properties where ~αi = Si/mi , the index ⊥ and k refer to perpen- dicular and parallel to the orbital angular momentum re- (Ferrarese and Merritt 2000; Marconi and Hunt 2003) spectively,e ˆ1, eˆ2 are orthogonal unit vectors in the orbital are to be maintained, peak recoil velocities are con- −1 plane and ξ measures the angle between the unequal mass strained to be ∼< 500 km s (Libeskind et al. 2006); and spin contribution to the recoil velocity in the orbital the upper limit on Vrecoil is relaxed if most of the plane. The constants H and K can be determined from merger-induced growth of SMBHs took place at low newly available runs. The angle Θ is defined as the angle redshifts (z ∼< 2) when potential wells were deeper between the in-plane component of ∆~ and the infall direc- (Libeskind et al. 2006). Ejection of SMBHs from shal- tion at merger. We have confirmed this cos Θ dependence low potential wells at high redshift implies a maximum by evolving a set of runs similar to SP2 but with initial z at which the progenitors of present-day SMBHs could spins rotated by δΘ = π/4, π/2, and π. The resulting have started merging (Merritt et al. 2004), and the exis- kicks were well modeled by a cos(Θ − Θ0) dependence, tence of bright quasars at z ≈ 6 is difficult to reconcile −1 > 2 −1 with Vz = (1873±30)km s cos[δΘ−(0.18±0.02)]. Note with recoil velocities ∼ 10 km s unless their SMBHs that we measured a maximum kick of (1830 ± 30)km s−1 grew very quickly via accretion (Haiman 2004). However for δΘ = 0 and δΘ = π, and a minimum kick of we note that these and similar conclusions are based on (352±10)km s−1 for δΘ= −π/2. This will be the subject an assumed mass ratio dependence for the kicks that is of an upcoming paper by the authors. The total recoil invalid if recoil velocities are dominated by spin effects. velocity also acquires a correction (Sopuerta et al. 2006) Displacement: The long return time for a SMBH for small eccentricities, e, of the form V~e = V~recoil (1 + e). ejected near escape velocity implies a substantial prob- From González et al. (2006) A =1.2 × 104 kms−1 and ability of finding a displaced SMBH in a luminous E B = −0.93. From fits to Herrmann et al. (2007) and galaxy, especially if the latter was the site of a recent −1 merger (Merritt et al. 2004; Madau and Quataert 2004; Koppitz et al. (2007) we find H = (7.3±0.3)×103 kms Vicari et al. 2006). A recoiling SMBH carries with it ma- and from SP2 and Gonzalez et al. (2007) (which ap- terial that was orbiting with velocity v > V before peared after this paper had been submitted) we find ∼ recoil 4 −1 the kick; the size of the region containing this mass is K cos(Θ−Θ0)=(6, −5.3)×10 kms respectively. Note 2 the sign difference showing some of the Vrecoil dependence GM• −2 ve 2 ≈ 1 pc M8σ200 (3) on Θ. Vrecoil Vrecoil The in-plane recoil velocity for our SP6 configuration 8 ◦ where M8 is the SMBH mass in units of 10 M⊙ and σ200 is consistent with Eq. (2) with ξ ≈ 88 , however our sim- −1 ulation shows strong precession of the spin near merger, is the nuclear velocity dispersion in units of 200 km s . where a large fraction of the recoil velocity is built up, This radius is sufficient to include the inner accretion disk hence it is difficult to accurately determine the spin pa- and the broad-line region gas, implying that a kicked BH rameters ~α and Θ to be used in Eq. (2). can continue shining for some time as a quasar. Plau- sibility of models that explain the “naked” quasar HE 4 After completion of this work we become aware of a new paper 0450-2958as an ejected SMBH (Haehnelt et al. 2006) are Baker et al. (2007e) also modeling v⊥ enhanced by the larger kick velocities found here, since 4

−1 ve from the nearby galaxy is ∼> 500 km s ; however verifying the spin-flip phenomenon first discussed by the presence of spectral features associated with narrow Merritt and Ekers (2002). Thus, our simulation repre- emission line region gas in the quasar is still difficult to sents a possible model for the merger process responsible reconcile with the recoil hypothesis (Merritt et al. 2006). for generating radio sources with changing jet directions. Galaxy cores: The kinetic energy of a displaced SMBH In particular, the highly-spinning large mass black hole is transferred to the stars in a galactic nucleus via dy- merging with the smaller mass non-spinning hole is a pos- namical friction, lowering the stellar density and enlarg- sible model for both the gradual semi-periodic deviations ing the core before the hole returns to its central lo- of the jet directions from a straight line (Komossa 2006) cation (Merritt et al. 2004; Boylan-Kolchin et al. 2004). due to precession of the spin (and hence jet) direction, “Damage” to the core is maximized for Vrecoil/ve ≈ 0.7 and the abrupt change in jet direction forming X-shaped (Merritt et al. 2004), hence the effect could be large even patterns (Parma et al. 1985; Leahy and Parma 1992). in the brightest E galaxies. Observed core masses are mostly in the range 0.5 − 1.5M•, consistent with the cores having been generated by binary SMBHs without We thank Erik Schnetter for valuable discussions the help of kicks (Merritt 2006); however a significant and providing Carpet. We thank Marcus Ansorg for fraction have core masses exceeding 2M• suggesting an providing the TwoPunctures initial data thorn and additional contribution from recoils. Anomalously large Johnathan Thornburg for providing AHFinderDirect. cores in BCG’s (“brightest cluster galaxies”) might be We gratefully acknowledge NSF for financial support explained in this way, since these galaxies have experi- from grant PHY-0722315. D. M. was supported by enced the largest number of mergers; this explanation grants AST-0420920 and AST-0437519 from the NSF would lessen the necessity for alternatives that require and grant NNG04GJ48G from NASA. Computational BCGs to contain hypermassive BHs (Lauer et al. 2006). resources were provided by Lonestar cluster at TACC. Jet Directions: We measure both a significant pre- M.C. thanks the Center for Gravitational Wave Astron- merger spin precession of ∼ 45◦ and a change in ex- omy, University of Texas, Brownsville for travel and com- cess of 90◦ between the initial and final spin vectors, puting support.

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