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When Black Holes Collide

When Black Holes Collide. Frans Pretorius Princeton University STScI Colloquium February 18, 2009. Outline I. Motivation: why explore black hole collisions? gravitational wave astronomy, studying dynamical strong-field general relativity

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When Black Holes Collide

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  1. When Black Holes Collide Frans Pretorius Princeton University STScI ColloquiumFebruary 18, 2009

  2. Outline I • Motivation: why explore black hole collisions? • gravitational wave astronomy, studying dynamical strong-field general relativity • The conventional picture of generic non-extreme-mass-ratio mergers • phases of the merger • “Newtonian” • inspiral  quasi-circular inspiral • plunge/merger • ringdown • highlights from the recent explosion of numerical results on the late-inspiral/merger phase • how well post-Newtonian techniques model the late stages of inspiral • large re-coil velocities

  3. Outline II • Is this the complete story? • theoretical studies suggests modest to high eccentricity mergers may be as likely, if not the dominant source of detectable signals • if this is the case, search strategies will need to be updated • orbital dynamics becomes much more interesting, exhibiting zoom-whirl behavior • unstable circular orbits are the key to understanding zoom-whirl behavior for elliptic orbits in general relativity • consequences for binary black hole mergers • more speculative implications for black hole/neutron star mergers • Conclusions

  4. Motivation: why explore black hole collisions? • gravitational wave astronomy • almost overwhelming circumstantial evidence that black holes exist in our universe • to obtain conclusive evidence, we need to “see” the black holes in the “light” they emit … gravitational waves. However, isolated single black holes do not radiate, so we need to look for binary mergers for the cleanest direct signature of the existence of black holes • understanding the nature of the waves emitted in the process is important for detecting such events, and moreover will be crucial in deciphering the signals • extracting the parameters of the binary • obtain clues about the environment of the binary • how accurately does Einstein’s theory describe the event?

  5. The network of gravitational wave detectors LIGO/VIRGO/GEO/TAMA LISA ground based laser interferometers space-based laser interferometer (hopefully with get funded for a 20?? Launch) LIGO Hanford LIGO Livingston ALLEGRO/NAUTILUS/AURIGA/… Pulsar timing network, CMB anisotropy resonant bar detectors Segment of the CMB from WMAP AURIGA The Crab nebula … a supernovae remnant harboring a pulsar ALLEGRO

  6. Overview of expected gravitational wave sources Pulsar timing LISA LIGO/… Bar detectors CMB anisotropy >106 M๏ BH/BH mergers 102-106 M๏ BH/BH mergers source “strength” 1-10 M๏ BH/BH mergers NS/BH mergers NS/NS mergers pulsars, supernovae EMR inspiral NS binaries WD binaries exotic physics in the early universe: phase transitions, cosmic strings, domain walls, … relics from the big bang, inflation 10-12 10-8 10-4 1 104 source frequency (Hz)

  7. Anatomy of a Merger • In the conventional scenario of a black hole merger in the universe, one can break down the evolution into 4 stages: Newtonian, inspiral, plunge/merger and ringdown • Newtonian • in isolation, radiation reaction will cause two black holes of mass M in a circular orbit with initial separation R to merge within a time tm relative to the Hubble time tH • label the phase of the orbit Newtonian when the separation is such that the binary will take longer than the age of the universe to merge, for then to be of relevance to gravitational wave detection, other “Newtonian” processes need to operate, e.g. dynamical friction, n-body encounters, gas-drag, etc. For e.g., • two solar mass black holes need to be within 1 million Schwarzschild radii ~ 3 million km • two 109 solar mass black holes need to be within 6 thousand Schwarzschild radii ~ 1 parsec

  8. Anatomy of a Merger • inspiral  quasi-circular inspiral (QSI) • In the inspiral phase, energy loss through gravitational wave emission is the dominate mechanism forcing the black holes closer together • to get an idea for the dominant timescale during inspiral, for equal mass, circular binaries the Keplarian orbital frequency offers a good approximation until very close to merger • the dominant gravitational wave frequency is twice this • Post-Newtonian techniques provide an accurate description of certain aspects of the process until remarkably close to merger • if the initial pericenter of the orbit is sufficiently large, the orbit will loose its eccentricity long before merger [Peters & Matthews, Phys.Rev. 131 (1963)] and become quasi-circular

  9. Anatomy of a Merger • plunge/merger • this is the time in the merger when the two event horizons coalesce into one • we know the two black holes must merge into one if cosmic censorship holds (and no indications of a failure yet in any merger simulations) • full numerical solution of the field equations are required to solve for the geometry of spacetime in this stage • Only within the last 3 years, following a couple of breakthroughs, has numerical relativity been able to complete the picture by filling in the details of the final, non-perturbative phase of the merger • At present two known stable formulations of the field equations, generalized harmonic[FP, PRL 95, 121101 (2005) ], and BSSN with moving punctures[M. Campanelli, C. O. Lousto, P. Marronetti, Y. Zlochower PRL 96, 111101, (2006); J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. van Meter PRL 96, 111102, (2006)] • in all cases studied to date, this stage is exceedingly short, leaving its imprint in on the order of 1-2 gravitational wave cycles, at roughly twice the final orbital frequency

  10. Anatomy of a Merger • ringdown • in the final phase of the merger, the remnant black hole “looses all its hair”, settling down to a Kerr black hole • one possible definition for when plunge/merger ends and ringdown begins, is when the spacetime can adequately be described as a Kerr black hole perturbed by a set of quasi-normal modes (QNM) • the ringdown portion of the waveform will be dominated by the fundamental harmonic of the quadrupole QNM, with characteristic frequency and decay time [Echeverria, PRD 34, 384 (1986)]:j=a/Mf , the Kerr spin parameter of the black hole

  11. Sample evolution --- Cook-Pfeiffer Quasi-circular initial data A. Buonanno, G.B. Cook and F.P.; Phys.Rev.D75:124018,2007 • This animation shows the lapse function in the orbital plane.The lapse function represents the relative time dilation between a hypothetical observer at the given location on the grid, and an observer situated very far from the system --- the redder the color, the slower local clocks are running relative to clocks at infinityIf this were in “real-time” it would correspond to the merger of two ~5000 solar mass black holes • Initial black holes are close to non-spinning Schwarzschild black holes; final black hole is a Kerr a black hole with spin parameter ~0.7, and ~4% of the total initial rest-mass of the system is emitted in gravitational waves

  12. Gravitational waves from the simulation A depiction of the gravitational waves emitted in the orbital plane of the binary. Shown is the real component of the Newman Penrose scalar y4, which in the wave zone is proportional to the second time derivative of the usual plus-polarization The plus-component of the wave from the same simulation, measured on the axis normal to the orbital plane

  13. What does the merger wave represent? • Scale the system to two 10 solar mass (~2x1031 kg) BHs • radius of each black hole in the binary is ~ 30km • radius of final black hole is ~ 60km • distance from the final black hole where the wave was measured ~ 1500km • frequency of the wave ~ 200Hz (early inspiral) - 800Hz (ring-down)

  14. What does the merger wave represent? • fractional oscillatory “distortion” in space induced by the wave transverse to the direction of propagation has a maximum amplitude DL/L~ 3x10-3 • a 2m tall person will get stretched/squeezed by ~ 6 mm as the wave passes • LIGO’s arm length would change by ~ 12m. Wave amplitude decays like 1/distance from source; e.g. at 10Mpc the change in arms ~ 5x10-17m (1/20 the radius of a proton, which is well within the ballpark of what LIGO is trying to measure!!) • despite the seemingly small amplitude for the wave, the energy it carries is enormous — around 1030 kg c2 ~ 1047 J ~ 1054 ergs • peak luminosity is about 1/100th the Planck luminosity of 1059ergs/s !! • luminosity of the sun ~ 1033ergs/s, a bright supernova or milky-way type galaxy ~ 1042 ergs/s • if all the energy reaching LIGO from the 10Mpc event could directly be converted to sound waves, it would have an intensity level of ~ 80dB

  15. Highlights of recent results: simplicity of merger waveform • the “non-linear” phase of the merger is surprisingly short • great boon for data analysis, as this suggests an efficient LIGO template bank could be compiled by stitching together quick-to-calculate perturbative waveforms, guided by a handful of numerical waveforms • to-date, the furthest the idea has been pushed is for quasi-circular inspiral of non-spinning BH’s [A. Buonanno et al., Phys.Rev.D76:104049,2007] • effective-one-body (EOB) PN inspiral connected to the 3 dominant quasi normalmodes (QNMs) • added “pseudo” 4PN term to EOB model, with coefficient determined by a best-fit match to a set of numerical results • used simulation results for final spin and black hole mass to fix the QNM frequencies and decay constants 4:1 mass ratio example

  16. Highlights of recent results: large recoil velocities • significant recoil can be imparted to the remnant black hole due to asymmetric beaming of radiation during the merger, up to 4000km/s in some cases • Herrmann et al., gr-qc/0701143; Koppitz et al., gr-qc/0701163; Campanelli et al. gr-qc/0701164 & gr-qc/0702133, Gonzalez et al, arXiv:gr-qc/0702052, Tichy & Marronetti, arXiv:gr-qc/0703075v1 • there are far reaching consequences to this, some that could be detected via electromagnetic observations, in particular for supermassive black hole mergers • offset or double galactic nuclei, displaced active galactic nuclei, wiggling jets, enlarged cores, lopsided cores, x-ray afterglows, feedback trails, off-center flares from tidally disrupted stars, hypervelocity stars, a population of galaxies without supermassive black holes, etc. • Merritt et al., ApJ. 607 (2004) L9-L12; Milosavljevic & Phinney, ApJ 622, L93(2005); Gualandris & Merrit arXiv:0708.0771 & , arXiv:0708.3083; Lippai et al. arXiv:0801.0739; Kornreich & Lovelace, arXiv:0802.2058; Devecchi et al. arXiv:0805.2609; Komossa & Merrit arXiv:0807.0223 & arXiv:0811.1037; Fujita arXiv:0808.1726 & arXiv:0810.1520 • a 2650km/s recoiling black hole could explain the emission line spectra from quasar SDSSJ092712.65+294344.0 [S. Komossa et al., ApJ.678:L81,2008]

  17. What is “wrong” with the QCI picture • If we want LIGO be anything more than a simple detector, i.e. be able to identify the gravitational waves, we need templates for all plausible sources; however • limited computational power for template searches • having too many templates increases the probability of false detections • LIGO does need to be selective in what it looks for • Recent studies suggest QCI may not be the dominant LIGO (or LISA) source • Eccentric mergers, potentially transitioning from inspiral to merger through a series of zoom-whirl orbits, may be more likely

  18. Merging with eccentricity • Binary stars are unlikely progenitors for BH binaries that could merge within the Hubble time, as such close binaries will likely evolve through a common envelope phase, causing a stellar merger before BH formation [Belczynski et al., ApJ 662, 2007]. • this cuts off the most promising channel for QCI • A promising source for stellar mass BH binaries is then n-body interactions involving BHs in dense stellar environments [e.g. Sigurdsson & Hernquist, Nature 364 (1993) , Portegies Zwart & McMilla, ApJ 528 L17 (2000), Sadowski et al., arXiv:0710.0878] • these often lead to binaries with large eccentricities that are sufficiently tight that they do not have enough time to circularize before merging • O’Leary et al. (arXiv:0807.2638) estimate 90% will have e>0.9 when entering the LIGO band, with Advanced LIGO rates of ~ 1-103/year from mergers in galactic nuclei alone • For supermassive BH mergers, studies also suggest mergers may occur with non-negligible eccentricity, e.g. Berentzen et al., arXiv:0812.2756

  19. Why may eccentric mergers be a problem? • 1 extra parameter … not too much of a issue for template searches • However, how the transition from inspiral to plunge happens could affect the feasability of present PN techniques • the expansions are accurate for adiabatic evolution of the orbital parameters, and as long as v/c < 1 • For QCI of comparable mass binaries, v/c ~ 0.2-0.3 before common horizon formation, which is one reason why PN-techniques work so well modeling the entire inspiral • For eccentric orbits v/c will become much larger

  20. Why may eccentric mergers be a problem? • a second argument given why PN matches numerical simulations so well, is the regime where it breaks down is very short, and happens well within the effective potential barrier of the spacetime and so can not leave a significant imprint on the waveform • this argument will fail if zoom-whirl behavior sets in at the transition from inspiral to merger, and this may generically happen with high-eccentricity inspirals

  21. Zoom-whirl orbits • At a first glance might look like “extreme’’ pericenter precession • examples: geodesics about a Schwarzschild BH, apoapsis 30M, inner circle is event horizon (2M), outer circle ISCO (6M) usual (but large) pericenter precession zoom-whirl orbit

  22. Zoom-whirl orbits • However, what’s different about zoom-whirl behavior is once the pericenter distance crosses the isco, you can find orbits which are essentially indistinguishable at apoapsis but that exhibit an arbitrary number of zooms per whirl at the same pericenter distance 300 zoom-whirl orbits, initial tangential velocity ranging from 0.1207600 to 0.12076290 150 “regular” orbits, initial tangential velocity ranging from 0.128 to 0.132

  23. Zoom-whirl orbits • Zoom-whirl orbits are perturbations of unstable circular orbits that exists within the ISCO • In Schwarzschild, radial perturbations of circular orbits in the range • 4M to 6M lead to elliptic zoom-whirl orbits • 3M (the “light ring”) to 4M lead to a hyperbolic orbit with one whirl episode • depend on the sign of the perturbation, the geodesic will fall into the black hole or not after a whirl phase • The number of whirls n is related to the magnitude of the perturbation dr and the instability exponent gof the orbit via

  24. Beyond geodesics • Levin, Grossman & Perez-Giz [arXiv:0811.3815, arXiv:0811.3814, arXiv:0811.3798, arXiv:0809.3838, arXiv:0802.0459]have shown the behavior persists in the conservative dynamics of the PN expansion up to 3rd order, including spin-orbit interactions • with spin (even for geodesics), the orbital plane precesses, and so the unstable orbits are “spherical” rather than circular • they introduce an interesting taxonomy of the subset of exactly periodic orbits, where each orbit is classified by a rational number qwhere w is the number of whirls, zthe number of leaves that make up the zooms, and v describes the sequence in which the leaves are traced out (v/z <1) • any non-closed orbit is arbitrarily close to some periodic orbit q=1 + 3/4 q=1 + 753/1000

  25. Beyond geodesics • Numerical simulations of equal mass non-QCI binaries also show zoom-whirl behavior [FP & Khurana, CQG 24 (2007); Washik et al. PRL 101 (2008)] • Will argue that this must generically be present in the GR two-body problem because of the possibility of two distinct end-states— one or two black holes — and this is intimately related to the existence of unstable orbits • simulations are beginning to confirm this • However, unlike with geodesics, there must be a limit to the number of whirls because of radiation-reaction • eccentric orbits have more energy than a QC orbit with radius ~ the pericenter radius; the whirling could in principle persist until this excess energy is radiated away

  26. The threshold of immediate merger • Consider the black hole scattering problem • in general two, distinctend-states possible • one black hole, after a collision • two isolated black holes, after a deflection • because there are two distinct end-states, there must be some kind of threshold behavior approaching a critical impact parameter b* m2,v2 b m1,v1

  27. The threshold of immediate merger • The following illustrates what could happen as one tunes to threshold, assuming smooth dependence of the trajectories as a function of b • non-spinning case (so we have evolution in a plane) • only showing one of the BH trajectories for clarity • solid blue (black) – merger (escape) • dashed blue (black) – merger (escape) for values of b closer to threshold

  28. The threshold of immediate merger : geodesics • We know the previous argument works for geodesics … a couple more examples below repeating the “scattering” experiment for hyperbolic and elliptic geodesics, tuned to the threshold to within ~ 1 part in 1016 (giving ~ 8 whirl orbits here) unbound orbits (green scatter, blue capture) bound orbits [the non-capture case is not a two-leaf orbit … integration just stopped after the second zoom]

  29. The threshold of immediate merger : equal mass binaries • The figures below are from full numerical simulations of the field equations for equal mass orbits, showing qualitatively the same behavior as the geodesic problem • however, the binary in the whirl phase is emitting copious amounts of gravitational radiation; on the order of 1-1.5% of the total mass of the system per orbit two cases tuned close to threshold (only 1 BH trajectory shown) dominant component of emitted gravitational waves as measure by NP scalars

  30. Animations from merger case … Lapse function a, orbital plane Real component of the Newman-Penrose scalar Y4( times rM), orbital plane

  31. Key Open Question • The scattering problem highlights a potential show-stopper for the relevance of zoom-whirl behavior for generic astrophysical binaries — excessive fine tuning of initial conditions • However, accessing the probability of a single near-critical encounter is not the relevant question. Rather, in a binary inspiral scenario where the pericenter distance reaches an effective ISCO while the binary still possesses a large eccentricity, does the transition from inspiral to merger cross a separatrix of unstable quasi-circular orbits? • we know the answer is “yes” for extreme-mass-ratio inspirals (an important source for LISA) • Levin et al. claim generically it will be “yes”, given in their taxonomy the QCIs are in a sense a set of measure zero of all possible orbits • energy arguments suggest it should be “yes” for some sufficiently large eccentricity that will depend on the mass-ratio of the binary

  32. Consequences if “yes” • Eccentric orbits have a larger GW luminosity near periapsis in general; if whirliness occurs the luminosity will be even higher • so even if these events are rarer, the can be seen to a much larger distance than QCI, hence could be an important LIGO source [O’Leary et al. (arXiv:0807.2638)] • but need appropriate templates to see it! Case-and-point results of NINJA (Numerical INJection Analysis) [arXiv:0901.4399], where a zoom-whirl merger was regularly missed in the simulation detections • Such events will offer exquisite tests of general relativity, as more of the GW signal comes from the strong-field region • Some interesting alternative theories/extensions of GR, such as Chern-Simons modified gravity, are consistent will all existing weak field tests, but have quite different strong field solutions

  33. More speculative consequence if “yes” • arguments for a high eccentricity BH binary population may apply to black hole/neutron star binaries. • a back-of-the-envelope calculation shows that a 1.5 M๏ neutron star will reach it’s Roche-limit within the range of unstable circular orbits (3-6M) for black holes with masses ~ 5-14 M๏ • if the whirl phase sets in, the black hole could “peel” the outer layers of the neutron star, with a sizeable amount of the material flung back out into an accretion disk • this is in contrast to tidal disruption in a QCI, where within less that an orbit almost all of the material falls • would also be a significant source of E&M activity (a flavor of GRB?) • The highest luminosity GW burst could even come after the GRB, if the peeled NS zooms out again before merging in a subsequent whirl.

  34. Conclusions • It is not too much of a stretch of the imagination to state that we are on the verge of a new era in observational astronomy with gravitational wave detectors • To realize the full potential of this generation of detectors requires that we understand the theory of expected sources … both the astrophysical populations and the nature of the gravitational wave emission • However, given the many open questions in the theoretical models, the complexity of the plausible scenarios, and the infeasibility of simulating them all, one can anticipate that the most exciting discoveries and advances will come through a synergistic interplay between observation and theory • For more details, check out the Observational Signatures of Black Hole Mergers conference at the STSCI March 30-April 1

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