When Black Holes CollideWhen Black Holes Collide

Frans PretoriusFrans PretoriusPrinceton UniversityPrinceton University

STScI ColloquiumSTScI Colloquium

February 18, 2009February 18, 2009

Outline IOutline I• Motivation: why explore black hole collisions?Motivation: why explore black hole collisions?

– gravitational wave astronomy, studying dynamical strong-field gravitational wave astronomy, studying dynamical strong-field general relativitygeneral relativity

• The conventional picture of generic non-extreme-mass-ratio The conventional picture of generic non-extreme-mass-ratio mergersmergers

– phases of the mergerphases of the merger

• ““Newtonian”Newtonian”• inspiral inspiral quasi-circular inspiral quasi-circular inspiral• plunge/mergerplunge/merger• ringdownringdown

– highlights from the recent explosion of numerical results on highlights from the recent explosion of numerical results on the late-inspiral/merger phasethe late-inspiral/merger phase

• how well post-Newtonian techniques model the late stages of how well post-Newtonian techniques model the late stages of inspiralinspiral

• large re-coil velocitieslarge re-coil velocities

Outline IIOutline II• Is this the complete story?Is this the complete story?

– theoretical studies suggests modest to high eccentricity theoretical studies suggests modest to high eccentricity mergers may be as likely, if not the dominant source of mergers may be as likely, if not the dominant source of detectable signalsdetectable signals

• if this is the case, search strategies will need to be updatedif this is the case, search strategies will need to be updated

– orbital dynamics becomes much more interesting, exhibiting orbital dynamics becomes much more interesting, exhibiting zoom-whirlzoom-whirl behavior behavior

– unstable circular orbitsunstable circular orbits are the key to understanding zoom- are the key to understanding zoom-whirl behavior for whirl behavior for elliptic orbitselliptic orbits in general relativity in general relativity

• consequences for binary black hole mergersconsequences for binary black hole mergers

• more speculative implications for black hole/neutron star mergersmore speculative implications for black hole/neutron star mergers

• ConclusionsConclusions

Motivation: why explore black hole Motivation: why explore black hole collisions?collisions?

• gravitational wave astronomygravitational wave astronomy

– almost overwhelming circumstantial evidence that black holes almost overwhelming circumstantial evidence that black holes exist in our universeexist in our universe

– to obtain conclusive evidence, we need to “see” the black to obtain conclusive evidence, we need to “see” the black holes in the “light” they emit … gravitational waves. However, holes in the “light” they emit … gravitational waves. However, isolated single black holes do not radiate, so we need to look isolated single black holes do not radiate, so we need to look for binary mergers for the cleanest direct signature of the for binary mergers for the cleanest direct signature of the existence of black holesexistence of black holes

– understanding the nature of the waves emitted in the process understanding the nature of the waves emitted in the process is important for detecting such events, and moreover will be is important for detecting such events, and moreover will be crucialcrucial in deciphering the signals in deciphering the signals

• extracting the parameters of the binaryextracting the parameters of the binary

• obtain clues about the environment of the binaryobtain clues about the environment of the binary

• how accurately does Einstein’s theory describe the event?how accurately does Einstein’s theory describe the event?

The network of gravitational wave The network of gravitational wave detectorsdetectors

LIGO HanfordLIGO Hanford

LIGO LivingstonLIGO Livingston

ground based laser interferometersground based laser interferometersLIGO/VIRGO/GEO/TAMALIGO/VIRGO/GEO/TAMA

space-based laser interferometer (hopefully space-based laser interferometer (hopefully with get funded for a 20?? Launch)with get funded for a 20?? Launch)

LISALISA

ALLEGRO/NAUTILUS/AURIGA/…ALLEGRO/NAUTILUS/AURIGA/…resonant bar detectorsresonant bar detectors

ALLEGROALLEGROAURIGAAURIGA

Pulsar timing network, CMB anisotropyPulsar timing network, CMB anisotropy

The Crab nebula … a supernovae The Crab nebula … a supernovae remnant harboring a pulsar remnant harboring a pulsar

Segment of the CMB Segment of the CMB from WMAP from WMAP

source frequency (Hz)source frequency (Hz)

sou

rce

sou

rce

“str

en

gth

”“s

tren

gth

”

1010441010-12-12 1010-8-8 1010-4-4 11

relics from the big bang, inflationrelics from the big bang, inflation

exotic physics in the early universe: phase transitions, cosmic strings, domain walls, …exotic physics in the early universe: phase transitions, cosmic strings, domain walls, …

1-10 M1-10 M๏๏ BH/BH BH/BH

mergersmergers

NS/BH mergersNS/BH mergers

NS/NS mergersNS/NS mergers

pulsars, pulsars, supernovaesupernovae

EMR inspiralEMR inspiral

NS binariesNS binaries

WD binariesWD binaries

101022-10-1066 M M๏๏ BH/BH BH/BH

mergersmergers

>10>1066 M M๏๏ BH/BH mergersBH/BH mergers

CMB CMB anisotropyanisotropy

Pulsar timingPulsar timing LISALISA LIGO/…LIGO/…Bar Bar detectordetectorss

Overview of expected gravitational wave Overview of expected gravitational wave sourcessources

Anatomy of a MergerAnatomy of a Merger

• In the conventional scenario of a black hole merger in the universe, one In the conventional scenario of a black hole merger in the universe, one can break down the evolution into 4 stages: can break down the evolution into 4 stages: Newtonian, inspiral, Newtonian, inspiral, plunge/merger and ringdownplunge/merger and ringdown

• NewtonianNewtonian

– in isolation, radiation reaction will cause two black holes of mass in isolation, radiation reaction will cause two black holes of mass MM in a in a circular orbit with initial separation circular orbit with initial separation RR to merge within a time to merge within a time ttmm relative to the relative to the Hubble time Hubble time ttHH

– label the phase of the orbit label the phase of the orbit Newtonian Newtonian when the separation is such that the when the separation is such that the binary will take longer than the age of the universe to merge, for then to be 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 of relevance to gravitational wave detection, other “Newtonian” processes need to operate, e.g. dynamical friction, n-body encounters, gas-drag, etc. need to operate, e.g. dynamical friction, n-body encounters, gas-drag, etc. For e.g., For e.g.,

• two solar mass black holes need to be within 1 million Schwarzschild radii ~ 3 two solar mass black holes need to be within 1 million Schwarzschild radii ~ 3 million kmmillion km

• two 10two 1099 solar mass black holes need to be within 6 thousand Schwarzschild radii ~ solar mass black holes need to be within 6 thousand Schwarzschild radii ~

1 parsec1 parsec

4

610

sH

m

R

R

M

M

t

t

Anatomy of a MergerAnatomy of a Merger

• inspiral inspiral quasi-circular inspiral (QSI) quasi-circular inspiral (QSI)

– In the inspiral phase, energy loss through gravitational wave In the inspiral phase, energy loss through gravitational wave emission is the dominate mechanism forcing the black holes closer emission is the dominate mechanism forcing the black holes closer togethertogether

– to get an idea for the dominant timescale during inspiral, for equal to get an idea for the dominant timescale during inspiral, for equal mass, circular binaries the Keplarian orbital frequency offers a good mass, circular binaries the Keplarian orbital frequency offers a good approximation until very close to merger approximation until very close to merger

• the dominant gravitational wave frequency is twice thisthe dominant gravitational wave frequency is twice this

– Post-Newtonian techniques provide an accurate description of Post-Newtonian techniques provide an accurate description of certain aspects of the process until remarkably close to mergercertain aspects of the process until remarkably close to merger

– if the initial pericenter of the orbit is sufficiently large, the orbit will if the initial pericenter of the orbit is sufficiently large, the orbit will loose its eccentricity long before merger loose its eccentricity long before merger [Peters & Matthews, Phys.Rev. [Peters & Matthews, Phys.Rev. 131 (1963)]131 (1963)] and become and become quasi-circularquasi-circular

2/3

3kHz11

2

1

2

R

R

M

M

R

M s

Anatomy of a MergerAnatomy of a Merger• plunge/mergerplunge/merger

– this is the time in the merger when the two event horizons this is the time in the merger when the two event horizons coalesce into onecoalesce into one

• we know the two black holes we know the two black holes mustmust merge into one if cosmic censorship merge into one if cosmic censorship holds (and no indications of a failure yet in any merger simulations)holds (and no indications of a failure yet in any merger simulations)

– full numerical solution of the field equations are required to solve full numerical solution of the field equations are required to solve for the geometry of spacetime in this stagefor the geometry of spacetime in this stage

• Only within the last 3 years, following a couple of breakthroughs, has Only within the last 3 years, following a couple of breakthroughs, has numerical relativity been able to complete the picture by filling in the numerical relativity been able to complete the picture by filling in the details of the final, non-perturbative phase of the mergerdetails of the final, non-perturbative phase of the merger

• At present two known stable formulations of the field equations, At present two known stable formulations of the field equations, generalized harmonicgeneralized harmonic [FP, PRL 95, 121101 (2005) ], [FP, PRL 95, 121101 (2005) ], and and BSSN with moving BSSN with moving puncturespunctures [M. Campanelli, C. O. Lousto, P. Marronetti, Y. Zlochower PRL 96, 111101, [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); J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. van Meter PRL 96, 111102, (2006)](2006)]

– in all cases studied to date, this stage is exceedingly short, leaving 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 its imprint in on the order of 1-2 gravitational wave cycles, at roughly twice the final orbital frequencyroughly twice the final orbital frequency

Anatomy of a MergerAnatomy of a Merger

• ringdownringdown

– in the final phase of the merger, the remnant black hole “looses all its in the final phase of the merger, the remnant black hole “looses all its hair”, settling down to a Kerr black holehair”, settling down to a Kerr black hole

– one possible definition for when plunge/merger ends and ringdown begins, one possible definition for when plunge/merger ends and ringdown begins, is when the spacetime can adequately be described as a Kerr black hole is when the spacetime can adequately be described as a Kerr black hole perturbed by a set of perturbed by a set of quasi-normal modes (QNM)quasi-normal modes (QNM)

– the ringdown portion of the waveform will be dominated by the the ringdown portion of the waveform will be dominated by the fundamental harmonic of the quadrupole QNM, with characteristic fundamental harmonic of the quadrupole QNM, with characteristic frequency and decay time frequency and decay time [Echeverria, PRD 34, 384 (1986)]:[Echeverria, PRD 34, 384 (1986)]:

j=a/Mj=a/Mf f , the Kerr spin parameter of the black hole , the Kerr spin parameter of the black hole

3.0

45.0

3.0

163.01

120

)1(63.01kHz322

j

j

M

Ms

jM

M

QNM

QNM

Sample evolution --- Cook-Sample evolution --- Cook-Pfeiffer Quasi-circular initial dataPfeiffer Quasi-circular initial data

This animation shows the This animation shows the lapse functionlapse function in the orbital in the orbital plane.plane.

The lapse function The lapse function represents the relative time represents the relative time dilation between a dilation between a hypothetical observer at the hypothetical observer at the given location on the grid, given location on the grid, and an observer situated and an observer situated very far from the system --- very far from the system --- the redder the color, the the redder the color, the slower local clocks are slower local clocks are running relative to clocks at running relative to clocks at infinityinfinity

If this were in “real-time” it If this were in “real-time” it would correspond to the would correspond to the merger of two ~5000 solar merger of two ~5000 solar mass black holesmass black holes

Initial black holes are close Initial black holes are close to non-spinning to non-spinning Schwarzschild black holes; Schwarzschild black holes; final black hole is a Kerr a final black hole is a Kerr a black hole with spin black hole with spin parameter parameter ~0.7~0.7, , and ~and ~4%4% of of the total initial rest-mass of the total initial rest-mass of the system is emitted in the system is emitted in gravitational wavesgravitational waves

A. Buonanno, G.B. Cook and F.P.; A. Buonanno, G.B. Cook and F.P.; Phys.Rev.D75:124018,2007Phys.Rev.D75:124018,2007

Gravitational waves from the Gravitational waves from the simulationsimulation

A depiction of the gravitational A depiction of the gravitational waves emitted in the orbital waves emitted in the orbital plane of the binary. Shown is plane of the binary. Shown is the real component of the the real component of the Newman Penrose scalar Newman Penrose scalar , , which in the wave zone is which in the wave zone is proportional to the second time proportional to the second time derivative of the usual plus-derivative of the usual plus-polarizationpolarization

The plus-component of the wave The plus-component of the wave from the same simulation, from the same simulation, measured on the axis normal to measured on the axis normal to the orbital planethe orbital plane

What does the merger wave represent? What does the merger wave represent?

• Scale the system to two Scale the system to two 10 solar mass (~10 solar mass (~ 2x102x103131 kg) BHs kg) BHs

– radius of each black hole in the binary is ~ radius of each black hole in the binary is ~ 30km30km

– radius of final black hole is ~ radius of final black hole is ~ 60km60km

– distance from the final black hole where the wave distance from the final black hole where the wave was measured ~was measured ~ 1500km 1500km

– frequency of the wave ~frequency of the wave ~ 200Hz (early inspiral) - 200Hz (early inspiral) - 800Hz (ring-down) 800Hz (ring-down)

What does the merger wave represent? What does the merger wave represent?

• fractional oscillatory “distortion” in space induced by the wave fractional oscillatory “distortion” in space induced by the wave transverse to the direction of propagation has a transverse to the direction of propagation has a maximummaximum amplitude amplitude L/LL/L ~ 3x10~ 3x10-3-3

• a 2m tall person will get stretched/squeezed by ~ a 2m tall person will get stretched/squeezed by ~ 6 mm6 mm as the wave as the wave passespasses

• LIGO’s arm length would change by ~ LIGO’s arm length would change by ~ 12m12m. Wave amplitude decays like . Wave amplitude decays like 1/distance from source; e.g. at 10Mpc the change in arms ~ 1/distance from source; e.g. at 10Mpc the change in arms ~ 5x105x10-17-17m m (1/20 the radius of a proton, which is well within the ballpark of what (1/20 the radius of a proton, which is well within the ballpark of what LIGO is trying to measure!!)LIGO is trying to measure!!)

• despite the seemingly small amplitude for the wave, the energy despite the seemingly small amplitude for the wave, the energy it carries is enormous — around it carries is enormous — around 10103030 kg c kg c22 ~ 10 ~ 104747 J ~ 10 J ~ 105454 ergs ergs

• peak luminosity is about 1/100peak luminosity is about 1/100thth the Planck luminosity of 10 the Planck luminosity of 105959ergs/s !!ergs/s !!

• luminosity of the sun ~ 10luminosity of the sun ~ 103333ergs/s, a bright supernova or milky-way type ergs/s, a bright supernova or milky-way type galaxy ~ 10galaxy ~ 104242 ergs/s ergs/s

• if all the energy reaching LIGO from the 10Mpc event could directly be if all the energy reaching LIGO from the 10Mpc event could directly be converted to sound waves, it would have an intensity level of ~ 80dBconverted to sound waves, it would have an intensity level of ~ 80dB

Highlights of recent results: simplicity of merger Highlights of recent results: simplicity of merger waveformwaveform

• the “non-linear” phase of the merger is surprisingly shortthe “non-linear” phase of the merger is surprisingly short

• great boon for data analysis, as this great boon for data analysis, as this suggestssuggests an efficient LIGO an efficient LIGO template bank could be compiled by stitching together quick-to-template bank could be compiled by stitching together quick-to-calculate perturbative waveforms, guided by a handful of numerical calculate perturbative waveforms, guided by a handful of numerical waveformswaveforms

• to-date, the furthest the idea has been to-date, the furthest the idea has been pushed is for quasi-circular inspiral of pushed is for quasi-circular inspiral of non-spinning BH’s non-spinning BH’s [A. Buonanno et al., [A. Buonanno et al., Phys.Rev.D76:104049,2007]Phys.Rev.D76:104049,2007]

– effective-one-body (EOB) PN inspiral effective-one-body (EOB) PN inspiral connected to the 3 dominant quasi normalconnected to the 3 dominant quasi normalmodes (QNMs)modes (QNMs)

– added “pseudo” 4PN term to EOB model, added “pseudo” 4PN term to EOB model, with coefficient determined by a best-fit with coefficient determined by a best-fit match to a set of numerical resultsmatch to a set of numerical results

– used simulation results for final spin and used simulation results for final spin and black hole mass to fix the QNM black hole mass to fix the QNM frequencies and decay constants frequencies and decay constants 4:1 mass ratio 4:1 mass ratio

exampleexample

Highlights of recent resultsHighlights of recent results : large recoil velocities: large recoil velocities• significant recoil can be imparted to the remnant black hole due to significant recoil can be imparted to the remnant black hole due to

asymmetric beaming of radiation during the merger, up to 4000km/s in asymmetric beaming of radiation during the merger, up to 4000km/s in some cases some cases

– Herrmann et al., gr-qc/0701143; Koppitz et al., gr-qc/0701163; Campanelli et al. gr-qc/0701164 & 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/0703075v1gr-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 there are far reaching consequences to this, some that could be detected via electromagnetic observations, in particular for supermassive black via electromagnetic observations, in particular for supermassive black hole mergershole mergers

– offset or double galactic nuclei, displaced active galactic nuclei, offset or double galactic nuclei, displaced active galactic nuclei, wiggling jets, enlarged cores, lopsided cores, x-ray afterglows, wiggling jets, enlarged cores, lopsided cores, x-ray afterglows, feedback trails, off-center flares from tidally disrupted stars, feedback trails, off-center flares from tidally disrupted stars, hypervelocity stars, a population of galaxies without supermassive hypervelocity stars, a population of galaxies without supermassive black holes, etc.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 a 2650km/s recoiling black hole could explain the emission line spectra from quasar SDSSJ092712.65+294344.from quasar SDSSJ092712.65+294344.0 0 [S. Komossa et al., ApJ.678:L81,2008][S. Komossa et al., ApJ.678:L81,2008]

What is “wrong” with the QCI pictureWhat is “wrong” with the QCI picture

• If we want LIGO be anything more than a simple If we want LIGO be anything more than a simple detectordetector, i.e. be able to , i.e. be able to identifyidentify the gravitational waves, the gravitational waves, we need templates for all plausible sources; howeverwe need templates for all plausible sources; however

– limited computational power for template searches limited computational power for template searches – having too many templates increases the probability of false having too many templates increases the probability of false

detections detections

• LIGO does need to be selective in what it looks forLIGO does need to be selective in what it looks for

• Recent studies suggest QCI may not be the dominant Recent studies suggest QCI may not be the dominant LIGO (or LISA) sourceLIGO (or LISA) source

– Eccentric mergers,Eccentric mergers, potentially potentially transitioning from inspiral to transitioning from inspiral to merger through a series ofmerger through a series of zoom-whirl zoom-whirl orbits, may be more orbits, may be more likely likely

Merging with eccentricityMerging with eccentricity

• Binary stars are Binary stars are unlikelyunlikely progenitors for BH binaries that could progenitors for BH binaries that could merge within the Hubble time, as such close binaries will likely merge within the Hubble time, as such close binaries will likely evolve through a common envelope phase, causing a stellar evolve through a common envelope phase, causing a stellar merger before BH formation merger before BH formation [Belczynski et al., ApJ 662, 2007].[Belczynski et al., ApJ 662, 2007].

– this cuts off the most promising channel for QCI this cuts off the most promising channel for QCI

• A promising source for stellar mass BH binaries is then n-body A promising source for stellar mass BH binaries is then n-body interactions involving BHs in dense stellar environments interactions involving BHs in dense stellar environments [e.g. [e.g. Sigurdsson & Hernquist, Nature 364 (1993) , Portegies Zwart & McMilla, ApJ 528 Sigurdsson & Hernquist, Nature 364 (1993) , Portegies Zwart & McMilla, ApJ 528 L17 (2000), Sadowski et al., arXiv:0710.0878]L17 (2000), Sadowski et al., arXiv:0710.0878]

– these often lead to binaries with large eccentricities that are sufficiently these often lead to binaries with large eccentricities that are sufficiently tight that they do not have enough time to circularize before mergingtight that they do not have enough time to circularize before merging

• O’Leary et al. (O’Leary et al. (arXiv:0807.2638) estimate 90% will have e>0.9 when arXiv:0807.2638) estimate 90% will have e>0.9 when entering the LIGO band, with Advanced LIGO rates of ~ 1-10entering the LIGO band, with Advanced LIGO rates of ~ 1-1033/year from /year from mergers in galactic nuclei alonemergers in galactic nuclei alone

• For supermassive BH mergers, studies also suggest mergers may For supermassive BH mergers, studies also suggest mergers may occur with non-negligible eccentricity, e.g. occur with non-negligible eccentricity, e.g. Berentzen et al., Berentzen et al., arXiv:0812.2756arXiv:0812.2756

Why may eccentric mergers be a Why may eccentric mergers be a problem?problem?

• 1 extra parameter … not 1 extra parameter … not too muchtoo much of a issue for of a issue for template searchestemplate searches

• However, how the transition from inspiral to plunge However, how the transition from inspiral to plunge happens could affect the feasability of present PN happens could affect the feasability of present PN techniquestechniques

– the expansions are accurate for adiabatic evolution of the the expansions are accurate for adiabatic evolution of the orbital parameters, and as long as orbital parameters, and as long as v/c < 1v/c < 1

• For QCI of comparable mass binaries, For QCI of comparable mass binaries, v/c ~ 0.2-0.3 v/c ~ 0.2-0.3 before before common horizon formation, which is one reason why PN-common horizon formation, which is one reason why PN-techniques work so well modeling the entire inspiraltechniques work so well modeling the entire inspiral

• For eccentric orbits For eccentric orbits v/cv/c will become much larger will become much larger

Why may eccentric mergers be a Why may eccentric mergers be a problem?problem?

• a second argument given why PN matches a second argument given why PN matches numerical simulations so well, is the regime numerical simulations so well, is the regime where it breaks down is very short, and where it breaks down is very short, and happens well within the effective potential happens well within the effective potential barrier of the spacetime and so can not leave a barrier of the spacetime and so can not leave a significant imprint on the waveformsignificant imprint on the waveform

– this argument will fail if this argument will fail if zoom-whirlzoom-whirl behavior sets in at behavior sets in at the transition from inspiral to merger, and this the transition from inspiral to merger, and this maymay generically happen with high-eccentricity inspiralsgenerically happen with high-eccentricity inspirals

Zoom-whirl orbitsZoom-whirl orbits

• At a first glance might look like “extreme’’ pericenter At a first glance might look like “extreme’’ pericenter precessionprecession

– examples: geodesics about a Schwarzschild BH, apoapsis 30M, examples: geodesics about a Schwarzschild BH, apoapsis 30M, inner circle is event horizon (2M), outer circle ISCO (6M)inner circle is event horizon (2M), outer circle ISCO (6M)

usual (but large) pericenter usual (but large) pericenter precessionprecession

zoom-whirl orbitzoom-whirl orbit

Zoom-whirl orbitsZoom-whirl orbits• However, what’s different about zoom-whirl behavior is once the pericenter However, what’s different about zoom-whirl behavior is once the pericenter

distance crosses the isco, you can find orbits which are essentially distance crosses the isco, you can find orbits which are essentially indistinguishableindistinguishable at apoapsis but that exhibit an at apoapsis but that exhibit an arbitraryarbitrary number of zooms number of zooms per whirl at the per whirl at the samesame pericenter distance pericenter distance

300 zoom-whirl orbits, initial 300 zoom-whirl orbits, initial tangential velocity ranging from tangential velocity ranging from

0.1207600 to 0.120762900.1207600 to 0.12076290

150 “regular” orbits, initial 150 “regular” orbits, initial tangential velocity ranging from tangential velocity ranging from

0.128 to 0.1320.128 to 0.132

Zoom-whirl orbitsZoom-whirl orbits

• Zoom-whirl orbits are perturbations of Zoom-whirl orbits are perturbations of unstable circular orbitsunstable circular orbits that exists within the ISCOthat exists within the ISCO

– In Schwarzschild, radial perturbations of circular orbits in the In Schwarzschild, radial perturbations of circular orbits in the rangerange

• 4M to 6M lead to elliptic zoom-whirl orbits 4M to 6M lead to elliptic zoom-whirl orbits

• 3M (the “light ring”) to 4M lead to a hyperbolic orbit with one whirl 3M (the “light ring”) to 4M lead to a hyperbolic orbit with one whirl episodeepisode

– depend on the sign of the perturbation, the geodesic will fall into depend on the sign of the perturbation, the geodesic will fall into the black hole or not after a whirl phasethe black hole or not after a whirl phase

• The number of whirls The number of whirls nn is related to the magnitude of the is related to the magnitude of the perturbation perturbation rr and the instability exponent and the instability exponent of the orbit viaof the orbit via

ren 1

Beyond geodesicsBeyond geodesics• Levin, Grossman & Perez-Giz Levin, Grossman & Perez-Giz [[arXiv:0811.3815, arXiv:0811.3815,

arXiv:0811.3814, arXiv:0811.3798, arXiv:0809.3838, arXiv:0811.3814, arXiv:0811.3798, arXiv:0809.3838, arXiv:0802.0459]arXiv:0802.0459] have shown the behavior persists have shown the behavior persists in the in the conservativeconservative dynamics of the PN expansion dynamics of the PN expansion up to 3up to 3rdrd order, including spin-orbit interactions order, including spin-orbit interactions

– with spin (even for geodesics), the orbital plane with spin (even for geodesics), the orbital plane precesses, and so the unstable orbits are precesses, and so the unstable orbits are “spherical” rather than circular“spherical” rather than circular

– they introduce an interesting taxonomy of the they introduce an interesting taxonomy of the subset of exactly periodic orbits, where each orbit subset of exactly periodic orbits, where each orbit is classified by a rational number is classified by a rational number qq

where where ww is the number of whirls, is the number of whirls, zz the number of the number of leaves that make up the zooms, and leaves that make up the zooms, and vv describes the describes the sequence in which the leaves are traced out (v/z sequence in which the leaves are traced out (v/z <1)<1)

– any non-closed orbit is arbitrarily close to some any non-closed orbit is arbitrarily close to some periodic orbitperiodic orbit

zvwq /

q=1 + 753/1000q=1 + 753/1000

q=1 + 3/4q=1 + 3/4

Beyond geodesicsBeyond geodesics

• Numerical simulations of equal mass non-QCI binaries also Numerical simulations of equal mass non-QCI binaries also show zoom-whirl behavior show zoom-whirl behavior [FP & Khurana, CQG 24 (2007); Washik et [FP & Khurana, CQG 24 (2007); Washik et al. PRL 101 (2008)]al. PRL 101 (2008)]

• Will argue that this must generically be present in the GR two-Will argue that this must generically be present in the GR two-body problem because of the possibility of body problem because of the possibility of two distinct end-two distinct end-statesstates —— one or two black holes one or two black holes —— and this is intimately and this is intimately related to the existence of unstable orbitsrelated to the existence of unstable orbits

– simulations are beginning to confirm thissimulations are beginning to confirm this

• However, unlike with geodesics, there must be a limit to the However, unlike with geodesics, there must be a limit to the number of whirls because of radiation-reactionnumber of whirls because of radiation-reaction

– eccentric orbits have more energy than a QC orbit with radius ~ eccentric orbits have more energy than a QC orbit with radius ~ the pericenter radius; the whirling could in principle persist until the pericenter radius; the whirling could in principle persist until this excess energy is radiated awaythis excess energy is radiated away

The threshold of immediate mergerThe threshold of immediate merger• Consider the black hole scattering problemConsider the black hole scattering problem

• in general two, distinctin general two, distinct end-states possibleend-states possible

• one black hole, after a collisionone black hole, after a collision

• two isolated black holes, after a deflectiontwo isolated black holes, after a deflection

• because there are because there are two distinct end-statestwo distinct end-states, there must be , there must be some kind of threshold behavior approaching a critical impact some kind of threshold behavior approaching a critical impact parameter parameter b*b*

bbmm11,v,v11

mm22,v,v22

The threshold of immediate mergerThe threshold of immediate merger• The following illustrates what could happen as one tunes to The following illustrates what could happen as one tunes to

threshold, assuming smooth dependence of the trajectories as a threshold, assuming smooth dependence of the trajectories as a function of function of b b

• non-spinning case (so we have evolution in a plane)non-spinning case (so we have evolution in a plane)

• only showing one of the BH trajectories for clarity only showing one of the BH trajectories for clarity

• solid blue (black) – merger (escape)solid blue (black) – merger (escape)

• dashed blue (black) – merger (dashed blue (black) – merger (escapeescape) for values of ) for values of bb closer to threshold closer to threshold

The threshold of immediate merger : geodesicsThe threshold of immediate merger : geodesics• We know the previous argument works for geodesics … a couple We know the previous argument works for geodesics … a couple

more examples below repeating the “scattering” experiment for more examples below repeating the “scattering” experiment for hyperbolic and elliptic geodesics, tuned to the threshold to within ~ 1 hyperbolic and elliptic geodesics, tuned to the threshold to within ~ 1 part in 10part in 1016 16 (giving ~ 8 whirl orbits here) (giving ~ 8 whirl orbits here)

unbound orbits (green scatter, blue unbound orbits (green scatter, blue capture)capture)

bound orbits [the non-capture case is bound orbits [the non-capture case is notnot a a two-leaf orbit … integration just stopped two-leaf orbit … integration just stopped after the second zoom]after the second zoom]

The threshold of immediate merger : equal mass The threshold of immediate merger : equal mass binariesbinaries

• The figures below are from full numerical simulations of the field equations The figures below are from full numerical simulations of the field equations for equal mass orbits, showing qualitatively the same behavior as the for equal mass orbits, showing qualitatively the same behavior as the geodesic problemgeodesic problem

– however, the binary in the whirl phase is emitting copious amounts of gravitational 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 orbitradiation; on the order of 1-1.5% of the total mass of the system per orbit

two cases tuned close to thresholdtwo cases tuned close to threshold(only 1 BH trajectory shown)(only 1 BH trajectory shown)

dominant component of emitted gravitational dominant component of emitted gravitational waves as measure by NP scalarswaves as measure by NP scalars

Animations from merger case …Animations from merger case …

Lapse function Lapse function , orbital plane, orbital plane Real component of the Newman-Penrose Real component of the Newman-Penrose scalar scalar 44( times rM), orbital plane( times rM), orbital plane

Key Open QuestionKey Open Question

• The scattering problem highlights a potential show-stopper for the The scattering problem highlights a potential show-stopper for the relevance of zoom-whirl behavior for generic astrophysical relevance of zoom-whirl behavior for generic astrophysical binaries binaries — excessive fine tuning of initial conditions— excessive fine tuning of initial conditions

• However, accessing the probability of a single near-critical However, accessing the probability of a single near-critical encounter is not the relevant question. Rather, encounter is not the relevant question. Rather, in a binary inspiral in a binary inspiral scenario where the pericenter distance reaches an effective ISCO scenario where the pericenter distance reaches an effective ISCO while the binary still possesses a large eccentricity, does the while the binary still possesses a large eccentricity, does the transition from inspiral to merger cross a separatrix of unstable transition from inspiral to merger cross a separatrix of unstable quasi-circular orbits?quasi-circular orbits?

– we know the answer is “yes” for extreme-mass-ratio inspirals (an we know the answer is “yes” for extreme-mass-ratio inspirals (an important source for LISA)important source for LISA)

– Levin et al. claim generically it will be “yes”, given in their taxonomy 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 orbitsthe QCIs are in a sense a set of measure zero of all possible orbits

– energy arguments suggest it should be “yes” for some sufficiently energy arguments suggest it should be “yes” for some sufficiently large eccentricity that will depend on the mass-ratio of the binarylarge eccentricity that will depend on the mass-ratio of the binary

Consequences if “yes”Consequences if “yes”

• Eccentric orbits have a larger GW luminosity near Eccentric orbits have a larger GW luminosity near periapsis in general; if whirliness occurs the luminosity periapsis in general; if whirliness occurs the luminosity will be even higherwill be even higher

– so even if these events are rarer, the can be seen to a much so even if these events are rarer, the can be seen to a much larger distance than QCI, hence could be an important LIGO larger distance than QCI, hence could be an important LIGO source source [[O’Leary et al. (O’Leary et al. (arXiv:0807.2638)]arXiv:0807.2638)]

• but need appropriate templates to see it! Case-and-point results of but need appropriate templates to see it! Case-and-point results of NINJA (Numerical INJection Analysis) NINJA (Numerical INJection Analysis) [arXiv:0901.4399][arXiv:0901.4399], where a zoom-, where a zoom-whirl merger was regularly missed in the simulation detectionswhirl merger was regularly missed in the simulation detections

• Such events will offer exquisite tests of general Such events will offer exquisite tests of general relativity, as more of the GW signal comes from the relativity, as more of the GW signal comes from the strong-field regionstrong-field region

– Some interesting alternative theories/extensions of GR, such as Some interesting alternative theories/extensions of GR, such as Chern-Simons modified gravity, are consistent will all existing Chern-Simons modified gravity, are consistent will all existing weak field tests, but have quite different strong field solutionsweak field tests, but have quite different strong field solutions

More speculative consequence if “yes”More speculative consequence if “yes”

• arguments for a high eccentricity BH binary population may arguments for a high eccentricity BH binary population may apply to black hole/neutron star binaries. apply to black hole/neutron star binaries.

• a back-of-the-envelope calculation shows that a 1.5 Ma back-of-the-envelope calculation shows that a 1.5 M ๏ ๏ neutron neutron star will reach it’s Roche-limit star will reach it’s Roche-limit withinwithin the range of unstable the range of unstable circular orbits (3-6M) for black holes with masses ~ 5-14 Mcircular orbits (3-6M) for black holes with masses ~ 5-14 M๏๏

– if the whirl phase sets in, the black hole could “peel” the outer 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 layers of the neutron star, with a sizeable amount of the material flung back out into an accretion diskflung back out into an accretion disk

• this is in contrast to tidal disruption in a QCI, where within less that an this is in contrast to tidal disruption in a QCI, where within less that an orbit almost all of the material fallsorbit almost all of the material falls

– would also be a significant source of E&M activity (a flavor of would also be a significant source of E&M activity (a flavor of GRB?)GRB?)

• The highest luminosity GW burst could even come The highest luminosity GW burst could even come afterafter the GRB, if the the GRB, if the peeled NS zooms out again before merging in a subsequent whirl.peeled NS zooms out again before merging in a subsequent whirl.

ConclusionsConclusions

• It is not too much of a stretch of the imagination to state that 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 we are on the verge of a new era in observational astronomy with gravitational wave detectorswith gravitational wave detectors

• To realize the full potential of this generation of detectors To realize the full potential of this generation of detectors requires that we understand the theory of expected sources requires that we understand the theory of expected sources … both the astrophysical populations and the nature of the … both the astrophysical populations and the nature of the gravitational wave emissiongravitational wave emission

• However, given the many open questions in the theoretical However, given the many open questions in the theoretical models, the complexity of the plausible scenarios, and the models, the complexity of the plausible scenarios, and the infeasibility of simulating them all, one can anticipate that the infeasibility of simulating them all, one can anticipate that the most exciting discoveries and advances will come through a most exciting discoveries and advances will come through a synergistic interplay between observation and theorysynergistic interplay between observation and theory

• For more details, check out the For more details, check out the Observational Signatures of Observational Signatures of Black Hole MergersBlack Hole Mergers conference at the STSCI March 30-April 1 conference at the STSCI March 30-April 1