Frans Pretorius- When Black Holes Collide

8/3/2019 Frans Pretorius- When Black Holes Collide

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When Black Holes CollideWhen Black Holes Collide

Frans PretoriusFrans PretoriusPrinceton UniversityPrinceton University

STScI ColloquiumSTScI Colloquium

February 18, 2009February 18, 2009


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Outline IOutline I

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

gravitational wave astronomy, studying dynamical stronggravitational wave astronomy, studying dynamical strong--field generalfield generalrelativityrelativity

The conventional picture of generic nonThe conventional picture of generic non--extremeextreme--massmass--ratioratiomergersmergers

phases of the mergerphases of the merger

NewtonianNewtonian inspiralinspiral quasiquasi--circular inspiralcircular inspiral plunge/mergerplunge/merger ringdownringdown

highlights from the recent explosion of numerical results on the latehighlights from the recent explosion of numerical results on the late--inspiral/merger phaseinspiral/merger phase

how well posthow well post--Newtonian techniques model the late stages of inspiralNewtonian techniques model the late stages of inspiral large relarge re--coil velocitiescoil velocities


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Outline IIOutline II

Is this the complete story?Is this the complete story?

theoretical studies suggests modest to high eccentricity mergers may betheoretical studies suggests modest to high eccentricity mergers may beas likely, if not the dominant source of detectable signalsas likely, if not the dominant source of detectable 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, exhibitingorbital dynamics becomes much more interesting, exhibiting zoomzoom--whirlwhirl behaviorbehavior

unstable circular orbitsunstable circular orbits are the key to understanding zoomare the key to understanding zoom--whirlwhirlbehavior forbehavior for elliptic orbitselliptic orbits in general relativityin 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


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

gravitational wave astronomygravitational wave astronomy

almost overwhelming circumstantial evidence that black holesalmost overwhelming circumstantial evidence that black holesexist in our universeexist in our universe

to obtain conclusive evidence, we need to see the black holesto obtain conclusive evidence, we need to see the black holes

in the light they emit gravitational waves. However, isolatedin the light they emit gravitational waves. However, isolatedsingle black holes do not radiate, so we need to look for binarysingle black holes do not radiate, so we need to look for binarymergers for the cleanest direct signature of the existence of blackmergers for the cleanest direct signature of the existence of blackholesholes

understanding the nature of the waves emitted in the process isunderstanding the nature of the waves emitted in the process isimportant for detecting such events, and moreover will beimportant for detecting such events, and moreover will be crucialcrucial

in deciphering the signalsin 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 Einsteins theory describe the event?how accurately does Einsteins theory describe the event?


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The network of gravitational wave detectorsThe network of gravitational wave detectors

LIGO HanfordLIGO Hanford

LIGO LivingstonLIGO Livingston

ground based laser interferometersground based laser interferometers

LIGO/VIRGO/GEO/TAMALIGO/VIRGO/GEO/TAMA

spacespace--based laser interferometer (hopefullybased laser interferometer (hopefullywith 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

ALLEGROALLEGRO

AURIGAAURIGA

Pulsar timing network, CMB anisotropyPulsar timing network, CMB anisotropy

TheCrab nebula a supernovaeTheCrab nebula a supernovae

remnantharboring a pulsarremnantharboring a pulsar

Segment of the CMBSegment of the CMB

fromWMAPfromWMAP


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source frequency (Hz)source frequency (Hz)

so

urce

strength

so

urce

strength

101044

1010--1212

1010--88

1010--44

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,

11--1010 MM

BH/BHBH/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--101066 MM

BH/BHBH/BH

mergersmergers

>>101066 MM

BH/BH mergersBH/BH mergers

CMBCMB

anisotropyanisotropy

Pulsar timingPulsar timing LISALISA LIGO/LIGO/BarBardetectorsdetectors

Overview of expected gravitational wave sourcesOverview of expected gravitational wave sources


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Anatomy of a MergerAnatomy of a Merger

In the conventional scenario of a black hole merger in the universe, one canIn the conventional scenario of a black hole merger in the universe, one canbreak down the evolution into 4 stages:break down the evolution into 4 stages: Newtonian, inspiral, plunge/mergerNewtonian, inspiral, plunge/mergerand ringdownand ringdown

NewtonianNewtonian

in isolation, radiation reaction will cause two black holes of massin isolation, radiation reaction will cause two black holes of massMMin a circular orbitin a circular orbit

with initial separationwith initial separationRR to merge within a timeto merge within a time ttmm relative to the Hubble timerelative to the Hubble time ttHH

label the phase of the orbitlabel the phase of the orbit NewtonianNewtonian when the separation is such that the binarywhen the separation is such that the binarywill take longer than the age of the universe to merge, for then to be of relevance towill take longer than the age of the universe to merge, for then to be of relevance togravitational wave detection, other Newtonian processes need to operate, e.g.gravitational wave detection, other Newtonian processes need to operate, e.g.dynamical friction, ndynamical friction, n--body encounters, gasbody encounters, gas--drag, etc. For e.g.,drag, etc. For e.g.,

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

two 10two 1099 solar mass black holes need to be within 6 thousand Schwarzschild radii ~ 1solar mass black holes need to be within 6 thousand Schwarzschild radii ~ 1parsecparsec

4

610

}

3 sH

m

R

R

M

M

t

t


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inspiralinspiral quasiquasi--circular inspiral (QSI)circular inspiral (QSI) In the inspiral phase, energy loss through gravitational wave emission isIn the inspiral phase, energy loss through gravitational wave emission is

the dominate mechanism forcing the black holes closer togetherthe dominate mechanism forcing the black holes closer together

to get an idea for the dominant timescale during inspiral, for equal mass,to get an idea for the dominant timescale during inspiral, for equal mass,circular binaries the Keplarian orbital frequency offers a goodcircular binaries the Keplarian orbital frequency offers a good

approximation until very close to mergerapproximation until very close to merger

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

Post Post--Newtonian techniques provide an accurate description of certainNewtonian techniques provide an accurate description of certainaspects of the process until remarkably close to mergeraspects of the process until remarkably close to merger

if the initial pericenter of the orbit is sufficiently large, the orbit will looseif the initial pericenter of the orbit is sufficiently large, the orbit will looseits eccentricity long before mergerits eccentricity long before merger [Peters & Matthews, Phys.Rev. 131 (1963)][Peters & Matthews, Phys.Rev. 131 (1963)]

and becomeand become quasiquasi--circularcircular

2/3

3kHz11

2

1

2

}! 3

R

R

M

M

R

Ms

TT

[


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plunge/mergerplunge/merger

this is the time in the merger when the two event horizons coalesce intothis is the time in the merger when the two event horizons coalesce intooneone

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

full numerical solution of the field equations are required to solve for thefull numerical solution of the field equations are required to solve for thegeometry of spacetime in this stagegeometry of spacetime in this stage

Only within the lastOnly within the last 33 years, following a couple of breakthroughs, has numericalyears, following a couple of breakthroughs, has numericalrelativity been able to complete the picture by filling in the details of the final,relativity been able to complete the picture by filling in the details of the final,nonnon--perturbative phase of the mergerperturbative phase of the merger

At present two known stable formulations of the field equations,At present two known stable formulations of the field equations, generalizedgeneralizedharmonicharmonic [FP,PRL[FP,PRL 9595,, 121101121101 ((20052005) ],) ],andand BSSN with moving puncturesBSSN with moving punctures [M.[M.Campanelli, C. O. Lousto,P. Marronetti, Y. ZlochowerPRLCampanelli, C. O. Lousto,P. Marronetti, Y. ZlochowerPRL 9696,, 111101111101, (, (20062006); J. G.); J. G.Baker, J. Centrella, D. Choi, M. Koppitz, J. van MeterPRLBaker, J. Centrella, D. Choi, M. Koppitz, J. van MeterPRL 9696,, 111102111102, (, (20062006)])]

in all cases studied to date, this stage is exceedingly short, leaving itsin all cases studied to date, this stage is exceedingly short, leaving itsimprint in on the order ofimprint in on the order of 11--22 gravitational wave cycles, at roughly twicegravitational wave cycles, at roughly twicethe final orbital frequencythe final orbital frequency


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ringdownringdown

in the final phase of the merger, the remnant black hole looses all its hair, settlingin the final phase of the merger, the remnant black hole looses all its hair, settlingdown to a Kerr black holedown to a Kerr black hole

one possible definition for when plunge/merger ends and ringdown begins, is whenone possible definition for when plunge/merger ends and ringdown begins, is whenthe spacetime can adequately be described as a Kerr black hole perturbed by a setthe spacetime can adequately be described as a Kerr black hole perturbed by a setofof quasiquasi--normal modes (QNM)normal modes (QNM)

the ringdown portion of the waveform will be dominated by the fundamentalthe ringdown portion of the waveform will be dominated by the fundamentalharmonic of the quadrupole QNM, with characteristic frequency and decay timeharmonic of the quadrupole QNM, with characteristic frequency and decay time[Echeverria,PRD[Echeverria,PRD 3434,, 384384 ((19861986)]:)]:

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

? A

3.0

45.0

3.0

163.01

120

)1(63.01kHz32

2

j

j

M

Ms

j

M

M

QNM

QNM

}

}

3

3

QXT

[


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Sample evolutionSample evolution ------ CookCook--PfeifferPfeifferQuasiQuasi--circular initial datacircular initial data

This animation shows theThis animation shows the lapselapsefunctionfunction in the orbital plane.in the orbital plane.

The lapse function representsThe lapse function representsthe relative time dilation betweenthe relative time dilation betweena hypothetical observer at thea hypothetical observer at thegiven location on the grid, andgiven location on the grid, andan observer situated very faran observer situated very farfrom the systemfrom the system ------ the redderthe redderthe color, the slower local clocksthe color, the slower local clocksare running relative to clocks atare running relative to clocks atinfinityinfinity

If this were in realIf this were in real--time ittime itwould correspond to the mergerwould correspond to the mergerof two ~5000 solar mass blackof two ~5000 solar mass blackholesholes

Initial black holes are close toInitial black holes are close tononnon--spinning Schwarzschild blackspinning Schwarzschild blackholes; final black hole is a Kerr aholes; final black hole is a Kerr ablack hole with spin parameterblack hole with spin parameter~0.7~0.7,, and ~and ~4%4% of the total initialof the total initialrestrest--mass of the system ismass of the system isemitted in gravitational wavesemitted in gravitational waves

A. Buonanno, G.B. Cook and F.P.;A. Buonanno, G.B. Cook and F.P.;Phys.Rev.DPhys.Rev.D7575::124018124018,,20072007


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Gravitational waves from the simulationGravitational waves from the simulation

A depiction of the gravitationalA depiction of the gravitationalwaves emitted in the orbital planewaves emitted in the orbital planeof the binary. Shown is the realof the binary. Shown is the realcomponent of the Newman Penrosecomponent of the Newman Penrosescalarscalar ]], which in the wave zone is, which in the wave zone isproportional to the second timeproportional to the second timederivative of the usual plusderivative of the usual plus--polarizationpolarization

The plusThe plus--component of the wave fromcomponent of the wave from

the same simulation, measured on thethe same simulation, measured on theaxis normal to the orbital planeaxis normal to the orbital plane


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

Scale the system to twoScale the system to two 10 solar mass (~10 solar mass (~ 2x102x103131 kg)kg)BHsBHs

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 wasdistance from the final black hole where the wave wasmeasured ~measured ~ 1500km1500km

frequency of the wave ~frequency of the wave ~ 200Hz (early inspiral)200Hz (early inspiral) -- 800Hz800Hz(ring(ring--down)down)


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

fractional oscillatory distortion in space induced by the wave transversefractional oscillatory distortion in space induced by the wave transverseto the direction of propagation has ato the direction of propagation has a maximummaximum amplitudeamplitude ((L/LL/L ~ 3x10~ 3x10--33

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

LIGOs arm length would change by ~LIGOs arm length would change by ~ 12m12m. Wave amplitude decays like. Wave amplitude decays like1/distance from source; e.g. at 10Mpc the change in arms ~1/distance from source; e.g. at 10Mpc the change in arms ~ 5x105x10--1717mm (1/20 the(1/20 the

radius of a proton, which is well within the ballpark of what LIGO is trying toradius of a proton, which is well within the ballpark of what LIGO is trying tomeasure!!)measure!!)

despite the seemingly small amplitude for the wave, the energy it carriesdespite the seemingly small amplitude for the wave, the energy it carriesis enormousis enormous aroundaround 10103030 kg ckg c22 ~ 10~ 104747 J ~ 10J ~ 105454 ergsergs

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

luminosity of the sun ~ 10luminosity of the sun ~ 103333ergs/s, a bright supernova or milkyergs/s, a bright supernova or milky--way type galaxy ~way type galaxy ~10104242 ergs/sergs/s

if all the energy reaching LIGO from the 10Mpc event could directly be convertedif all the energy reaching LIGO from the 10Mpc event could directly be convertedto sound waves, it would have an intensity level of ~ 80dBto sound waves, it would have an intensity level of ~ 80dB


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Highlights of recent results: simplicity of merger waveformHighlights of recent results: simplicity of merger waveform

the nonthe non--linear phase of the merger is surprisingly shortlinear phase of the merger is surprisingly short

great boon for data analysis, as thisgreat boon for data analysis, as this suggestssuggests an efficient LIGO template bankan efficient LIGO template bankcould be compiled by stitching together quickcould be compiled by stitching together quick--toto--calculate perturbativecalculate perturbativewaveforms, guided by a handful of numerical waveformswaveforms, guided by a handful of numerical waveforms

toto--date, the furthest the idea has beendate, the furthest the idea has beenpushed is for quasipushed is for quasi--circular inspiral ofcircular inspiral of

nonnon--spinning BHsspinning BHs [A. Buonanno et al.,[A. Buonanno et al.,Phys.Rev.DPhys.Rev.D7676::104049104049,,20072007]]

effectiveeffective--oneone--body (EOB) PN inspiralbody (EOB) PN inspiralconnected to theconnected to the 33 dominant quasi normaldominant quasi normalmodes (QNMs)modes (QNMs)

added pseudoadded pseudo 44PN term to EO

B model,PN term to EO

B model,with coefficient determined by a bestwith coefficient determined by a best--fitfitmatch to a set of numerical resultsmatch to a set of numerical results

used simulation results for final spin andused simulation results for final spin andblack hole mass to fix the QNMblack hole mass to fix the QNMfrequencies and decay constantsfrequencies and decay constants

44::11 mass ratio examplemass ratio example


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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 asymmetricsignificant recoil can be imparted to the remnant black hole due to asymmetricbeaming of radiation during the merger, up tobeaming of radiation during the merger, up to 40004000km/s in some caseskm/s in some cases

Herrmann et al., grHerrmann et al., gr--qc/qc/07011430701143; Koppitz et al., gr; Koppitz et al., gr--qc/qc/07011630701163; Campanelli et al. gr; Campanelli et al. gr--qc/qc/07011640701164 & gr& gr--qc/qc/07021330702133, Gonzalez et al, arXiv:gr, Gonzalez et al, arXiv:gr--qc/qc/07020520702052, Tichy & Marronetti,, Tichy & Marronetti,arXiv:grarXiv:gr--qc/qc/07030750703075vv11

there are far reaching consequences to this, some that could be detected viathere are far reaching consequences to this, some that could be detected viaelectromagnetic observations, in particular for supermassive black hole mergerselectromagnetic observations, in particular for supermassive black hole mergers

offset or double galactic nuclei, displaced active galactic nuclei, wigglingoffset or double galactic nuclei, displaced active galactic nuclei, wigglingjets, enlarged cores, lopsided cores, xjets, enlarged cores, lopsided cores, x--ray afterglows, feedback trails, offray afterglows, feedback trails, off--center flares from tidally disrupted stars, hypervelocity stars, a populationcenter flares from tidally disrupted stars, hypervelocity stars, a populationof galaxies without supermassive black holes, etc.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; FujitaarXiv:0808.1726 & arXiv:0810.1520

aa 26502650km/s recoiling black hole could explain the emission line spectrakm/s recoiling black hole could explain the emission line spectra

from quasar SDSSJfrom quasar SDSSJ092712092712..6565++294344294344..00 [S. Komossa et al., ApJ.[S. Komossa et al., ApJ.678678:L:L8181,,20082008]]


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

If we want LIGO be anything more than a simpleIf we want LIGO be anything more than a simple detectordetector,,i.e. be able toi.e. be able to identifyidentify the gravitational waves, we needthe gravitational waves, we needtemplates for all plausible sources; howevertemplates for all plausible sources; however

limited computational power for template searcheslimited computational power for template searches

having too many templates increases the probability of falsehaving too many templates increases the probability of falsedetectionsdetections

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 LIGORecent studies suggest QCI may not be the dominant LIGO(or LISA) source(or LISA) source

Eccentric mergers,Eccentric mergers, potentiallypotentially transitioning from inspiral to mergertransitioning from inspiral to mergerthrough a series ofthrough a series of zoomzoom--whirlwhirl orbits, may be more likelyorbits, may be more likely


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Merging with eccentricityMerging with eccentricity

Binary stars areBinary stars are unlikelyunlikely progenitors for BH binaries that could mergeprogenitors for BH binaries that could merge

within the Hubble time, as such close binaries will likely evolve throughwithin the Hubble time, as such close binaries will likely evolve througha common envelope phase, causing a stellar merger before BHa common envelope phase, causing a stellar merger before BHformationformation [Belczynski et al., ApJ[Belczynski et al., ApJ 662662,, 20072007].].

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

A promising source for stellar mass BH binaries is then nA promising source for stellar mass BH binaries is then n--bodybodyinteractions involving BHs in dense stellar environmentsinteractions involving BHs in dense stellar environments [e.g. Sigurdsson[e.g. Sigurdsson& Hernquist, Nature& Hernquist, Nature 364364 ((19931993) , Portegies Zwart & McMilla, ApJ) , Portegies Zwart & McMilla, ApJ 528528 LL1717((20002000), Sadowski et al., arXiv:), Sadowski et al., arXiv:07100710..08780878]]

these often lead to binaries with large eccentricities that are sufficientlythese 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

OLeary et al. (OLeary et al. (arXiv:arXiv:08070807..26382638) estimate) estimate 9090% will have e>% will have e>00..99 when enteringwhen enteringthe LIGO band, with Advanced LIGO rates of ~the LIGO band, with Advanced LIGO rates of ~ 11--101033/year from mergers in/year from mergers ingalactic nuclei alonegalactic nuclei alone

For supermassive BH mergers, studies also suggest mergers may occurFor supermassive BH mergers, studies also suggest mergers may occur

with nonwith non--negligible eccentricity, e.g.negligible eccentricity, e.g. Berentzen et al., arXiv:Berentzen et al., arXiv:08120812..27562756


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

1 extra parameter not1 extra parameter not too muchtoo much of a issue for templateof a issue for templatesearchessearches

However, how the transition from inspiral to plungeHowever, how the transition from inspiral to plunge

happens could affect the feasability of present PNhappens could affect the feasability of present PNtechniquestechniques

the expansions are accurate for adiabatic evolution of the orbitalthe expansions are accurate for adiabatic evolution of the orbitalparameters, and as long asparameters, and as long as v/c < 1v/c < 1

For QCI of comparable mass binaries,For QCI of comparable mass binaries, v/c ~ 0.2v/c ~ 0.2--0.30.3 before commonbefore commonhorizon formation, which is one reason why PNhorizon formation, which is one reason why PN--techniques work so welltechniques work so wellmodeling the entire inspiralmodeling the entire inspiral

For eccentric orbitsFor eccentric orbits v/cv/c will become much largerwill become much larger


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

a second argument given why PN matches numericala second argument given why PN matches numericalsimulations so well, is the regime where it breakssimulations so well, is the regime where it breaksdown is very short, and happens well within thedown is very short, and happens well within the

effective potential barrier of the spacetime and so caneffective potential barrier of the spacetime and so cannot leave a significant imprint on the waveformnot leave a significant imprint on the waveform

this argument will fail ifthis argument will fail ifzoomzoom--whirlwhirl behavior sets in at thebehavior sets in at thetransition from inspiral to merger, and thistransition from inspiral to merger, and this maymay genericallygenerically

happen with highhappen with high--eccentricity inspiralseccentricity inspirals


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ZoomZoom--whirl orbitswhirl orbits

At a first glance might look like extreme pericenterAt a first glance might look like extreme pericenterprecessionprecession

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

usual (but large) pericenter precessionusual (but large) pericenter precession zoomzoom--whirl orbitwhirl orbit


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However, whats different about zoomHowever, whats different about zoom--whirl behavior is once thewhirl behavior is once thepericenter distance crosses the isco, you can find orbits which arepericenter distance crosses the isco, you can find orbits which are

essentiallyessentially indistinguishableindistinguishable at apoapsis but that exhibit anat apoapsis but that exhibit an arbitraryarbitrarynumber of zooms per whirl at thenumber of zooms per whirl at the samesame pericenter distancepericenter distance

300300 zoomzoom--whirl orbits, initial tangentialwhirl orbits, initial tangentialvelocity ranging fromvelocity ranging from

00..12076001207600 toto 00..1207629012076290

150150 regular orbits, initial tangentialregular orbits, initial tangentialvelocity ranging fromvelocity ranging from 00..128128 toto 00..132132


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ZoomZoom--whirl orbits are perturbations ofwhirl orbits are perturbations of unstable circular orbitsunstable circular orbits thatthat

exists within the ISCOexists within the ISCO

In Schwarzschild, radial perturbations of circular orbits in the rangeIn Schwarzschild, radial perturbations of circular orbits in the range

44M toM to 66M lead to elliptic zoomM lead to elliptic zoom--whirl orbitswhirl orbits

33M (the light ring) toM (the light ring) to 44M lead to a hyperbolic orbit with one whirl episodeM lead to a hyperbolic orbit with one whirl episode

depend on the sign of the perturbation, the geodesic will fall into the blackdepend on the sign of the perturbation, the geodesic will fall into the blackhole or not after a whirl phasehole or not after a whirl phase

The number of whirlsThe number of whirls nn is related to the magnitude of the perturbationis related to the magnitude of the perturbationHHrrand the instability exponentand the instability exponentKK of the orbit viaof the orbit via

KHr

en 1w


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Beyond geodesicsBeyond geodesics

Levin, Grossman & PerezLevin, Grossman & Perez--GizGiz [[arXiv:0811.3815,arXiv:0811.3815,

arXiv:0811.3814, arXiv:0811.3798,arXiv:0811.3814, arXiv:0811.3798, arXiv:0809.3838,arXiv:0809.3838,arXiv:0802.0459]arXiv:0802.0459] have shown the behavior persists inhave shown the behavior persists inthethe conservativeconservative dynamics of the PN expansion updynamics of the PN expansion upto 3to 3rdrd order, including spinorder, including spin--orbit interactionsorbit interactions

with spin (even for geodesics), the orbital planewith spin (even for geodesics), the orbital plane

precesses, and so the unstable orbits are sphericalprecesses, and so the unstable orbits are sphericalrather than circularrather than circular

they introduce an interesting taxonomy of the subsetthey introduce an interesting taxonomy of the subsetof exactly periodic orbits, where each orbit is classifiedof exactly periodic orbits, where each orbit is classifiedby a rational numberby a rational number qq

wherewhere ww is the number of whirls,is the number of whirls,zz the number ofthe number ofleaves that make up the zooms, andleaves that make up the zooms, and vv describes thedescribes thesequence in which the leaves are traced out (v/z


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Beyond geodesicsBeyond geodesics

Numerical simulations of equal mass nonNumerical simulations of equal mass non--QCI binaries also show zoomQCI binaries also show zoom--

whirl behaviorwhirl behavior [FP & Khurana, CQG 24 (2007); Washik et al. PRL 101[FP & Khurana, CQG 24 (2007); Washik et al. PRL 101(2008)](2008)]

Will argue that this must generically be present in the GR twoWill argue that this must generically be present in the GR two--bodybodyproblem because of the possibility ofproblem because of the possibility of two distinct endtwo distinct end--statesstates one orone or

two black holestwo black holes and this is intimately related to the existence ofand this is intimately related to the existence ofunstable orbitsunstable orbits

simulations are beginning to confirm thissimulations are beginning to confirm this

However, unlike with geodesics, there must be a limit to the number ofHowever, unlike with geodesics, there must be a limit to the number ofwhirls because of radiationwhirls because of radiation--reactionreaction

eccentric orbits have more energy than a QC orbit with radius ~ theeccentric orbits have more energy than a QC orbit with radius ~ thepericenter radius; the whirling could in principle persist until this excesspericenter radius; the whirling could in principle persist until this excessenergy is radiated awayenergy is radiated away


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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 endend--states possiblestates 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 arebecause there are two distinct endtwo distinct end--statesstates, there must be some kind of, there must be some kind ofthreshold behavior approaching a critical impact parameterthreshold behavior approaching a critical impact parameter b*b*

bb

mm11,v,v11

mm22,v,v22


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The threshold of immediate mergerThe threshold of immediate merger

The following illustrates what could happen as one tunes to threshold,The following illustrates what could happen as one tunes to threshold,assuming smooth dependence of the trajectories as a function ofassuming smooth dependence of the trajectories as a function ofbb

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

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

solid blue (black)solid blue (black) merger (escape)merger (escape)

dashed blue (black)dashed blue (black) merger (merger (escapeescape) for values of) for values ofbb closer to thresholdcloser to threshold


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The threshold of immediate merger : geodesicsThe threshold of immediate merger : geodesics

We know the previous argument works for geodesics a couple moreWe know the previous argument works for geodesics a couple moreexamples below repeating the scattering experiment for hyperbolic andexamples below repeating the scattering experiment for hyperbolic and

elliptic geodesics, tuned to the threshold to within ~ 1 part in 10elliptic geodesics, tuned to the threshold to within ~ 1 part in 101616

(giving ~ 8(giving ~ 8whirl orbits here)whirl orbits here)

unbound orbits (green scatter, blueunbound orbits (green scatter, bluecapture)capture)

bound orbits [the nonbound orbits [the non--capture case iscapture case is notnot aatwotwo--leaf orbit integration just stoppedleaf orbit integration just stopped

after the second zoom]after the second zoom]


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The threshold of immediate merger : equal mass binariesThe threshold of immediate merger : equal mass binaries

The figures below are from full numerical simulations of the field equations forThe figures below are from full numerical simulations of the field equations forequal mass orbits, showing qualitatively the same behavior as the geodesicequal mass orbits, showing qualitatively the same behavior as the geodesic

problemproblem however, the binary in the whirl phase is emitting copious amounts of gravitationalhowever, the binary in the whirl phase is emitting copious amounts of gravitational

radiation; on the order of 1radiation; on the order of 1--1.5% of the total mass of the system per orbit1.5% 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 ofemitted gravitationaldominant component ofemitted gravitational

waves as measure by NPscalarswaves as measure by NPscalars


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Animations from merger case Animations from merger case

Lapse functionLapse function EE, orbital plane, orbital plane Real component of the NewmanReal component of the Newman--PenrosePenrose

scalarscalar==44( times rM), orbital plane( times rM), orbital plane


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Key Open QuestionKey Open Question

The scattering problem highlights a potential showThe scattering problem highlights a potential show--stopper for thestopper for the

relevance of zoomrelevance of zoom--whirl behavior for generic astrophysical binarieswhirl behavior for generic astrophysical binaries excessive fine tuning of initial conditionsexcessive fine tuning of initial conditions

However, accessing the probability of a single nearHowever, accessing the probability of a single near--critical encounter iscritical encounter isnot the relevant question. Rather,not the relevant question. Rather, in a binary inspiral scenario wherein a binary inspiral scenario where

the pericenter distance reaches an effective ISCO while the binary stillthe pericenter distance reaches an effective ISCO while the binary stillpossesses a large eccentricity, does the transition from inspiral topossesses a large eccentricity, does the transition from inspiral tomerger cross a separatrix of unstable quasimerger cross a separatrix of unstable quasi--circular orbits?circular orbits?

we know the answer is yes for extremewe know the answer is yes for extreme--massmass--ratio inspirals (an importantratio inspirals (an importantsource for LISA)source for LISA)

Levin et al. claim generically it will be yes, given in their taxonomy theLevin et al. claim generically it will be yes, given in their taxonomy theQCIs are in a sense a set of measure zero of all possible orbitsQCIs are in a sense a set of measure zero of all possible orbits

energy arguments suggest it should be yes for some sufficiently largeenergy arguments suggest it should be yes for some sufficiently large

eccentricity that will depend on the masseccentricity that will depend on the mass--ratio of the binaryratio of the binary


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Consequences if yesConsequences if yes

Eccentric orbits have a larger GW luminosity near periapsisEccentric orbits have a larger GW luminosity near periapsis

in general; if whirliness occurs the luminosity will be evenin general; if whirliness occurs the luminosity will be evenhigherhigher

so even if these events are rarer, the can be seen to a much largerso even if these events are rarer, the can be seen to a much largerdistance than QCI, hence could be an important LIGO sourcedistance than QCI, hence could be an important LIGO source

[[OLeary et al. (OLeary et al. (arXiv:arXiv:08070807..26382638)])]

but need appropriate templates to see it! Casebut need appropriate templates to see it! Case--andand--point results ofpoint results ofNINJA (Numerical INJection Analysis)NINJA (Numerical INJection Analysis) [arXiv:[arXiv:09010901..43994399]], 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 relativity, asSuch events will offer exquisite tests of general relativity, asmore of the GW signal comes from the strongmore of the GW signal comes from the strong--field regionfield region

Some interesting alternative theories/extensions of GR, such asSome interesting alternative theories/extensions of GR, such asChernChern--Simons modified gravity, are consistent will all existing weakSimons modified gravity, are consistent will all existing weak

field tests, but have quite different strong field solutionsfield tests, but have quite different strong field solutions


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More speculative consequence if yesMore speculative consequence if yes

arguments for a high eccentricity BH binary population may apply toarguments for a high eccentricity BH binary population may apply to

black hole/neutron star binaries.black hole/neutron star binaries.

a backa back--ofof--thethe--envelope calculation shows that aenvelope calculation shows that a 11..55 MM neutron star willneutron star willreach its Rochereach its Roche--limitlimit withinwithin the range of unstable circular orbits (the range of unstable circular orbits (33--66M)M)for black holes with masses ~for black holes with masses ~ 55--1414 MM

if the whirl phase sets in, the black hole could peel the outer layers of theif the whirl phase sets in, the black hole could peel the outer layers of theneutron star, with a sizeable amount of the material flung back out into anneutron star, with a sizeable amount of the material flung back out into anaccretion diskaccretion disk

this is in contrast to tidal disruption in a QCI, where within less that an orbitthis is in contrast to tidal disruption in a QCI, where within less that an orbitalmost all of the material fallsalmost all of the material falls

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

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


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ConclusionsConclusions

It is not too much of a stretch of the imagination to state that we areIt is not too much of a stretch of the imagination to state that we areon the verge of a new era in observational astronomy withon the verge of a new era in observational astronomy withgravitational wave detectorsgravitational wave detectors

To realize the full potential of this generation of detectors requires thatTo realize the full potential of this generation of detectors requires thatwe understand the theory of expected sources both thewe understand the theory of expected sources both the

astrophysical populations and the nature of the gravitational waveastrophysical populations and the nature of the gravitational waveemissionemission

However, given the many open questions in the theoretical models,However, given the many open questions in the theoretical models,the complexity of the plausible scenarios, and the infeasibility ofthe complexity of the plausible scenarios, and the infeasibility ofsimulating them all, one can anticipate that the most excitingsimulating them all, one can anticipate that the most excitingdiscoveries and advances will come through a synergistic interplaydiscoveries and advances will come through a synergistic interplaybetween observation and theorybetween observation and theory

For more details, check out theFor more details, check out the Observational Signatures of Black HoleObservational Signatures of Black HoleMergersMergers conference at the STSCI March 30conference at the STSCI March 30--April 1April 1

Frans Pretorius- When Black Holes Collide

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