1 Ulrich Sperhake California Institute of Technology Black-hole binary systems as GW source Astro-GR...

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Ulrich Sperhake

California Institute of Technology

Black-hole binary systems as GW sourceBlack-hole binary systems as GW source

Astro-GR meetingBarcelona, Sep 7th – Sep 11th 2009

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OverviewOverview

The basics of numerical relativity

Results

Future research directions

Equal-mass, nonspinning Unequal-mass Spinning binaries NR and DA

Motivation

Animations

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1. Motivation1. Motivation

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Black Holes predicted by GRBlack Holes predicted by GR

valuable insight into theory

Black holes predicted by Einstein’s theory of relativity

Vacuum solutions with a singularity

For a long time: mathematical curiosity

Term “Black hole” by John A. Wheeler 1960s

but real objects in the universe?

That picture has changed dramatically!

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How to characterize a black hole?How to characterize a black hole?

Consider light cones

Outgoing, ingoing light

Calculate surface area

of outgoing light

Expansion:=Rate of

change of that area

Apparent horizon:=

Outermost surface with zero expansion

“Light cones tip over” due to curvature

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Black Holes in astrophysicsBlack Holes in astrophysics

Structure formation in the early universe

Black holes are important in astrophysics

Structure of galaxies

Black holes found at centers of galaxies

Important sources of electromagnetic radiation

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Fundamental physics of black holesFundamental physics of black holes

Allow for unprecedented tests of fundamental physics

Strongest sources of Gravitational Waves (GWs) Test alternative theories of gravity No-hair theorem of GR Production in Accelerators

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Gravitational wave (GW) physicsGravitational wave (GW) physics

Einstein GWs; Analog of electromagnetic waves

Strongest source: coalescing black holes

Latest laser technology: GEO600, LIGO, TAMA, VIRGO

GWs change in separation

Atomic nucleus over km 1

Space mission: LISA

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Targets of GW physicsTargets of GW physics

Confirmation of GR

Parameter estimation of black holes

Optical counterparts

SM

,

Neutron stars: Equation of state

Standard sirens (candles)

Graviton mass

Test the Kerr nature

Cosmological sources

Hulse & Taylor 1993 Nobel Prize

Waveforms crucial for detection and parameter estimation

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Space interferometer LISASpace interferometer LISA

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Pulsar timing arraysPulsar timing arrays

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Modelling of black-hole binariesModelling of black-hole binaries

Approximation theories (PN, Perturbation theory,…)

Analytic solutions for dynamic systems: Hopeless!!!

Modelling:

Numerical Relativity (this talk!)

Strenght and weaknesses

Appr.: efficient, approximative, works?, available

NR: slow, “exact theory”, works, availability?

Good GW modeling uses both!

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The big pictureThe big picture

Model GR (NR) PN Perturbation theory Alternative Theories?

External Physics Astrophysics Fundamental Physics Cosmology

DetectorsPhysical system

describes

observe

test Provide info

Help d

etec

tion

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2. The basics of numerical relativity2. The basics of numerical relativity

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A list of tasksA list of tasks

Target: Predict time evolution of BBH in GR

Einstein equations: Cast as evolution system Choose specific formulation Discretize for Computer

Choose coordinate conditions: Gauge

Fix technical aspects: Mesh-refinement / spectral domains Excision Parallelization Find large computer

Construct realistic initial data

Start evolution and wait…

Extract physics from the dataGourgoulhon gr-qc/0703035

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2.1. The Einstein equations2.1. The Einstein equations

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Theoretical framework of GW course modelingTheoretical framework of GW course modeling

Description of spacetime

Metric g

Field equations:

TgggG 8, , 2

0 RGIn vacuum:

10 PDEs of order for the metricnd2

MTW: “Spacetime tells matter how to move, matter tells spacetime how to curve”

System of equations very complex: Pile of paper!

Numerical methods necessary for general scenarios!

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3+1 Decomposition3+1 Decomposition

GR: “Space and time exist as unity: Spacetime”

NR: ADM 3+1 Split Arnowitt, Deser, Misner (1962)York (1979)Choquet-Bruhat, York (1980)3-Metric ij

Lapse

Shift

i

lapse, shift Gauge

Einstein equations 6 Evolution eqs.

4 Constraints

Constraints preserved under time evolution!

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ADM EquationsADM Equations

Evolution equations

ijijt KL 2)(

]2[)( KKKKRDDKL ijjm

imijjiijt

Constraints02 ij

ijKKKR

0 KDKD iijj

Evolution

Solve constraints Evolve data Construct spacetime Extract physics

US et al., PRD 69, 024012

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GR specific problemsGR specific problems

Initial data must satisfy constraints

Numerical solution of elliptic PDEs

Formulation of the Einstein equations

Coordinates are constructed Gauge conditions

Different length scales Mesh refinement

Equations extremely long Turnover time Paralellization, Super computer

Interpretation of the results? What is “Energy”, “Mass”?

Here: Puncture data Brandt & Brügmann ‘97

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Eqs.: Baumgarte, Shapiro, Shibata, Nakamura (BSSN)Eqs.: Baumgarte, Shapiro, Shibata, Nakamura (BSSN)

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Generalized harmonic (GHG)Generalized harmonic (GHG)

Harmonic gauge: choose coordinates so that

0 x

4-dim. Version of Einstein equations

...2

1

ggR (no second derivatives!!)

Principal part of wave equation

Generalized harmonic gauge: xgH :

HHggR 2

1...

2

1

Still principal part of wave equation!!!

Alternative: GHG Pretorius ‘05

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Coordinate and gauge freedomCoordinate and gauge freedom

Reminder: Einstein Eqs. say nothing about i ,

Avoid coordinate singularities! González et al. ‘08

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Reminder: Einstein Eqs. Say nothing about i ,

Avoid coordinate singularities!

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Coordinate- and Gauge freedomCoordinate- and Gauge freedom

General scenarios require “live” conditions

),,( iji

t F ),,( ijii

t G

Hyperbolic, parabolic or elliptic PDEs

Pretorius ‘05 Generalized Harmonic Gauge

Goddard, Brownsville ‘06 moving punctures

slicing, driverlog1

based on Alcubierre et al. (AEI)

Bona, Massó 1990s

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Diagnostik: WellenformenDiagnostik: Wellenformen

In and outgoing direction are specified via Basis vectors Kinnersley ‘69

mmn , , ,

Newman-Penrose scalar

mnmnR4

At Null-Infinity ! But cf. Nerozzi & Ellbracht ‘08

Waves are normally extracted at fixed radius

,,44 t Decompose angular dependence

m

mm Yt,

24 ,

“Multipoles”

Gives directly radradrad J , , PE

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A brief history of BH simulationsA brief history of BH simulations

Pioneers: Hahn, Lindquist ’60s, Eppley, Smarr et.al. ‘70s

Grand Challenge: First 3D Code Anninos et.al. ‘90s

Codes unstable

AEI-Potsdam Alcubierre et al.

Further attempts: Bona & Massó, Pitt-PSU-Texas, …

PSU: first orbit Brügmann et al. ‘04

_______________________________________________________ Breakthrough: Pretorius ’05 “GHG”

UTB, Goddard ’05 “Moving Punctures”

Currently: codes, a.o.10Pretorius, UTB/RIT, Goddard, PSU/GT, Sperhake, Jena/FAU, AEI/LSU, Caltech-Cornell, UIUC, Tainan/Beijing

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3. Animations3. Animations

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AnimationsAnimations

Ktr

Extrinsic curvature

Lean Code Sperhake ‘07

Apparent horizon

AHFinderDirectThornburg

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]Re[ 4

2,2 mdominant

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Event horizon of binary inspiral and merger BAM

Thanks to Marcus Thierfelder

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4. Results on black-hole binaries4. Results on black-hole binaries

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Free parameters of BH binariesFree parameters of BH binaries

Total mass ADMM

Relevant for detection: Frequencies depend on ADMM

Not relevant for source modeling: trivial rescaling

Mass ratio 221

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2

1 ,MM

MM

M

Mq

Spin 21 , SS

Initial parameters

Binding energy Separation bE Orbital angular momentum EccentrictyL

Alternatively: frequency, eccentricity

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4.1. Non-spinning equal-mass holes4.1. Non-spinning equal-mass holes

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The BBH breakthroughThe BBH breakthrough

Simplest configuration

GWs circularize orbit quasi-circular initial data

Pretorius PRL ‘05

Initial data: scalar field

Radiated energy

]%[

][ ex

ME

MR 25 50 75 100 4.7 3.2 2.7 2.3

Eccentricity

2.0...0e

BBH breakthrough

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Non-spinning equal-mass binariesNon-spinning equal-mass binaries

Total radiated energy: ADM %6.3 M

mode dominant: %982,2 m

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The merger part of the inspiralThe merger part of the inspiral

merger lasts short: 0.5 – 0.75 cycles

Buonanno, Cook, Pretorius ’06 (BCP)

Eccentricity small

01.0

non-vanishing

Initial radial velocity

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Samurei: Comparing NR resultsSamurei: Comparing NR results

Nonspinning, equal-mass binaries

Hannam et al. ‘08

5 codes: Bam, AEI, Caltech/Cornell, Goddard, PSU/GT

Agreement: in amplitude% 5 rad, 1 ... 1.0

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Comparison with Post-NewtonianComparison with Post-Newtonian

14 cycles, 3.5 PN phasing

Goddard ‘07

Match waveforms: ,

Accumulated phase error rad 1

Buonanno, Cook, Pretorius ’06 (BCP)

3.5 PN phasing 2 PN amplitude

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Comparison with Post-NewtonianComparison with Post-Newtonian

18 cycles

Hannam et al. ‘07

phase error rad 16th order differencing !!

30 cycles

First comparison with spin; not conclusive yet

Cornell/Caltech & Buonanno

phase error rad 02.0

RIT

Effective one body (EOB)

Amplitude: % range

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CCE: Wave extraction at infinityCCE: Wave extraction at infinity

“Cauchy characteristic extraction”

Reisswig et al. ‘09

Waves extracted at null infinity

Comparison with finite radii: % 08.1/ rad, 019.0 AA

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Zoom whirl orbitsZoom whirl orbits

1-parameter family of initial data: linear momentum

Pretorius & Khurana ‘07

Fine-tune parameter ”Threshold of

immediate merger”

Analogue in geodesics !

Reminiscent of

”Critical phenomena”

Similar observations by

PSU

Max. spin for 78.0fin j 2ML

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Zoom whirl orbits: How much finetuning needed?Zoom whirl orbits: How much finetuning needed?

Larger mass ratio Stronger zoom-whirl

Healy et al. ’09b

Perihelion precession vs. zoom-whirl?

Separatrix other than ISCO

Zoom-whirl a common

feature?

Impact on GW detection?

High-energy collisions

US et al. ‘09

Zoom-whirl present in

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Is there a “golden hole” ?Is there a “golden hole” ?

Sequences of binaries with aligned

Healy et al. ’09a

Change direction of

Similar end state…

SL

,

P

Oscillations in

finfin ,Mj

What happens

for larger ?iniJ

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4.2. Unequal masses4.2. Unequal masses

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Unequal massesUnequal masses

Still zero spins

Astrophysically much more likely !!

Symmetry breaking

Anisotropic emission of GWs

Certain modes are no longer suppressed

Mass ratios

Stellar sized BH into supermassive BH

Intermediate mass BHs

Galaxy mergers

610310

310...1

Currently possible numerically: 10...1

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Gravitational recoilGravitational recoil

Anisotropic emission of GWs radiates momentum recoil of remaining system

Leading order: Overlap of Mass-quadrupole with octopole/flux-quadrupole Bonnor & Rotenburg ’61, Peres ’62, Bekenstein ‘73

Merger of galaxies

Merger of BHs

Recoil

BH kicked out?

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Gravitational recoilGravitational recoil

Ejection or displacement of BHs has repercussions on:

Escape velocities

km/s 30Globular clustersdSphdE

Giant galaxies

km/s 10020 km/s 300100

km/s 1000

Structure formation in the universe

BH populations

Growth history of Massive Black Holes

IMBHs via ejection?

Structure of galaxies

Merrit et al ‘04

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Kicks of non-spinning black holesKicks of non-spinning black holes

Parameter study Jena ‘07

4...1/ 21 MM

3/ 21 MMkm/s 178

Target: Maximal Kick

Mass ratio:

150,000 CPU hours

Maximal kick for

Convergence 2nd order

%25 %,3 radrad JE

Spin 7.0...45.0

Simulations PSU ’07, Goddard ‘07

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Features of unequal-mass mergersFeatures of unequal-mass mergers

Distribution of radiated energy

More energy in higher modes

Odd modes suppressed for equal masses

Important for GW-DA

Berti et al ‘07

Same for spins! Vaishnav et al ‘07

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Mass ratio 10:1Mass ratio 10:1

Mass ratio ;

6th order convergence

Astrophysically likely configuration: Sesana et al. ‘07

10q

Test fitting formulas for spin and kick!

González, U.S., Brügmann ‘09

Gergeley & Biermann ‘08

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(Fitchett ‘83 Gonzalez et al. ’07)

V~67 km/s

)93.01(41102.1 24 vKick:

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Radiated energy:

ΔE/M~0.004018

(Berti et al. ’07)2 5802.0

M

E

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Final spin: (Damour and Nagar 2007)

aaF/MF~0.2602

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4.3. Spinning black holes4.3. Spinning black holes

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Spinning holes: The orbital hang-upSpinning holes: The orbital hang-up

Spins parallel to more orbits, largerL

UTB/RIT ‘07

radrad JE ,

Spins anti-par. to fewer orbits smallerL

radrad JE ,

no extremal Kerr BHs

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Spin precession and flipSpin precession and flip

X-shaped radio sources Merritt & Ekers ‘07

Jet along spin axis

Spin re-alignment new + old jet

Spin precession Spin flip UTB, Rochester ‘06

9871

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Recoil of spinning holesRecoil of spinning holes

Kidder ’95: PN study with Spins

= “unequal mass” + “spin(-orbit)”

Penn State ‘07: SO-term larger

extrapolated:

8.0,...,2.0m

a

km/s 475v

AEI ’07: One spinning hole, extrapolated: km/s 440v

UTB-Rochester:

km/s 454v

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Super KicksSuper Kicks

Side result RIT ‘07, Kidder ’95: maximal kick predicted for

Test hypothesis

González, Hannam, US, Brügmann & Husa ‘07

Use two codes: Lean, BAM

km/s 1300v

Generates kick for spinkm/s 2500v 0.75a

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Super KicksSuper Kicks

Side result RIT ‘07, Kidder ’95: maximal kick predicted for

Test hypothesis

González, Hannam, US, Brügmann & Husa ‘07

Use two codes: Lean, BAM

km/s 1300v

Generates kick for spinkm/s 2500v

Extrapolated to maximal spin RIT ‘07

0.75a

km/s 4000v

Highly eccentric orbits PSU ‘08

km/s 10000v

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What’s happening physically?What’s happening physically?

Black holes “move up and down”

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A closer look at super kicksA closer look at super kicks

Physical explanation: “Frame dragging”

Recall: rotating BH drags objects along with its rotation

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Physical explanation: “Frame dragging”

Recall: rotating BH drags objects along with its rotation

Thanks to F. Pretorius

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But: frame dragging is conservative!

Study local momentum distribution in head-on collision

Lovelace et al. ‘09

Blue shifted GW emission…

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How realistic are superkicks?How realistic are superkicks?

Observations BHs are not generically ejected!

Are superkicks real?

Gas accretion may align spins with orbit Bogdanovic et al.

Kick distribution function: 2121kickkick /,, MMSSvv

Analytic models and fits: Boyle, Kesden & Nissanke,

AEI, RIT, Tichy & Marronetti,…

EOB study only 12% of all mergers have km/s 500v

Use numerical results to determine free parameters

7-dim. Parameter space: Messy! Not yet conclusive…

Schnittman & Buonanno ‘08

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NR/PN comparison of spinning binariesNR/PN comparison of spinning binaries

Equal mass, aligned spin

Hannam et al. ‘09

0.85j

Up to :0.1 rad, 3 % 12A/A

Campanelli et al. ‘09

Precessing configuration: 4.0 ,6.0 0.8, 21 jjq

9 orbits

overlap in 6 orbits% 99

Higher order PN needed

Vaishnav et al. ’08a,b

Higher order multipoles needed to break degeneracy!

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4.4. Numerical relativity and data analysis4.4. Numerical relativity and data analysis

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The Hulse-Taylor pulsarThe Hulse-Taylor pulsar

Binary pulsar 1913+16

Hulse, Taylor ‘93

GW emission

Inspiral

Change in period

Excellent agreement with relativistic prediction

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The data stream: Strong LISA sourceThe data stream: Strong LISA source

SMBH binary

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The data stream: Matched filteringThe data stream: Matched filtering

Matched filtering (not real data)

Filter with one waveform per parameter combination

Problem: 7-dim parameter space

We need template banks!

Noise + Signal

TheoreticallyPredicted signal

Overlap

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Numerical relativity meets data analysisNumerical relativity meets data analysis

Ajith et al. ‘07

PN, NR hybrid waveforms

Approximate hybrid WFs with phenomenological WFs

Fitting factors: 99.0

Alternative: EOB Buonanno, Damour, Nagar and collaborators.

Use NR to determine free parameters

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Pan et al. ‘07

Numerical relativity meets data analysisNumerical relativity meets data analysis

PSU ‘07

Investigate waveforms from spinning binaries Detection of spinning holes likely to require inclusion

of higher order multipoles

Cardiff ‘07

Higher order multipoles important for parameter estimates

Equal-mass, non-spinning binaries

Plot combined waveforms for different masses

Ninja: Aylott et al. ’09, Cadonatti et al. ‘09

Large scale effort to use NR in DA

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Noise curvesNoise curves

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Size doesn’t matter… or does it?Size doesn’t matter… or does it? Only in last 25 cycles plus Merger and RDsol 10M % 50 in last 23 cycles + MRDsol 20M % 90 in last 11 cycles + MRD NR can do that!sol 30M % 90 in last cycle + MRD Burst!% 90

sol 100M

Buonannoet al.’07

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Expected GW sourcesExpected GW sources

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How far can we observe?How far can we observe?% 50

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Main future research directionsMain future research directions

Gravitational wave detection

PN comparisons with spin

Understand how to best generate/use hybrid wave forms

Astrophysics

Distribution functions for

Fundamental physics High energy collisions: radiated energy, cross sections

Higher dimensional BH simulations

Generate template banks

Improve understanding of Accretion, GW bursts,…

Kick, BH-spin, BH-mass

Simulate extreme mass ratios

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7.4. High energy collisions7.4. High energy collisions

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MotivationMotivation

US, Cardoso, Pretorius, Berti & González ‘08

Head-on collision of BHs near the speed of light

Test cosmic censorship

Maximal radiated energy

First step to estimate GW leakage in LHC collisions

Model GR in most violent regime

Numerically challenging

Resolution, Junk radiation

Shibata et al. ‘08

Grazing collisions, cross sections

Radiated energy even larger

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Example: Head-on with Example: Head-on with 75.2

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Total radiated energyTotal radiated energy

Total radiated energy: about half of Penrose’s limit% 314

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7.5. Neutron star – BH binaries7.5. Neutron star – BH binaries

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Neutron star is disruptedNeutron star is disrupted

Etienne et al. ‘08

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WaveformsWaveforms


Ringdown depends on mass ratio

Active research area:

UIUC, AEI,Caltech/Cornell

5 3, 1,q

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Future researchFuture research

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Main future research directionsMain future research directions

Gravitational wave detection

PN comparisons with spin

Understand how to best generate/use hybrid wave forms

Astrophysics

Distribution functions for

Fundamental physics High energy collisions: radiated energy, cross sections

Higher dimensional BH simulations

Generate template banks

Improve understanding of Accretion, GW bursts,…

Kick, BH-spin, BH-mass

Simulate extreme mass ratios

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1 Ulrich Sperhake California Institute of Technology Black-hole binary systems as GW source Astro-GR...

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