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Building Bridges: CGWA Inauguration15 December 2003

Lazarus Approach to Binary Black Hole Modeling

John BakerLaboratory for High Energy Astrophysics

NASA/Goddard Space Flight Center

Lazarus Group

•Lazarus Group

•UTB: CGWA •Manuela Campanelli•Carlos Lousto•Mark Hannam•Enrique Pazos•Yosef Zlochower

•Goddard Space Flight Center:•John Baker

• Louisiana State University:•Ryoji Takahashi

•Goddard Gravitational Wave Astrophysics Numerical Relativity Group

•Joan Centrella•John Baker•Dae-Il Choi•Jim Van Meter•David Fiske•Breno Imbiriba•David Brown (NCSU)

Modeling Binary Black Hole Coalescence

NumericalSimulations

Far LimitMethods

Close Limit

TerrestrialGW

Detectors

Model

LISA

LISA

•How much can we learn about sources from merging SMBH?•How do we test GR using merging SMBH? •Last few cycles high SNR representing strong field interactions.

108x108 at z=2

107x107 at z=1

106x106 at z=1

106x105.5 at z=1

105x105 at z=10

104x104 at z=2

103x103 at z=2

Modeling Binary Black Hole Coalescence

NumericalSimulations

Far LimitMethods

Close Limit

TerrestrialGW

Detectors

Model

LISAPost Newtonian Approximation

• Slow moving particles (BH,NS,…)• Standard for early inspiral dynamics

Kinematical models (no dynamics)•Solutions of initial value equations •Astrophysical and theoretical choices• Quasi-circular orbit initial data families

Other ideas•Further creativity may be needed for late inspiral dynamics

Black hole perturbation theory• Linear dynamics Kerr black hole

distortions• Good for radiation and ringdown• Easy 2+1 stable evolution• Agrees well with numerical simulation

Numerical Relativity• Full General Relativity on a computer• Large system of coupled nonlinear PDEs• Coordinate gauge choice issues• Boundaries• Need stable formalisms• Constrained evolution?• Specialized software platforms - CACTUS, PARAMESH• Making the best application of existing technology

• Binary black holes• Initial values (must be modeled)• Range of space/time scales• Singularities … excision/punctures• Limited accurate evolution time (so far)• Supercomputers 102 GB, 104 CPU-hours

Binary Black HoleSpacetime

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NumericalSimulation

ModelError

Close Limit

Far Limit

LazarusModel

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Lazarus Model Results: Equal mass non-spinning black holes

• Rapid plunge• Some support for simple “far limit” model• Circular polarization pattern

– As for a rotating body– Efficient angular momentum radiation (∆J=/2 ∆E)– Instantaneous frequency

• ~2.5% of system energy radiated “post-ISCO”• Simple dynamical picture

– Analytic waveform fit...

• More physics…– Spins– Unequal masses

Polarization angle

Polarization amplitude

Lazarus Model Results: Equal mass non-spinning black holes

Spins

• Rapid plunge• Some support for simple “far limit” model• Circular polarization pattern

– As for a rotating body– Efficient angular momentum radiation (∆J=/2 ∆E)– Instantaneous frequency

• ~2.5% of system energy radiated “post-ISCO”• Simple dynamical picture

– Analytic waveform fit...

• More physics…– Spins– Unequal masses

Lazarus Model Results: Equal mass spinning black holes

• Simple waveforms– Like non-spinning case– Also seen in PN studies

– Similar after rescaling by QN

• Circular polarization pattern • Post-ISCO Energy: ~2-2.5%• Angular momentum: final BH a/m?

– Roughly half the “added” angular momentum retained– Seems difficult to form a maximally rotating BH

• What’s next?– Unequal masses– improvements

NumericalSimulation

Close Limit

Far Limit

NumericalSimulation

Close Limit

Far Limit

Improved Model

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NumericalSimulation

Close Limit

Far Limit

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Improved Model

Problems•Limited accuracy•Instability•Outer boundaries•Error grows rapidly in timeLazEv

•Higher order finite differencing•Better coordinate gauge choice•ADM/BSSN systems•New (Cactus) evolution code LazEv

•Mathematica based coding•Allows greater complexity•Adaptable

NumericalSimulation

Close Limit

Far Limit

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Improved Model

Problems•Limited accuracy•Instability•Outer boundaries•Error grows rapidly in time

Goddard Approach•Fixed/Adaptive Refinement•Better coordinate gauge choice•BSSN system•Collaboration with CGWA on Lazarus model application

NumericalSimulation

Close Limit

Far Limit

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Improved Model

ApplicationComing 2004

• Applications– Refinement of previous results with greater sensitivity

• Initial data transients

• Waveform spin dependence

• Higher-order multipole radiation components

– Enlarged applicable problem space• Increased range of mass ratios (“kicks”)

• Increased initial separations

• Emerging technology– Improved NS-CL interface (with C. Beetle,Y. Mino)

– Greater application of post-Newtonian techniques

– Initial data varieties

– Further advances in Numerical Sims.

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