1 Building Bridges: CGWA Inauguration 15 December 2003 Lazarus Approach to Binary Black Hole Modeling John Baker Laboratory for High Energy Astrophysics NASA/Goddard Space Flight Center 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 Numerical Simulations Far Limit Methods Close Limit Terrestrial GW Detectors Model 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.

10 8 x10 8 at z= x10 7 at z= x10 6 at z= x at z= x10 5 at z= x10 4 at z= x10 3 at z=2

Modeling Binary Black Hole Coalescence Numerical Simulations Far Limit Methods Close Limit Terrestrial GW Detectors Model LISA Post 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 10 2 GB, 10 4 CPU-hours

Binary Black Hole Spacetime time

Numerical Simulation Model Error Close Limit Far Limit Lazarus Model time

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

Numerical Simulation Close Limit Far Limit Numerical Simulation Close Limit Far Limit Improved Model time

Numerical Simulation Close Limit Far Limit time Improved Model Problems Limited accuracy Instability Outer boundaries Error grows rapidly in time LazEv Higher order finite differencing Better coordinate gauge choice ADM/BSSN systems New (Cactus) evolution code LazEv Mathematica based coding Allows greater complexity Adaptable

Numerical Simulation Close Limit Far Limit time 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

Numerical Simulation Close Limit Far Limit time Improved Model Application Coming 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.

End