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07 Nov 2003Gravitational Wave Phenomenology Workshop1 Numerical Relativity Deirdre ShoemakerCornell University The role of numerical relativity in gravitational-wave astrophysics Status of Binary Black Hole (BBH) simulations In the absence of a complete solution to the BBH problem, what can we do today? –Introduce approximations Sequences of quasi-circular orbits Lazarus approach to BBH mergers –Extract info from single BH evolutions The spectrum of highly distorted black-holes Open Questions

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07 Nov 2003Gravitational Wave Phenomenology Workshop2 Numerical Relativity: Modeling gravitational wave sources Full NR: Compact object binaries Supernovae ? Less NR: Extreme mass ratio binaries NS oscillations

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07 Nov 2003Gravitational Wave Phenomenology Workshop3 Today’s black-hole source simulations 1.Single BH evolutions: Static Boosted Wobbling Distorted 2.BBH Mergers 3.BBH < 30% orbit

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07 Nov 2003Gravitational Wave Phenomenology Workshop4 Quasi-equilibrium orbits Binding Energy: We have the numerical infrastructure to solve elliptic equations (i.e. initial data) Quasi-adiabatic phase of the BBH system ~ sequences of quasi-circular initial data orbits Identification of the “innermost stable circular orbit” Effective Potential Method (Cook & Baumgarte)

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07 Nov 2003Gravitational Wave Phenomenology Workshop5 Thin-Sandwich Method (Meudon) Data Satisfy:Circular orbits found from:

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07 Nov 2003Gravitational Wave Phenomenology Workshop6 Goal: to resurrect a death non-linear calculation How: On the 3 rd day, match it to a perturbative calculation Lazarus Project: Start with ISCO data, merger takes place before code dies, continue with Teukolsky evolution. This approach is a natural extension of close limit approximation (Price & Pullin) Non-linear matching to perturbative regime

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07 Nov 2003Gravitational Wave Phenomenology Workshop7

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07 Nov 2003Gravitational Wave Phenomenology Workshop8

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07 Nov 2003Gravitational Wave Phenomenology Workshop9 Lazarus Equal mass spinning black holes (~2.25%) Baker et al (2003)

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07 Nov 2003Gravitational Wave Phenomenology Workshop10 Generating modes in black-hole spacetimes What modes are generated if you hit a black hole hard enough? Study highly distorted black-holes End result of the merger of two black holes Prediction of mode content impacts data analysis algorithms In the linear regime, the modes are well known In the non-linear regime, it is possible to study mode coupling Allen et. al (1998) Papadopoulos (2002) Zlochower et. al (2003) DS et. al (2003)

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07 Nov 2003Gravitational Wave Phenomenology Workshop11 Distorted black holes Using Characteristic codes: mode-mode coupling for Schwarzschild DBHs. Papadopoulos(2002) Zlochower et. al (2003)

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07 Nov 2003Gravitational Wave Phenomenology Workshop12 Distorted black holes in Cauchy formulism D. Shoemaker, H. Pfeiffer, L. Kidder, and S. Teukolsky log(A) vs evolution timeFFT(A) vs period Amplitude of the l=2,m=0 mode for A(t=0) = 0.01 and A(t=0) = 0.1

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07 Nov 2003Gravitational Wave Phenomenology Workshop13 Numerical Relativity We need more approaches that involve approximations. Lower dimension calculations (i.e. axisymmetry) Impact of numerical accuracy on data analysis tools. More astrophysical input in initial data And of course the usual

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Louisiana State University www.cct.lsu.edu Numerical Simulations of Colliding Black Holes General Motivation: why is this so important now? –Understanding.

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