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Gravitational Waveforms Gravitational Waveforms from Coalescing from Coalescing Binary Black Holes Binary Black Holes Dae-Il (Dale) Choi NASA Goddard Space Flight Center, MD, USA Universities Space Research Association, USA Supported by NASA ATP02-0043-0056 & NASA Advanced Supercomputing Project “Columbia” Numerical Relativity 2005 Workshop NASA Goddard Space Flight Center, Greenbelt, MD, NOV 2, 2005

Gravitational Waveforms from Coalescing Binary Black Holes

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Gravitational Waveforms from Coalescing Binary Black Holes. Dae-Il (Dale) Choi NASA Goddard Space Flight Center, MD, USA Universities Space Research Association, USA Supported by NASA ATP02-0043-0056 & NASA Advanced Supercomputing Project “Columbia” - PowerPoint PPT Presentation

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Page 1: Gravitational Waveforms                   from Coalescing Binary Black Holes

Gravitational Waveforms Gravitational Waveforms from Coalescing Binary Black Holesfrom Coalescing Binary Black Holes

Dae-Il (Dale) Choi NASA Goddard Space Flight Center, MD, USA

Universities Space Research Association, USA

Supported by NASA ATP02-0043-0056 & NASA Advanced Supercomputing Project “Columbia”

Numerical Relativity 2005 Workshop NASA Goddard Space Flight Center, Greenbelt, MD, NOV 2, 2005

Page 2: Gravitational Waveforms                   from Coalescing Binary Black Holes

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

CollaboratorsCollaboratorsIt’s teamworkIt’s teamwork

Joan Centrella, John Baker (NASA/GSFC)

Jim van Meter, Michael Koppitz (National Research Council)

Breno Imbiriba, W. Darian Boggs, Stefan Mendez-Diez (University of Maryland)

Other collaborators

J. David Brown (North Carolina State Univ.)

David Fiske (DAC, formerly NASA/GSFC)

Kevin Olson (NASA/GSFC)

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

OutlineOutline

Methodology: Hahndol Code [Hahndol= 한돌 =translation of “Ein-stein” into Korean]

Results: Inspiral merger from the ISCO (QC0)

Results: Head-on collision (if time allows)

Movie of the real part of Psi4

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

Hahndol CodeHahndol Code

3+1 Numerical Relativity Code

– BSSN formalism following Imbiriba et al, PRD70, 124025 (2004), Alcubierre at al PRD67, 084023 (2003) except the new gauge conditions.

– Uses finite differencing (mixed 2nd and 4th order FD, Mesh-Adapted-Differencing–see posters for details), iterative Crank-Nicholson time integrator.

– Computational infrastructure based on PARAMESH (MacNiece, Olson) Scalability shown up to 864 CPUs with ~ 95% efficiency.

Mesh refinement

– Currently use fixed mesh structure with mesh boundaries at (2,4,8,16,32,64)M for QC0 runs.

– The innermost level contains the both black holes.

– For higher QC-sequence, AMR implementation being tested.

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

Hahndol CodeHahndol CodeOuter boundary conditions

– Impose outgoing Sommerfeld conditions on all BSSN variables.

– But, basic strategy is to push OB far away so that OB does not contaminate regions of interests.

– With OB=128M, no harmful effects on the dynamics of black holes nor waveform extraction (QC0). If desired, OB can be put at 256M or beyond.

Initial data solver

– Uses multi-grid method on a non-uniform grid using Brown’s algorithm: Brown & Lowe, JCP 209, 582-598, 2005 (gr-qc/0411112).

– Generate QC ID by solving HCE using puncture method (Brandt & Bruegmann, 1997).

– Bowen-York prescription for the extrinsic curvature for binary black holes.

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

Hahndol CodeHahndol CodeTraditional gauge conditions (AEI, etc.)

– Split conformal factor into time-indep. singular part (ΨBL) and time-dep. regular part. Treat ΨBL analytically and evolve only the regular part.

– Use the following K-/Gamma-driver conditions for gauges. (BL factor)

– Problem is that, because of ΨBL factor, black holes cannot move.

– Requires co-rotation shift. But it involves superluminal shift.

Alternative gauge conditions

– Do not split into singular/regular part. No BL factor. – Combined with the driver conditions, let the black holes move across the grid.

– Does this really work?

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

Hahndol CodeHahndol CodeNot so fast! Two concerns.

– (a) Puncture memory effect: BHs move but still spiky errors at where the punctures were at t=0.

– (b) Messy stuff near the would-have-been puncture locations if they were moving.

The problem (a)

– Caused by the zero-speed mode in the Gamma driver shift condition

– Can be alleviated by “shifting shift”

[Movies] comparison bet. (1) Traditional (crashed at t=35M) (2) No BL factor (3) NoBL + Shifting Shift

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

Hahndol CodeHahndol CodeThe problem (b)

– In practice, we find that the stuff doesn’t seem to “spill over”.

– [Movie: Head-on collision w/ L/M~9 using NoBL+Shifting Shift] shows a good convergence of HC from 3 runs with different resolutions.

– Note, with the traditional gauge, HC too large and non-convergent.

For all the cases we considered, this new gauge conditions allow us to obtain convergent results (constraints, waveforms).

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

Hahndol CodeHahndol Code

Wave extraction

– Compute the Newman-Penrose Weyl scalar Ψ4 (a gauge invariant measure)

where C is weyl tensor and (l,n,m,mbar) is a tetrad.

– Analyze its harmonic decomposition using a novel technique due to Misner (Misner 2004; Fiske 2005).

– Compute waveforms r ~ 20M, 30M, 40M and 50M.

Coulomb scalar χ [Beetle, et al, PRD72, 024013 (2005); Burko, Baumgarte & Beetle, gr-qc/0505028.]

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

Evolution of Quasi Circular Initial DataEvolution of Quasi Circular Initial Data

QC-sequence (Minimization of effective potential, Cook 1994)

QC0, L/M=4.99, J/M^2=0.779

Re-Coulomb invariant: ReC(horizon) = -1/(8M2) for quiecent BHs. [Movie: Horizon at ReC~ -1/2 (yellowish) at T=0; Horizon at ReC~-1/8 (blue edge) late times.]

4M 180M

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

QC0 (BH source region)QC0 (BH source region)Comparison of Re (Coulomb) scalar for three different resolutions: M/16, M/32, M/48 runs. [Only in this movie, time label is in terms of (M/2)]

(In this talk, different runs are labeled by the resolution in the finest resolution grid.)

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

QC0 (BH source region)QC0 (BH source region)Convergence of HC near black holes along x-axis from M/24 (Dashed) and M/32 (Solid) runs. Data from Time=11M,19M,24M where BHs are crossing the x-axis. (Note FMR boundaries are at 2M, 4M, etc.)

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

QC0 WaveformsQC0 WaveformsWaveforms (Re L=2, M=2 mode) from three runs, M/16, M/24, M/32 extracted at rextract =20M (Solid), 40M(Dashed). Plotted are (r x Psi4).

Good O(1/r) propagation behavior; M/24, M/32 are very close.

Comparison with Lazarus I--Baker et al, PRD 65,124012 (2002)

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

QC0 (Waveforms)QC0 (Waveforms)Convergence of waveforms (real and imaginary parts of L=2, M=2 mode) at r=20M (upper panels), and 40M (lower panels).

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

QC0 (dE/dt, dJz/dt)QC0 (dE/dt, dJz/dt)Energy & angular momentum loss due to GWdE/dt, dJz/dt

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

QC0 QC0 (Energy and Angular momentum)(Energy and Angular momentum)

Total E and Total Jz loss (plotted for three resolutions and for 4 different extraction radii)

At r=30M,

Final J~0.65

Resolution E Jz

M/16 0.0494 -0.200 (26%)

M/24 0.0325 -0.133 (17%)

M/32 0.0315 -0.132 (17%)

Lazarus I 0.025 -0.093 (12%)

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

QC0 (Energy Conservation?)QC0 (Energy Conservation?)Calculate ADM Mass (Murchadha & York, 1974)

Energy conservation: Minit-Mfinal= EGW?

r=40M,50M, Solid represents M(t), Dashed M(t=0)-EGW(t).

Minit-Mfinal= EGW!

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

Head-On CollisionHead-On CollisionLeft Panel: Waveforms extracted at rextract = 20M, 30M, 40M, 50M

– Colored lines show O(1/r) propagation fall-off behavior (M1=M2=0.5)

Right Panel: dE/dt (total energy loss ~ 0.00040)

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Beyond Einstein: From the Big Bang to Black Holes

Numerical Relativity 2005 Workshop, NASA/GSFC, NOV 2,2005

Head-On CollisionHead-On CollisionLeft Pane: Waveforms in different resolutions. Proper separation ~9M

Right Panel: convergence behavior of the waveforms.

No apparent problems up to L~11-12M. Promising for collision with large initial separation