High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions

Journal Article · Sat Dec 15 04:00:00 EST 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.76.124038· OSTI ID:21024063

Boyle, Michael; Pfeiffer, Harald P; Scheel, Mark A ^[1]; Brown, Duncan A ^[1]; Kidder, Lawrence E; Mroue, Abdul H; Teukolsky, Saul A ^[2]; Cook, Gregory B ^[3]

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1. Theoretical Astrophysics 130-33, California Institute of Technology, Pasadena, California 91125 (United States)
2. Center for Radiophysics and Space Research, Cornell University, Ithaca, New York, 14853 (United States)
3. Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27106 (United States)

Numerical simulations of 15 orbits of an equal-mass binary black-hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasicircular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first {approx}15 cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, generic time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6%-7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly (<1% amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.

• OSTI ID: 21024063
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 76; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACCURACY
AMPLITUDES
BLACK HOLES
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
CORRECTIONS
COSMOLOGY
GRAVITATIONAL WAVES
MASS
ORBITS
SPIN
WAVE FORMS