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High-accuracy comparison of numerical relativity simulations with post-Newtonian expansion | | Michael Boyle
; Duncan A. Brown
; Lawrence E. Kidder
; Abdul H. Mroue
; Harald P. Pfeiffer
; Mark A. Scheel
; Gregory B. Cook
; Saul A. Teukolsky
; | | Date: |
30 Sep 2007 | | Abstract: | 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 quasi-circular 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 $sim 15$ cycles, thus validating the
numerical simulation and establishing a regime where PN theory is accurate. In
the last 15 cycles to merger, however, {em 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. | | Source: | arXiv, 0710.0158 | | Services: | Forum | Review | PDF | Favorites | |
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