High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
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 ~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.
© 2007 The American Physical Society. (Received 30 September 2007; published 27 December 2007) It is a pleasure to acknowledge useful discussions with Stuart Anderson, Alessandra Buonanno, Mark Hannam, Ian Hinder, Luis Lehner, Lee Lindblom, Geoffrey Lovelace, Sean McWilliams, Robert Owen, Yi Pan, Oliver Rinne, and Kip Thorne. In particular, we would like to thank Alessandra Buonanno for a careful reading of this manuscript, Rob Owen for estimating the BH spin, Geoffrey Lovelace for his help constructing initial data, Oliver Rinne for providing improved boundary conditions, and Lee Lindblom for his guidance and input throughout this project. This work was supported in part by grants from the Sherman Fairchild Foundation to Caltech and Cornell, and from the Brinson Foundation to Caltech; by NSF Grants No. PHY-0601459, No. PHY-0652995, No. DMS-0553302 and NASA Grant No. NNG05GG52G at Caltech; by NSF Grants No. PHY-0652952, No. DMS-0553677, No. PHY-0652929 and NASA Grant No. NNG05GG51G at Cornell; and by the Z. Smith Reynolds Foundation and NSF Grant No. PHY-0555617 at Wake Forest. We thank NASA/JPL for providing computing facilities that contributed to this work. Some of the simulations discussed here were produced with LIGO Laboratory computing facilities. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates under cooperative agreement No. PHY-0107417. This paper has been assigned LIGO document No. LIGO-P070101-00-Z.
Submitted - 0710.0158.pdf
Published - BOYprd07b.pdf