Consistency of post-Newtonian waveforms with numerical relativity

TL;DR

This work derives late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein's equations, suggesting that PN waveforms for this system are effective until the last orbit prior to final merger.

Abstract

General relativity predicts the gravitational wave signatures of coalescing binary black holes. Explicit waveform predictions for such systems, required for optimal analysis of observational data, have so far been achieved using the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late-inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein's equations. We compare waveform phasing from simulations of the last $\sim 14$ cycles of gravitational radiation from equal-mass, nonspinning black holes with the corresponding 2.5PN, 3PN, and 3.5PN orbital phasing. We find phasing agreement consistent with internal error estimates based on either approach, suggesting that PN waveforms for this system are effective until the last orbit prior to final merger.

Figures (3)

• Figure 1: Gravitational strain waveforms from the merger of equal-mass Schwarzschild black holes. The solid curve is the waveform from the high resolution numerical simulation, and the dashed curve is a PN waveform with 3.5PN order phasing Blanchet:2001axBlanchet:2004ek and 2.5PN order amplitude accuracy Arun:2004ff. Time $t = 0$ is the moment of peak radiation amplitude in the simulation.
• Figure 2: Gravitational wave phase, in radians, for numerical and PN waveforms. The solid curve is a Richardson extrapolation of the numerical results. The solid curve agrees well with the phase obtained by numerically integrating the 3.5PN expansion of the chirp rate $\dot \omega_c(\omega_c)$. Each successive PN order shown agrees better with the Richardson-extrapolated result, although this is not true of all the preceding terms in the PN sequence, since the sequence does not converge monotonically.
• Figure 3: Gravitational wave phase error estimates. Differences between phasing from the integrated 3.5PN chirp rate and Richardson extrapolation from the numerical simulations (solid curve) are small, and are consistent with internal error estimates for the numerical simulation results and the PN sequence. Curves which involve numerical phases are smoothed to remove high frequency noise.