Comparison between numerical relativity and a new class of post-Newtonian gravitational-wave phase evolutions: the non-spinning equal-mass case

TL;DR

This study evaluates how well PN inspiral phasing reproduces NR GW phasing for equal-mass, nonspinning binaries by comparing NR waveforms with three PN prescriptions: TaylorT1, TaylorT4, and the newer TaylorEt. Using a nine-orbit NR dataset with very low eccentricity and precise phase control within the window $M\omega \in [0.0455,0.1]$, the authors quantify the phase discrepancy $\Delta\phi$ across PN orders. They find that TaylorT4 matched at the highest reactive order provides the best NR agreement, while TaylorT1 and TaylorT4 oscillate with PN order; in contrast, TaylorEt shows monotonic convergence toward NR, attaining $\Delta\phi \approx -1.18$ rad at the highest order studied. These results suggest TaylorEt as a promising PN-NR hybrid template, especially for low-eccentricity inspirals, with future work extending the analysis to unequal masses and spins.

Abstract

We compare the phase evolution of equal-mass nonspinning black-hole binaries from numerical relativity (NR) simulations with post-Newtonian (PN) results obtained from three PN approximants: the TaylorT1 and T4 approximants, for which NR-PN comparisons have already been performed in the literature, and the recently proposed approximant TaylorEt. The accumulated phase disagreement between NR and PN results over the frequency range $Mω= 0.0455$ to $Mω= 0.1$ is greater for TaylorEt than either T1 or T4, but has the attractive property of decreasing monotonically as the PN order is increased.

Figures (4)

• Figure 1: Accumulated phase disagreement between NR and PN evolutions for TaylorT1, T4 and Et approximants at 2PN, 2.5PN, 3PN and 3.5PN reactive orders.
• Figure 2: Accumulated phase disagreement between NR results and the PN approximant TaylorEt, as in the lower panel of Figure \ref{['fig:Phase']}, with the difference that we now use numerical data from a simulation with slightly larger eccentricity, $e \approx 0.008$.
• Figure 3: The same comparison as in Figure \ref{['fig:PhaseQC']}, but we now match the phase and binding energy such that $E_b = -0.01383 M$ at the matching time.
• Figure 4: Accumulated phase disagreement between NR and PN results, for each of the three approximants, TaylorT1, TaylorT4 and TaylorEt at 2PN, 2.5PN, 3PN, 3.5PN orders. At 2.5PN the TaylorT1 and TaylorEt points are on top of each other. Note that the disagreement between NR and TaylorEt decreases monotonically as the reactive PN order is increased.