Comparisons of eccentric binary black hole simulations with post-Newtonian models

TL;DR

This work addresses the need for accurate gravitational-wave waveforms from eccentric binary black holes by directly comparing numerical-relativity simulations of equal-mass, non-spinning binaries with eccentric post-Newtonian models. It develops two eccentric PN formulations, $x$- and $n$-models, and fits them to NR data using the frequency $\omega_{\mathrm{gw}}$ to quantify agreement, finding that the $x$-model matches NR within $\pm 0.1$ rad for about 11 GW cycles before merger, while the $n$-model degrades. The key finding is that expressing PN dynamics in terms of the frequency-related variable $x=(M \omega)^{2/3}$ yields significantly better NR agreement than using the mean motion $n$, with implications for constructing hybrids and templates. The work lays groundwork for extending to fully 3PN radiation-reaction terms and spins, enhancing waveform modeling for eccentric binaries relevant to ground- and space-based detectors.

Abstract

We present the first comparison between numerical relativity (NR) simulations of an eccentric binary black hole system with corresponding post-Newtonian (PN) results. We evolve an equal-mass, non-spinning configuration with an initial eccentricity e ~ 0.1 for 21 gravitational wave cycles before merger, and find agreement in the gravitational wave phase with an adiabatic eccentric PN model with 2 PN radiation reaction within 0.1 radians for 10 cycles. The NR and PN phase difference grows to 0.7 radians by 5 cycles before merger. We find that these results can be obtained by expanding the eccentric PN expressions in terms of the frequency-related variable x = (omega M)^{2/3} with M the total mass of the binary. When using instead the mean motion n = 2 π/P, where P is the orbital period, the comparison leads to significant disagreements with NR.

Figures (7)

• Figure 1: Convergence order of the NR gravitational wave phase $\phi_\mathrm{gw}$. Deviations from the expected value of 6 may be caused by lower order components in the code.
• Figure 2: Errors in the NR gravitational wave phase $\phi_\mathrm{gw}$ from the effects of finite resolution and extrapolation to infinite radius
• Figure 3: Filtering of NR gravitational wave frequency in the Fourier domain. The solution in the region containing noise is truncated to the lowest 30 Fourier modes.
• Figure 4: PN parameters for the $x$ and $n$ models as determined from fitting windows $[t_1, t_2]$ for $t_1 = 210 M$ and various values of $t_2$.
• Figure 5: PN parameters for the $x$ and $n$ models as determined from fitting windows $[t_1, t_2]$ for various values of $t_1$ and $t_2 = t_1 + 400 M$.