A data-analysis driven comparison of analytic and numerical coalescing binary waveforms: nonspinning case

TL;DR

The paper evaluates how well current PN template families reproduce NR waveforms for nonspinning binary black-hole mergers by constructing NR-PN hybrids and computing FFs across LIGO/VIRGO noise spectra. It finds that time-domain Epn(3.5) and Tpn(3.5) templates perform well for total masses up to ≈$30\,M_⊙$, while frequency-domain SPA templates require modifications (SPA_c_ext(3.5), SPA_c^Y(4)) or are outperformed by Epn for higher masses; BCV templates offer competitive performance as well. The study demonstrates that including merger-ring-down physics (via QNMs in Epn or carefully tuned SPA templates) is essential for high FFs at high masses, and it quantifies NR cycle requirements to achieve desired mismatches, informing template-bank design and NR resource planning. Overall, hybrid NR-PN approaches enable faithful detection templates and guide future improvements in EOB matching, phase modeling, and high-mass template construction. The results have practical impact on GW searches by detailing which template families are effective across mass ranges and how to extend them to cover merger and ring-down phases.

Abstract

We compare waveforms obtained by numerically evolving nonspinning binary black holes to post-Newtonian (PN) template families currently used in the search for gravitational waves by ground-based detectors. We find that the time-domain 3.5PN template family, which includes the inspiral phase, has fitting factors (FFs) >= 0.96 for binary systems with total mass M = 10 ~ 20 Msun. The time-domain 3.5PN effective-one-body template family, which includes the inspiral, merger and ring-down phases, gives satisfactory signal-matching performance with FFs >= 0.96 for binary systems with total mass M = 10 ~ 120 Msun. If we introduce a cutoff frequency properly adjusted to the final black-hole ring-down frequency, we find that the frequency-domain stationary-phase-approximated template family at 3.5PN order has FFs >= 0.96 for binary systems with total mass M = 10 ~ 20 Msun. However, to obtain high matching performances for larger binary masses, we need to either extend this family to unphysical regions of the parameter space or introduce a 4PN order coefficient in the frequency-domain GW phase. Finally, we find that the phenomenological Buonanno-Chen-Vallisneri family has FFs >= 0.97 with total mass M=10 ~ 120Msun. The main analyses use the noise spectral-density of LIGO, but several tests are extended to VIRGO and advanced LIGO noise-spectral densities.

Figures (17)

• Figure 1: We show ${\rm FF}_0$s between waveforms generated from the three PN models Tpn(3), Tpn(3.5) and Epn(3.5) versus $\Delta {\rm N}_{\rm GW}$ [see Eq. \ref{['dn']}]. The ${\rm FF}_0$s are evaluated with LIGO's PSD. Note that for Tpn(3.5) and Epn(3.5) and a $(15+3)M_\odot$ binary, the lowest ${\rm FF}_0$ is 0.78 and the difference in the number of GW cycles $\Delta {\rm N}_{\rm GW} \simeq 2$. In the limit $\Delta {\rm N}_{\rm GW}\rightarrow0$, the FF$_0$ goes to unity.
• Figure 2: ${\rm FF}_0$ between NR waveforms as a function of the binary total-mass $M$. The solid curve are generated for waveforms from Pretorius and the Goddard group. The longer Goddard waveform is shortened such that both waveforms last $\simeq 671M$ and contain $\simeq8$ cycles. The dashed curve is generated for waveforms from the high-resolution and medium resolution simulations of the Goddard group. All ${\rm FF}$s are evaluated using LIGO's PSD.
• Figure 3: We show two examples of hybrid waveforms, starting from 40Hz. The PN waveforms are generated with the Tpn(3.5) model, and the NR waveforms in the upper and lower panels are generated from Pretorius' and Goddard's simulations, respectively. We mark with a dot the point where we connect the PN and NR waveforms.
• Figure 4: Distribution of GW signal power. In each panel, we plot a hybrid waveform (a Tpn waveform stitched to the Goddard waveform) in both its original form (blue curve) and its "whitened" form (red curve) DIS00. We show waveforms from six binary systems with total masses $10M_\odot$$20M_\odot$, $30M_\odot$, $40M_\odot$, $60M_\odot$ and $100M_\odot$. The vertical lines divide the waveforms into segments, where each segment contributes $10\%$ of the total signal power.
• Figure 5: We show the mismatch between hybrid waveforms as a function of the number of NR waveform cycles used to generate the hybrid waveforms. The LIGO PSD is used to evaluate the mismatches. In the left panel, we compare the Epn(3.5) and Tpn(3.5) models. In the right panel, we compare the Tpn(3) and Tpn(3.5) models. From top to bottom, the four curves correspond to four equal-mass binary systems, with total masses $10M_\odot$, $20M_\odot$, $30M_\odot$, and $40M_\odot$. The dots show mismatches taken between hybrid waveforms that are generated with different methods. In the left panel, we adjust the amplitude of restricted PN waveforms, such that they connect smoothly in amplitude to NR waveforms. In the right panel, to set the frequency of PN waveforms at the joining point, we use the original orbital frequency, instead of the quartic fitted one. (See Sec. \ref{['sec3.1']} for the discussion on amplitude scaling and frequency fitting).