A Comparison of search templates for gravitational waves from binary inspiral

TL;DR

The study evaluates three inspiral waveform templates—Taylor (T-approximants), Padé-resummed adiabatic P-approximants, and Effective-One-Body (EOB) approximants—for ground-based detectors, focusing on their ability to recover signals from binary mergers. It shows resummation improves PN convergence and that EOB, which models the inspiral–plunge transition, yields the largest SNR gains for higher-mass binaries ($m \gtrsim 30\,M_\odot$), enabling larger detection volumes. By using the EOB framework as a fiducial reference, the work demonstrates the importance of including plunge and merger content in template banks and argues for a multi-template strategy that combines validated resummation methods with non-adiabatic dynamics. The results have practical implications for constructing efficient and effective search pipelines for LIGO/Virgo–like observatories.

Abstract

We compare the performances of the templates defined by three different types of approaches: traditional post-Newtonian templates (Taylor-approximants), ``resummed'' post-Newtonian templates assuming the adiabatic approximation and stopping before the plunge (P-approximants), and further ``resummed'' post-Newtonian templates going beyond the adiabatic approximation and incorporating the plunge with its transition from the inspiral (Effective-one-body approximants). The signal to noise ratio is significantly enhanced (mainly because of the inclusion of the plunge signal) by using these new effective-one-body templates relative to the usual post-Newtonian ones for binary masses greater than $ 30 M_\odot$, the most likely sources for initial laser interferometers. Independently of the question of the plunge signal, the comparison of the various templates confirms the usefulness of using resummation methods. The paper also summarizes the key elements of the construction of various templates and thus can serve as a resource for those involved in writing inspiral search software.

Figures (3)

• Figure 1: Signal-to-noise ratios in GEO, LIGO-I and VIRGO when using as Fourier-domain template the post-Newtonian model Eq. (\ref{['eq:s3']}) ($T^{f2}$), truncated at the test-mass $F_{\rm lso}= 4400 M_\odot/m$ Hz (in thin lines), compared to the optimal one obtained when the template coincides with the fiducial "exact" (effective one-body) signal (thick lines). As usual, we averaged over all the angles. The overlaps are maximised over the time lags, the phases, and the two individual masses $m_1$ and $m_2$. The plots are jagged because we have computed the SNR numerically by first generating the fiducial "exact" waveform in the time-domain and then using its discrete Fourier transform in Eq.(\ref{['d6']}). The greater SNR achieved by effective one-body waveforms for higher masses, as compared to Fig 1 of DIS2, is due to the plunge phase present in these waveforms. Observe that the presence of the plunge phase in the latter significantly (up to a factor of 1.5) increases the SNR for masses $m>35M_\odot.$ Using the effective one-body templates will, therefore, enhance the search volume of the interferometric network by a factor of 3 or 4.
• Figure 2: The frequency evolution of the various approximate models is compared with the fiducial exact $(10,10) M_\odot$ model in the LIGO band. To indicate the effect on the overlap, we also plot the weighting function $1/h_n(f)$ for initial LIGO (not to scale), which is a measure of the detector's sensitivity.
• Figure 3: The effective noise $h_n=\sqrt{fS_h(f)}$ in various ground-based interferometers.