Gravitational waves from black hole binary inspiral and merger: The span of third post-Newtonian effective-one-body templates

TL;DR

The paper extends 3PN EOB gravitational-wave templates by introducing seven flexible parameters to probe unknown high-order PN physics and nonadiabatic effects in binary black-hole coalescences. It assesses robustness by computing overlaps between a fiducial 3PN EOB bank and flexed waveforms under physically motivated parameter variations, finding that the standard 3PN EOB bank remains effectual (overlaps above 0.965) across plausible ranges. It also analyzes the role of the unknown 4PN coefficient $b_5$, flux-pole position $c_P$, and flux-uncertainty $\theta$, showing that the span is large and often absorbable by intrinsic parameter shifts, with suggestions to refine template banks via a targeted $b_5$-flexed bank or universal phasing functions. Overall, the results support the use of 3PN EOB templates for detector searches in current interferometers and provide a framework to optimize template banks while maintaining high detection efficiency. The work highlights a path toward reducing template-count without sacrificing reach, leveraging both analytical resummation and physical insight into the effective dynamics near merger.

Abstract

We extend the description of gravitational waves emitted by binary black holes during the final stages of inspiral and merger by introducing in the third post-Newtonian (3PN) effective-one-body (EOB) templates seven new ``flexibility'' parameters that affect the two-body dynamics and gravitational radiation emission. The plausible ranges of these flexibility parameters, notably the parameter characterising the fourth post-Newtonian effects in the dynamics, are estimated. Using these estimates, we show that the currently available standard 3PN bank of EOB templates does ``span'' the space of signals opened up by all the flexibility parameters, in that their maximized mutual overlaps are larger than 96.5%. This confirms the effectualness of 3PN EOB templates for the detection of binary black holes in gravitational-wave data from interferometric detectors. The possibility to drastically reduce the number of EOB templates using a few ``universal'' phasing functions is suggested.

Figures (3)

• Figure 1: The potential $A(u)$ is plotted as a function $u=1/r \simeq GM/|{\bf x}_1-{\bf x}_2|$ at various PN orders. By varying the 4PN parameter $b_5$ we more than cover the behaviour of both the 2nd and 3rd post-Newtonian orders. In all the Figures, for a total mass $M=20 M_\odot$, the gray-shaded region corresponds to the frequency band $[65,235]$ Hz, centered at 150 Hz, in which the signal-to-noise ratio accumulated for inspirals is more than 80% of the total SNR in the entire LIGO band. The corresponding range in $u$ is $0.07372 \le u \le 0.1777$ and $r$ is $13.56 \ge r\ge 5.63$. The dashed vertical line at $u_{\rm lso}=0.2065$ near the shaded region corresponds to the radial coordinate $r_{\rm lso}=4.84$ at which the system reaches the last stable circular orbit.
• Figure 2: Variation in the (Newton-normalized) energy flux emitted by the system due to the 3PN parameter $\theta$ being different from zero. Clearly, negative values of $\theta$ have a greater effect on the behaviour of the flux as compared to the positive values.
• Figure 3: The (Newton-normalized) energy flux is plotted for different locations of the pole parametrised by $c_P.$ We vary the location of the pole by about 50% on either side of its nominal value predicted by the second post-Newtonian binding energy. The range of $c_P$ is perhaps far greater than what one could expect on physical grounds and causes a great variation in the flux function. Note that for $c_P=0.5$ the pole is moved to $v_{\rm pole}=0.4605$ which is near but still beyond the LSO.