Detecting gravitational waves from precessing binaries of spinning compact objects: Adiabatic limit

TL;DR

The paper tackles the challenge of detecting gravitational waves from precessing binaries of spinning compact objects within the adiabatic inspiral regime. It develops a fiducial target model using PN dynamics to describe precession-driven modulations and then builds modulated detection template families (DTFs) that capture both the carrier waveform and precession-induced amplitude/phase modulations. Through extensive Monte Carlo testing, the study demonstrates high fitting factors (FFs) for BBHs ($\overline{FF}\gtrsim0.93$–$0.99$) and NS–BH systems ($\overline{FF}\approx0.93$), with the most effective templates ($(\psi_0,\psi_{3/2},\mathcal{B})_6$) delivering substantial gains over standard nonspinning templates. The results justify using precession-informed DTFs in early GW searches, quantify the trade-offs with higher detection thresholds, and point toward specialized NS–BH templates and extensions beyond the adiabatic limit as promising future directions.

Abstract

Black-hole (BH) binaries with single-BH masses m=5--20 Msun, moving on quasicircular orbits, are among the most promising sources for first-generation ground-based gravitational-wave (GW) detectors. Until now, the development of data-analysis techniques to detect GWs from these sources has been focused mostly on nonspinning BHs. The data-analysis problem for the spinning case is complicated by the necessity to model the precession-induced modulations of the GW signal, and by the large number of parameters needed to characterize the system, including the initial directions of the spins, and the position and orientation of the binary with respect to the GW detector. In this paper we consider binaries of maximally spinning BHs, and we work in the adiabatic-inspiral regime to build families of modulated detection templates that (i) are functions of very few physical and phenomenological parameters, (ii) model remarkably well the dynamical and precessional effects on the GW signal, with fitting factors on average >~ 0.97, but (iii) might require increasing the detection thresholds, offsetting at least partially the gains in the fitting factors. Our detection-template families are quite promising also for the case of neutron-star--black-hole binaries, with fitting factors on average ~ 0.93. For these binaries we also suggest (but do not test) a further template family, which would produce essentially exact waveforms written directly in terms of the physical spin parameters.

Figures (16)

• Figure 1: Source and radiation frames in the FC convention FC.
• Figure 2: Detector and radiation frames in the FC convention FC.
• Figure 3: Specification of the initial Newtonian orbital angular momentum in the source frame $\{\mathbf{e}_x,\mathbf{e}_y,\mathbf{e}_z\}$.
• Figure 4: Specification of the initial directions of the spins with respect to the FC orthonormal basis $\{\mathbf{e}_1,\mathbf{e}_2,\mathbf{e}_3\}$ [Eq. (\ref{['eq:e1e2']})].
• Figure 5: Binary ending frequencies (gray dots) as functions of the initial value of $\kappa_{\rm eff}/\kappa_{\rm eff}^{\rm max}$, for 1000 initial spin configurations of $M=(15 + 15)M_\odot$ BBHs (in the left panel), and $M=(10 + 1.4)M_\odot$ NS--BH binaries (in the right panel), at 2PN and 3.5PN orders. The solid lines plot the SO-only predictions for the ending frequencies.