A quasi-physical family of gravity-wave templates for precessing binaries of spinning compact objects: Application to double-spin precessing binaries

TL;DR

The paper addresses detecting gravitational waves from precessing binaries with two spinning compact objects by using a quasi-physical single-spin template family derived from PN adiabatic inspiral dynamics. It demonstrates that these templates achieve high matching (FF) with double-spin signals for source masses in the range $m_1,m_2\in [3M_\u2099,15M_]$, at a computational cost corresponding to roughly $3.2\times 10^5$ templates for a minimum match of $0.97$. The study analyzes robustness across PN orders, explores the underlying double-spin dynamics to justify the single-spin approximation, and investigates parameter estimation capabilities, finding the chirp mass $\mathcal{M}=M\nu^{3/5}$ to be estimated especially accurately. These results have practical implications for template banks and parameter inference in ground-based detectors, with potential extensions to more realistic spin distributions and nonadiabatic models in future work.

Abstract

The gravitational waveforms emitted during the adiabatic inspiral of precessing binaries with two spinning compact bodies of comparable masses, evaluated within the post-Newtonian approximation, can be reproduced rather accurately by the waveforms obtained by setting one of the two spins to zero, at least for the purpose of detection by ground-based gravitational-wave interferometers. Here we propose to use this quasi-physical family of single-spin templates to search for the signals emitted by double-spin precessing binaries, and we find that its signal-matching performance is satisfactory for source masses (m1,m2) in [3,15]Msun x [3,15]Msun. For this mass range, using the LIGO-I design sensitivity, we estimate that the number of templates required to yield a minimum match of 0.97 is ~320,000. We discuss also the accuracy to which the single-spin template family can be used to estimate the parameters of the original double-spin precessing binaries.

Figures (7)

• Figure 1: Distribution of FFs for lower-mass ($M \leq 15 M_\odot$) binary configurations. See the caption to Table \ref{['Tab1']} for an explanation of how the FF distributions were obtained.
• Figure 2: Location in the (intrinsic) search parameter space $(M_s,\eta_s,\chi_{1s},\kappa_{1s})$ of the best-fit templates for target signals with $(m_1+m_2) = (3+3)M_\odot$, $(6+3)M_\odot$, $(9+3)M_\odot$, $(12+3)M_\odot$, $(15+3)M_\odot$, $(6+6)M_\odot$, $(12+6)M_\odot$, $(10+10)M_\odot$, $(15+10)M_\odot$, $(15+12)M_\odot$, and $(15+15)M_\odot$, with maximal spins, and with random angular distributions of the initial $\hat{\mathbf{L}}_N$, $\mathbf{S}_1$, $\mathbf{S}_2$. Dots are denser for the $(6+3)M_\odot$ and $(9+3)M_\odot$ configurations, for which more FF were computed. In the $(M_s,\eta_s)$ scatter plot (on top), the dashed contour encloses the region obtained by setting $M_s = M$ and $\eta_s = \eta$, and by taking $(m_1,m_2) \in [3,15] M_\odot \times [3,15] M_\odot$. The dotted and dashed line, drawn somewhat arbitrarily, encloses a possible template bank boundary, used in Sec. \ref{['seccounting']} to estimate the number of templates necessary to search for double-spin binaries in this mass range. The labels identify the search template clusters corresponding to each target mass configuration, and they are connected to the nominal projection point obtained by setting $M_s = M$ and $\eta_s = \eta$.
• Figure 3: Relative change of the opening angles as function of $\theta_{LS}$ for a $(6+3)M_{\odot}$ binary, with $\chi_{\rm tot}=0.4$, $|\mathbf{L}|=|\mathbf{L}_N| = \eta M^{5/3}\,\omega^{-1/3}$, and $\omega = 2 \pi \times 30$ Hz. The change shown corresponds to a 10% increase in $|\mathbf{S}_{\rm tot}|$. The solid and dashed curves refer to $\theta_{L}$ and $\theta_{S}$, respectively.
• Figure 4: Evolution of the opening angles $\theta_{L}$ and $\theta_{S}$, and of the total-spin magnitude $S_{\rm tot}$ (all plotted as dashed lines) for double-spin target systems yielding $\mathrm{FF} \ge 0.99$ (left column) and $\mathrm{FF} \simeq 0.94$ (right column) when matched by single-spin templates; the target system has $(m_1+m_2) = (6+3)M_{\odot}$. For comparison, the solid lines show the evolution of the analogous single-spin quantities [$\theta_{L}$, $\theta_{S}=\arccos(\hat{\mathbf{S}}_{1s}\cdot\hat{\mathbf{J}})$, and $S_{1s}$] for the best-fit single-spin systems.
• Figure 5: Percentage of initial spin configurations that yield FF $\le 0.99$ (light pattern) and FF $\le 0.97$ (dark pattern), as a function of the initial opening angle product $\lambda_{LS} = \hat{\mathbf{L}} \cdot \hat{\mathbf{S}}_{\rm tot}$, for $(m_1+m_2) = (6+3)M_{\odot}$ and $(9+3)M_{\odot}$ binaries. The numbers on top show the total number of configurations (among 500) randomly extracted within each bin of $\Delta \lambda_{LS} = 0.2$.