Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms

TL;DR

The paper develops a prototype effective-one-body (EOB) model for non-precessing spinning black-hole binaries, calibrated to seven numerical-relativity waveforms and Teukolsky-based small-mass-ratio results to cover a wide range of mass ratios and spins up to $-1 \leq \chi_i \lesssim 0.7$. It constructs inspiral-merger-ringdown waveforms using a factorized, spin-aware set of modes with non-quasicircular corrections and a merger-ringdown built from quasinormal modes and a pseudo-QNM, then calibrates key EOB parameters ($K$, $\rho_{22}^{(4)}$, $d_{\text{SO}}$, $d_{\text{SS}}$) against NR data. The resulting model achieves mismatches $\mathcal{M}$ typically below $3\times 10^{-3}$ for Advanced LIGO bands and demonstrates good merger-phase accuracy for nonspinning and moderately spinning cases, though its reliability degrades for $\chi_i \gtrsim 0.7$ due to limited spin information in the waveform modes. The study highlights the need for higher-order spin terms in the PN expansion of the waveform modes and radiation reaction, and the further incorporation of NR data to extend validity to larger spins; the prototype has been deployed in LAL as SEOBNRv1 for GW searches.

Abstract

We first use five non-spinning and two mildly spinning (chi_i \simeq -0.44, +0.44) numerical-relativity waveforms of black-hole binaries and calibrate an effective-one-body (EOB) model for non-precessing spinning binaries, notably its dynamics and the dominant (2,2) gravitational-wave mode. Then, we combine the above results with recent outcomes of small-mass-ratio simulations produced by the Teukolsky equation and build a prototype EOB model for detection purposes, which is capable of generating inspiral-merger-ringdown waveforms for non-precessing spinning black-hole binaries with any mass ratio and individual black-hole spins -1 \leq chi_i \lesssim 0.7. We compare the prototype EOB model to two equal-mass highly spinning numerical-relativity waveforms of black holes with spins chi_i = -0.95, +0.97, which were not available at the time the EOB model was calibrated. In the case of Advanced LIGO we find that the mismatch between prototype-EOB and numerical-relativity waveforms is always smaller than 0.003 for total mass 20-200 M_\odot, the mismatch being computed by maximizing only over the initial phase and time. To successfully generate merger waveforms for individual black-hole spins chi_i \gtrsim 0.7, the prototype-EOB model needs to be improved by (i) better modeling the plunge dynamics and (ii) including higher-order PN spin terms in the gravitational-wave modes and radiation-reaction force.

Figures (8)

• Figure 1: We show in the spacetime diagram $(\hat{t},r^\ast)$ the trajectory of the effective particle in the EOB description (black solid line in the left part of the diagram) and the EOB (2,2) gravitational mode (red solid oscillating line) for an equal-mass nonspinning black-hole binary. Although we only need to evolve the EOB trajectory until the orbital frequency reaches its maximum ("light ring"), the model's dynamics allows the trajectory to continue to negative $r^\ast$ (short-dashed black line in the left part of the diagram). The blue dashed lines represent $\hat{t}\pm r^*=\textrm{const.}$ surfaces and ingoing/outgoing null rays. The EOB (2,2) mode is a function of the retarded time $\hat{t}-r^*$, plotted here orthogonal to $\hat{t}- r^*=\textrm{const.}$ surfaces, at a finite $\hat{t}+r^*$ distance. The two outgoing null rays are drawn at the $\hat{t}-r^*$ retarded times when the EOB particle crosses the EOB ISCO and light-ring radii, respectively. The shaded green area is a rough sketch of the potential barrier around the newborn black hole.
• Figure 2: We show the quadratic fit in $\nu$ for the adjustable parameter $K$. This parameter is calibrated using the five nonspinning NR waveforms, assuming $\rho_{22}^{(4)}(\nu)$ in Eq. \ref{['A8']}. The error bars are determined by the intersection of the contours of $\Delta\phi_{\text{global}} = 0.1$ rads with $\rho_{22}^{(4)}(\nu)$ for each mass ratio considered.
• Figure 3: Comparison of the NR and EOB (2, 2) mode for $q\!=\!1$, $\chi_1\!=\!\chi_2\!=\!0$. In the upper panels we show the comparison between the real part of the two waveforms, zooming into the merger region in the upper right plot. In the lower panels we show the dephasing and relative amplitude difference over the same time ranges as the upper panels. A vertical dashed line marks the position of the NR amplitude peak. The dotted curves are the NR errors.
• Figure 4: Same as in Fig. \ref{['fig:NS_q_1']} but for $q=1/6$, $\chi_1=\chi_2=0$.
• Figure 5: Same as in Fig. \ref{['fig:NS_q_1']} but for $q=1$, $\chi_1=\chi_2=-0.43655$.