A new effective-one-body description of coalescing nonprecessing spinning black-hole binaries

TL;DR

The paper introduces a novel spinning effective-one-body (SEOB) model for coalescing black-hole binaries by leveraging a gauge-invariant centrifugal radius $r_c$ to multiplicatively blend spin and mass-ratio deformations. It defines a new SEOB Hamiltonian with an effective orbital part and spin couplings, including spin-orbit and spin-spin interactions, and employs Padé resummation to stabilize the potentials and gyrogravitomagnetic factors. The model is calibrated against 15 equal-mass, equal-spin SXS numerical-relativity waveforms across $-0.95\leq \chi \leq 0.98$, achieving NR-EOB phasing disagreements within $\lesssim \pm 0.15$ rad (and $\sim 0.1$ rad near maximal spin for long inspirals). The ringdown is tied to a NR-fitted approach, and the NR completion introduces three adjustable parameters ${a_6^c},{c_3},{\Delta t_{\rm NQC}}$; this minimal, spin-aligned SEOB model yields highly accurate waveforms suitable for GW detection and analysis, with room for incorporating higher PN and self-force insights in future work.

Abstract

We present a new, tunable effective-one-body (EOB) model of the motion and radiation of coalescing black hole binaries with arbitrary mass ratio and aligned spins. The most novel feature of our formalism is the introduction, and systematic use, of the (gauge-invariant) concept of {\it centrifugal radius} $r_{c}$. In the spinning small mass-ratio limit, the main radial potential expressed in terms of $r_{c}$ differs very little (and only multiplicatively so) from the usual Schwarzschild potential $1-2M/r_{c}$. This motivates a new, multiplicative way of blending finite-mass-ratio deformations with spin-deformations. In the present exploratory work we consider a minimal version of our spinning EOB model (containing essentially only two adjustable parameters: one in the Hamiltonian and one in the waveform) and calibrate its (dominant mode) waveform against a sample of fifteen equal-mass, equal-spin waveforms produced by the SXS collaboration, and covering the dimensionless spin range $-0.95\leq χ\leq +0.98$. The numerical relativity / EOB phasing disagreement remains remarkably small ($\lesssim \pm 0.15$ rad) over the entire spin range.

Figures (3)

• Figure 1: Weak dependence on $a^2$ of the equatorial Kerr radial potential $A_{\rm eq}$, Eq. \ref{['eq:AK_eq']}, as a function of $u_c=M/r_c$, up to the horizon $u_c^H=1/2$.
• Figure 2: Performance of the recalibrated nonspinning limit of our new SEOB model. The vertical dashed line indicates the NR NQC extraction point and matching time $t_{\rm extr}^{\rm NR}$. The two dash-dotted vertical lines during inspiral indicate the alignment time window corresponding to $\ell=m=2$ GW frequencies $[M\omega_L,M\omega_R]=[0.035,0.045]$. See text for details.
• Figure 3: SEOB/NR $\ell=m=2$ (Zerilli-normalized) waveform comparison when $\chi\neq 0$. Waves are aligned at early times for all spins. The dashed vertical line indicates the NR NQC extraction point and matching time $t^{\rm NR}_{\rm extr}$. The two dash-dotted vertical lines during inspiral indicate the alignment time window. See text for details.