Transition from inspiral to plunge in binary black hole coalescences

TL;DR

The paper develops a non-perturbative, resummed framework to describe the transition from inspiral to plunge in equal-mass and near-equal-mass binary black holes on quasi-circular orbits by combining DIS flux resummation with the BD99 effective-one-body mapping. It furnishes initial data suitable for numerical relativity, derives a universal description of the transition via a rho-equation in the small-ν limit, and provides a rough complete gravitational waveform that spans inspiral, plunge, merger, and ring-down. The results reveal that the adiabatic approximation breaks down before the LSO and demonstrate characteristic scaling laws near the transition, with practical implications for GW template construction and NR initialization. While promising, the approach calls for higher-PN inputs and spinning black-hole generalizations to fully capture realistic systems and maximize data-analysis utility.

Abstract

Combining recent techniques giving non-perturbative re-summed estimates of the damping and conservative parts of the two-body dynamics, we describe the transition between the adiabatic phase and the plunge, in coalescing binary black holes with comparable masses moving on quasi-circular orbits. We give initial dynamical data for numerical relativity investigations, with a fraction of an orbit left, and provide, for data analysis purposes, an estimate of the gravitational wave-form emitted throughout the inspiral, plunge and coalescence phases.

Figures (12)

• Figure 1: On the left panel we show the inspiraling circular (relative) orbit for $\nu = 1/4$. The location of the $r$-LSO, defined by the conservative part of the dynamics, is also indicated. On the right panel we compare the two kinetic contributions that enter the Hamiltonian: the "radial" and the "azimuthal" one. The figure shows that the assumption we made of quasi-circularity, i.e. $p_r^2 / B(r) \ll p_{\varphi}^2 / r^2$, is well satisfied throughout the transition from the adiabatic phase to the plunge.
• Figure 2: Variation with $\nu$ of the $\omega$-LSO values of the real reduced non-relativistic energy $E_{\rm real}^{\rm NR}/\mu = ({\cal E}_{\rm real} - M)/\mu$ (on the left), and of the real angular momentum $j = P_\varphi/(\mu G M)$ (on the right), computed integrating the full dynamics, i.e. with radiation reaction effects included.
• Figure 3: $\omega$-LSO values of the radial velocity (on the left) and of the radial position (on the right) versus $\nu$, derived integrating the full dynamical evolution.
• Figure 4: We compare the number of gravitational cycles (on the left) and the radial velocity (on the right), computed with the exact evolution and within the adiabatic approximation, versus $R/GM$.
• Figure 5: We contrast the orbital frequency (on the left), divided by the Schwarzschild value $\widehat{\omega}_{\rm LSO}(0) = 6^{-3/2}$, and the restricted waveform (on the right), evaluated with the exact dynamical system and within the adiabatic approximation. Note that in both plots the quantities are given as a function of the rescaled time variable $\widehat{\omega}_{\rm LSO}(0)(\hat{t} - \hat{t}_{\rm LSO})$, where $\hat{t}_{\rm LSO}$ is defined as the time at which the adiabatic solution reaches the $r$-LSO position.