Effects of Dynamical Capture on two equal-mass non-spinning black holes

TL;DR

The paper addresses how dynamical captures of equal-mass, non-spinning BHs proceed and how their gravitational-wave signatures encode the binding process. Using numerical relativity, it characterizes the dual-emission GW morphology (a CHE-like first burst and a merger-ringdown second burst), derives a threshold incidence angle $\theta_0$ distinguishing scattering from capture, and builds a two-stage phenomenological description of $\Psi_4$ with a sin-Gaussian CHE component and a merger-ringdown component. It additionally analyzes how the remnant BH spin, mass, irreducible mass, and radiated energy depend on $\theta/\theta_0$, highlighting horizon-absorption effects and the role of angular momentum exchange. The results provide a framework for DC waveform modeling, quantify energy and angular-momentum dynamics, and offer insights for interpreting potential gravitational-wave detections of DC events in current and future detectors.

Abstract

Dynamical captures of black holes are unique events that provide an exceptional opportunity to probe the strong-field regime of gravitational physics. In this article, we perform numerical relativity simulations to study the events of dynamical capture of two equal-mass non-spinning black holes. We consider a suite of scenarios within a range of initial linear momenta ($p/M=0.095-0.75$) and incidence angles ($θ=6.36^\circ-2.83^\circ$), and study the emitted Weyl scalar ($Ψ_4$) of each case, as well as the spins and masses of the black holes before and after they merge. We provide a simple analytical model which accurately fits the gravitational-wave emission. We study the dependence of the time-interval between the capture and the merger emissions with respect to the incidence angle, which can be well parametrized by a first-order divergent behavior, allowing to find the angle that separates a scattering event from a dynamical capture. We also find that, in general, the parameters that model the first emission can be well described by linear or exponentially decaying functions in terms of the incidence angle, while others display more complex behaviors that offer valuable insights into the nature of these events.

Figures (13)

• Figure 1: (Upper panel) Evolution of the $(2,2)$ multipole of the Weyl scalar measured at a detector located at a distance $r^*=80M$ from the center of mass (CM). (Lower panel) Trajectories of both BHs, initially hyperbolic. The arrows qualitatively indicate the initial momentum $\vec{p}$ of each BH. The solid and dashed lines roughly show when the BHs are in their CHE or merger phases, respectively. The initial conditions are $p/M=0.49$, $\theta=2.847^\circ$.
• Figure 2: (Upper panel) Evolution of the dimensionless spin parameter $\chi$ for each BH and for the final remnant. (Middle panel) Evolution of the ADM and irreducible masses of both BHs and of the merged remnant. (Lower panel) Evolution of the area ${\cal A}$ for both BHs and the final one. Insets in the two lower panels are shown around the CHE phase. The initial conditions are $p/M=0.49$, $\theta=2.847^\circ$. The black, vertical dashed lines indicate the moment of merger. Both BHs evolve in the same way, as their initial conditions are identical (see Subsec. \ref{['Subsec: setup']}).
• Figure 3: Fits of the real (blue) and imaginary (orange) parts (upper and lower panels, respectively) compared to the simulated rescaled Weyl scalar (black dashed line) at a detector located at $r^*=80M$ from the CM. The initial conditions correspond to the example case described in Sec. \ref{['subsec: gen. beh-DCs']}.
• Figure 4: Time intervals between peaks, $\Delta t = t_0^{\text{M}} - t_0^{\text{CHE}}$, as a function of the normalized incidence angle $\theta/\theta_0$. The data points are obtained from the sin-Gaussian fits, while the solid curves (which diverge at $\theta/\theta_0=1$) represent fits using Eq. \ref{['eq: divergence']}.
• Figure 5: Estimated threshold angles $\theta_0$ (from Tab. \ref{['Tab: fit-times']}) as a function of the initial momentum $p/M$. The solid curve represents the best-fit model given by Eq. \ref{['eq: theta0 vs p']}.