Phenomenology and origin of late-time tails in eccentric binary black hole mergers

TL;DR

This work investigates late-time Price tails in gravitational waves from eccentric binary black hole mergers using black hole perturbation theory, focusing on the dominant $h_{22}$ mode. The authors develop a BHPT-based pipeline that combines a Teukolsky solver with an analytical QNM+tail model and an iterative fitting procedure, applying it to highly eccentric (up to $e=0.98$) binaries with varying spins, and demonstrate tails that decay as a power law with exponent near the theoretical value $p_{tail}=-(\ell+2)$ (i.e., $-4$ for $\ell=2$). A key finding is that tail excitation is strongest when the lighter black hole is near apocenter, linking the phenomenon to low-frequency source content rather than near-horizon strong-field effects. The results are supported by non-spinning and spinning cases and are complemented by exploratory hints from numerical relativity; the methodology is made publicly available via the $gwtails$ package, enabling broader reuse and validation.

Abstract

We investigate the late-time tail behavior in gravitational waves from merging eccentric binary black holes (BBH) using black hole perturbation theory. For simplicity, we focus only on the dominant quadrupolar mode of the radiation. We demonstrate that such tails become more prominent as eccentricity increases. Exploring the phenomenology of the tails in both spinning and non-spinning eccentric binaries, with the spin magnitude varying from $χ=-0.6$ to $χ=+0.6$ and eccentricity as high as $e=0.98$, we find that these tails can be well approximated by a slowly decaying power law. We study the power law for varying systems and find that the power law exponent lies close to the theoretically expected value $-4$. Finally, using both plunge geodesic and radiation-reaction-driven orbits, we perform a series of numerical experiments to understand the origin of the tails in BBH simulations. Our results suggest that the late-time tails are strongly excited in eccentric BBH systems when the smaller black hole is in the neighborhood of the apocenter, as opposed to any structure in the strong field of the larger black hole. Our analysis framework is publicly available through the \texttt{gwtails} Python package.

Figures (20)

• Figure 1: We show the radiation-reaction driven trajectories and geodescic orbits of a plunging point-particle in a binary system with spin $\chi=0.6$ and eccentricity $e=0.9$. These orbits start with an initial energy of $E = 0.9823348$ and angular momentum $p_{\varphi}=3.1763217$. Unless stated otherwise, the 3PN RR driven inspiral orbit model is the default model used throughout this paper.
• Figure 2: We show the post-merger amplitude, exhibiting four distinct regimes, for a non-spinning binary with an eccentricity of $e=0.98$. These four regimes are (i) initial fast decaying QNM regime (blue), (ii) intermediate short oscillatory regime (orange), (iii) late-time regime with slowly varying tails (green), and (iv) a regime dominated by noise in numerical simulations (red, inset). More details are in Section \ref{['sec:fitting_method']}.
• Figure 3: We show the tail behavior observed in non-spinning binaries with various eccentricity configurations ranging from $e=0.8$ to $e=0.98$. More details are in Section \ref{['sec:nospin']}.
• Figure 4: We show the $(2,2)$ ringdown amplitude of a non-spinning binary with eccentricity $e=0.98$ (grey solid line). For comparison, we also show the QNM fit in blue dashed line, tail fit in orange dashed line and fit using both QNM and tail in black dashed line. Additionally, we show the fit residuals in the inset. More details are in Section \ref{['sec:nospin']}.
• Figure 5: We show the extracted best-fit tail parameters ${A_{\rm tail}, c_{\rm tail}, p_{\rm tail}}$ as a function of the initial time (blue pentagons) and as a function of the final time used in the fitting (green stars). In the first case, we fix the final time to be $t=1000M$, while in the latter case, we fix the initial time to be $t=200M$. Black dashed lines denote their values obtained using the full length of the tail data spanning from $t=200M$ to $t=1000M$. More details are in Section \ref{['sec:nospin']}.