Taming the plunge: A circularization trap of supermassive black hole binaries

TL;DR

This work analyzes the eccentricity evolution of SMBHBs from large-scale galaxy mergers to the gravitational-wave–driven regime, showing that non-spherical merger remnants impart high initial eccentricities, while thick nuclear discs impose a rapid deterministic circularization via 3D density-wave interactions. A self-consistent derivation reveals that 3D disc geometry suppresses high-$m$ torques (torque cutoff), yielding scalings $\tau_a^{-1} \propto h^{-3}$ and $\tau_e^{-1} \propto h^{-5}$ and a timescale hierarchy $\tau_e/\tau_a \propto h^2$; for $h\approx0.2$, eccentricity damping outpaces migration by a factor of ~25. A wavelet-based stochastic analysis shows fluctuations can drive diffusion in $e$, but unless fluctuations are highly nonlinear, the mean remains near circular, yielding a robust circularization trap that pushes binaries toward the GW-dominated, nearly circular regime with a substantial cosmological delay governed by stellar relaxation. The result has significant implications for LISA event rates and SMBH assembly in cosmological models, and motivates further multi-physics simulations to test the robustness of the trap under realistic disc turbulence and feedback.

Abstract

We investigate the orbital eccentricity evolution of supermassive black hole binaries within galactic environments. We analyze the dynamics in triaxial merger remnants and subsequent interactions with geometrically thick nuclear discs. We confirm that gravitational torques in triaxial potentials efficiently extract angular momentum, resulting in binary formation with high initial eccentricities. We then analyze the binary-disc interaction using a 3D analytical framework incorporating the Airy formalism and potential softening. We present a self-consistent derivation demonstrating that the 3D suppression of high-order torques leads to distinct scalings with disc thickness ($h$): migration rates $τ_a^{-1} \propto h^{-3}$ and eccentricity damping rates $τ_e^{-1} \propto h^{-5}$. This establishes a timescale hierarchy, $τ_e/τ_a \propto h^2$. For typical parameters ($h\approx 0.2$), eccentricity damping is significantly faster than orbital decay ($τ_e \approx 0.04 \, τ_a$). We further develop a wavelet-based formalism to quantify the impact of disc inhomogeneities arising from accretion feedback and turbulence. We derive the stochastic torque variance in the wavelet domain and employ a Fokker-Planck analysis to determine the equilibrium eccentricity distribution. While stochastic fluctuations counteract deterministic damping, the strong damping imposed by the thick disc geometry ensures the equilibrium eccentricity remains small unless the fluctuations are highly non-linear. Hence, even if born highly eccentric, SMBHBs are rapidly circularized. This circularization trap forces binaries to approach the gravitational wave-dominated regime on nearly circular orbits, prolonging the total merger timescale. This introduces a substantial cosmological delay governed by stellar relaxation, which impacts detection rates and the modeling of SMBH assembly in cosmological frameworks.