Taming the Plunge: A Circularization Trap of Supermassive Black Hole Binaries

Abstract We investigate the orbital eccentricity evolution of supermassive black hole binaries (SMBHBs; 10 4 –10 7 M ⊙ ) within galactic environments. Merger timescales depend on eccentricity when gravitational-wave (GW) emission dominates. We analyze the dynamics in triaxial merger remnants and subsequent interactions with geometrically thick nuclear disks. Gravitational torques in triaxial potentials extract angular momentum ( T J ≪ T E ), resulting in binary formation with high initial eccentricities ( e &gt; 0.95). We analyze the binary–disk interaction using a 3D analytical framework incorporating the Airy formalism and present a self-consistent derivation demonstrating that the 3D suppression of high-order torques leads to distinct scalings with disk thickness ( h ), with migration rates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> and eccentricity damping rates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:math> , which establish a timescale hierarchy, τ e / τ a ∝ h 2 . For typical parameters, eccentricity damping is significantly faster than orbital decay ( τ e ≈ 0.04 τ a ). We further develop a wavelet-based formalism to quantify the impact of disk 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 disk geometry ensures the equilibrium eccentricity remains small unless the fluctuations are highly nonlinear. Hence, highly eccentric born SMBHBs are rapidly circularized. This “circularization trap” forces binaries to approach the GW-dominated regime on nearly circular orbits, prolonging the total merger timescale. This introduces a cosmological delay (0.3–2.5 Gyr) governed by stellar relaxation.