Eccentric Binaries Accreting from Thin Disks: Orbital Evolution

Circumbinary disks crucially affect the orbital and electromagnetic properties of binary systems across the universe, from stars in our galactic neighborhood to supermassive black hole binaries formed as the result of tumultuous galactic mergers. Previous simulations have focused nearly exclusively on thick accretion disks, appropriate for studying stellar binaries, and have found encouraging agreement with observations thereof. We present herein the first systematic study of eccentric binary systems accreting from thin disks, focusing on binary orbital evolution. Our main results are that (1) thinner disk not only drive binaries to rapidly inspiral, but also excite binary eccentricities at much higher rates; (2) while thick disks may drive binaries to a stable fixed point of $e\approx0.425$, thinner disks pump binary eccentricities to $e\gtrsim0.6$; (3) the range of near-zero eccentricities that are damped towards zero depends on both disk thickness and viscosity, thinner disks and those with $α$ viscosities driving binaries towards circularity over a much narrower range of eccentricities. These differences follow largely from the effects of pressure support on accretion streams and shocks within the inner regions of the accretion flow. Our results suggest that accreting binary black holes should have high eccentricities well into the frequency range probed by pulsar timing arrays and space-based gravitational wave interferometers, affecting the spectrum and isotropy of the gravitational wave background. Our results also suggest that circumbinary disks may play an important role in shaping the orbits of close binary stars, but much less so those of wider binaries.

💡 Research Summary

This paper presents the first systematic investigation into the orbital evolution of eccentric binary systems accreting from thin circumbinary disks, a regime critical for supermassive black hole binaries but previously unexplored in favor of thick-disk studies relevant to stellar binaries.

The authors conduct a comprehensive suite of high-resolution, 2D vertically-integrated hydrodynamical simulations using the moving-mesh code Disco. They focus on equal-mass binaries, varying key parameters: initial binary eccentricity (0 to 0.6), disk thickness (characterized by azimuthal Mach numbers M=10, 20, 30), and viscosity prescription (constant kinematic and α-viscosity). The simulations track the gravitational and accretion torques/forces on the binary over 1800 orbital periods to compute the secular evolution of the semi-major axis (a) and eccentricity (e).

The core findings reveal a dramatic difference driven by disk thickness:

1. Enhanced Inspiral and Eccentricity Growth: Thinner disks not only drive faster binary inspiral (decrease in ‘a’) but also excite binary eccentricities at significantly higher rates compared to thick disks.
2. Shift in Stable Eccentricity: While thick disks (M=10) tend to drive binaries toward a stable fixed point at e ≈ 0.425, thinner disks (M=20, 30) pump eccentricities to values e ≳ 0.6, suggesting a different long-term orbital state.
3. Narrowed Circularization Regime: The range of very low initial eccentricities that are damped toward circular orbits depends strongly on disk thickness and viscosity. Thinner disks and those with an α-viscosity prescription circularize binaries over a much narrower range of initial e.

The physical mechanism underlying these differences is traced to the role of pressure support within the disk’s inner cavity. Thick disks have strong pressure support that smooths accretion streams and shocks, leading to gentler angular momentum exchange. In contrast, thin disks have weak pressure support, resulting in more focused, high-velocity accretion streams and stronger shocks, particularly near binary pericenter. This leads to more efficient and impulsive transfer of angular momentum, driving rapid inspiral and high eccentricity excitation.

The implications are profound for gravitational wave astronomy. The results suggest that accreting supermassive black hole binaries should maintain high eccentricities well into the nHz frequency band probed by Pulsar Timing Arrays (PTAs) and the mHz band targeted by space-based interferometers like LISA. This high eccentricity will affect the spectral shape and anisotropy of the gravitational wave background. For stellar binaries, the study indicates that circumbinary disks can significantly shape the orbits of close binaries, but their influence diminishes for wider separations. The work bridges a crucial gap between stellar and supermassive binary astrophysics and provides new predictions for multi-messenger observations.