Eccentric Binaries Accreting from Thin Disks: Orbital Evolution

TL;DR

This work demonstrates that eccentric binaries accreting from thin circumbinary disks experience rapid orbital decay and strong eccentricity growth, in stark contrast to thicker disks which tend toward modest eccentricities around $e\approx0.425$. Using 2D vertically integrated hydrodynamics with a moving-mesh code, the study maps how disk thickness, viscosity, and accretion geometry shape $\dot{a}$ and $\dot{e}$, highlighting the pivotal role of inner-ddisk streams and the cavity. The findings imply that binary supermassive black holes in thin-disk environments can retain high eccentricities into the gravitational-wave bands probed by PTAs and LISA, significantly affecting the stochastic GW background and waveform structure, while the implications for stellar binaries depend on binary separation and disk properties. The work also outlines caveats and directions for including additional physics (MHD, radiation, 3D effects) and varying mass ratios, underscoring the need for broader parameter exploration to fully capture disk-driven orbital evolution across astrophysical contexts.

Abstract

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.

Figures (11)

• Figure 1: Snapshots of the circumbinary disk surface density for a sample of the Mach numbers and binary eccentricities studied in this work. The binaries are shown here at pericenter. Tick markings are spaced in increments of the binary semi-major axis. Each case illustrates the fluid after 1800 orbital periods of the binary.
• Figure 2: Azimuthally integrated fluid profiles for Mach 10 and 30 disks around binaries with eccentricities of 0.1 and 0.5., time-averaged in each case over the final 1200 orbits of each simulation. The first and second rows plot the average disk surface density and eccentricity, demonstrating the mild eccentricities of the circumbinary disk and the even more pronounced eccentricity of fluid within the cavity. The bottom two rows plot the average angular and orbital frequencies of the fluid throughout the disk, normalized by the Keplerian frequency $\Omega_K\equiv (R/a)^{-3/2}$. All averages except that of the surface density were weighted by mass.
• Figure 3: Time-averaged measurements of the gravitational power and torque exerted on binaries by their disks, normalized by the energy and angular momentum of the binary respectively, in units of $\dot{m}/m$. We focus here on binaries with eccentricities $e\in[0.0125,0.6]$ and disks with Mach numbers $\mathcal{M}\in\{10,20,30\}$. All time-averaging was performed over the final 1200 binary orbits of each simulation.
• Figure 4: Time-averaged measurements of the rates of change of binary semi-major axes and eccentricities for the same simulations presented in Figure \ref{['fig:gravitationalScatter']}. Notably, while thicker disks can drive binaries to eccentricity equilibria near $e\sim0.45$, thinner disks drive binaries towards substantially higher eccentricities, $e>0.6$. All time-averaging was performed over the final 1200 binary orbits of each simulation.
• Figure 5: Profiles of the disk surface density (top row), the contribution of the disk to the eccentricity evolution of the binary as a function of radius (middle row, see Equation (\ref{['eq:dedr']})), and its integral (bottom row), each integrated in azimuth and averaged over the final 20 orbits of each simulation. Note that we have rescaled $d\dot{e}_g/dr$ by a factor of $e/(1-e^2)$ to highlight the role of the disk rather than the changing properties of the binary. In most cases the inner regions of the accretion flow surrounding the binary itself (at $R<a$) contribute negligibly to the evolution of the binary. Typically, the streams of gas flowing towards and being jettisoned away from the binary and the inner edge of the circumbinary cavity govern the orbital evolution of the binary.