Orbital Evolution of Equal-mass Eccentric Binaries due to a Gas Disk: Eccentric Inspirals and Circular Outspirals

Abstract

We solve the equations of two-dimensional hydrodynamics describing a circumbinary disk accreting onto an eccentric, equal-mass binary. We compute the time rate of change of the binary semi-major axis a and eccentricity e over a continuous range of eccentricities spanning e = 0 to e = 0.9. We find that binaries with initial eccentricities e 0 0.1 tend to e = 0, where the binary semi-major axis expands. All others are attracted to e ≈ 0.4, where the binary semi-major axis decays. The e ≈ 0.4 attractor is caused by a rapid change in the disk response from an apsidally locked, nearly symmetric state to a precessing asymmetric state. The state change causes the time rates of change ȧ and ė to steeply change sign at the same critical eccentricity resulting in an attracting solution where ȧ = ė = 0. This does not, however, result in a stalled, eccentric binary. Due to a finite transition time between disk states, the binary eccentricity continually overshoots the attracting eccentricity resulting in a constant drift of the semi-major axis. For fiducial disk parameters, binaries with e 0 0.1 evolve towards and then oscillate around e ≈ 0.4 where they steadily shrink in semi-major axis. Because unequal mass binaries grow towards equal mass through preferential accretion, our results are applicable to a wide range of initial binary mass ratios. Hence, these findings merit further investigations of this disk transition; understanding its dependence on disk parameters is vital for determining the fate of binaries undergoing orbital evolution with a circumbinary disk.

Multiband light curves from eccentric accreting supermassive black hole binaries

“…where = O(1) is an "eigenvalue" (Paczynski 1991;Popham & Narayan 1991) determined by gas accretion physics. For example, an effective value of 0.43 was reported for binaries with non-zero, near-equilibrium eccentricity (D'Orazio & Duffell 2021). The result of this substitution is Specializing to equal-mass binaries with eccentricities of either e = 0 or e = 0.45, and scaling Eq.…”

“…Roedig et al 2011;Roedig & Sesana 2014). Zrake et al (2021) found that binaries in the gas-driven regime are likely eccentric with e 0.4 − 0.5 (see also D'Orazio & Duffell 2021). Presentations of simulated light curves from eccentric binaries have been limited (see e.g.…”

Micro Tidal Disruption Events in Active Galactic Nuclei

“…The binary typically forms at small separations of only ∼ 10 times the star's tidal radius R t = R * (M bh /M * ) 1/3 , and could be eccentric at (or soon after) its birth, either due to its formation (c.f. Funato et al 2004) and/or subsequently driven to be eccentric by a circumbinary disk (Zrake et al 2021;D'Orazio & Duffell 2021). This could justify an impulsive disruption "event" at the pericenter of an ellipse, rather than a slow circular inspiral and gradual tidal "peeling".…”

Multi-band light curves from eccentric accreting supermassive black hole binaries

“…Bode et al 2012;Giacomazzo et al 2012;Noble et al 2012;Gold et al 2014;Farris et al 2015a,b;Tang et al 2018;Paschalidis et al 2021). However, Zrake et al (2021) showed that binaries in the gas-driven regime are likely eccentric with e 0.4 − 0.5 (see also D'Orazio & Duffell 2021). Presentations of simulated light curves from eccentric binaries have been limited (see e.g.…”