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

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 semimajor 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 e0 ≲ 0.1 tend to e = 0, where the binary semimajor axis expands. All others are attracted to e ≈ 0.4, where the binary semimajor axis decays. The e ≈ 0.4 attractor is caused by a rapid change in the disk response from a nearly origin-symmetric state to a precessing asymmetric state. The state change causes the time rates of change $\dot{a}$ and $\dot{e}$ to steeply change sign at the same critical eccentricity resulting in an attracting solution where $\dot{a}=\dot{e}=0$. This does not, however, result in a stalled, eccentric binary. The finite transition time between disk states causes the binary eccentricity to evolve beyond the attracting eccentricity in both directions resulting in oscillating orbital parameters and a drift of the semimajor axis. For the chosen disk parameters, binaries with e0 ≳ 0.1 evolve toward and then oscillate around e ≈ 0.4 where they shrink in semimajor axis. Because unequal mass binaries grow toward 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.