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We solve the equations of two-dimensional hydrodynamics describing acircumbinary disk accreting onto an eccentric, equal-mass binary. We computethe 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 findthat binaries with initial eccentricities $e_0 \lesssim 0.1$ tend to $e=0$,where the binary semimajor axis expands. All others are attracted to $e \approx0.4$, where the binary semimajor axis decays. The $e \approx 0.4$ attractor iscaused by a rapid change in the disk response from a nearly origin-symmetricstate to a precessing asymmetric state. The state change causes the time ratesof change $\dot{a}$ and $\dot{e}$ to steeply change sign at the same criticaleccentricity resulting in an attracting solution where $\dot{a} = \dot{e} = 0$.This does not, however, result in a stalled, eccentric binary. Thefinite-transition time between disk states causes the binary eccentricity toevolve beyond the attracting eccentricity in both directions resulting inoscillating orbital parameters and a drift of the semimajor axis. For thechosen disk parameters, binaries with $e_0 \gtrsim 0.1$ evolve toward and thenoscillate around $e \approx 0.4$ where they shrink in semimajor axis. Becauseunequal 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 thefate of binaries undergoing orbital evolution with a circumbinary disk.

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