Stars

Political science

Mass ratio

Mathematics

Eccentricity (behavior)

Accretion (finance)

Astrophysics

Attractor

Binary number

Arithmetic

Orbital eccentricity

Mathematical analysis

Circumbinary planet

Physics

The Astrophysical Journal Letters

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 $e_0 \lesssim 0.1$ tend to $e=0$, where the binary semimajor axis expands. All others are attracted to $e \approx 0.4$, where the binary semimajor axis decays. The $e \approx 0.4$ 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 e...

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