Dynamical Tide-modified Roche Limit in Eccentric, Asynchronous Binaries

Abstract

The Roche limit, or the threshold separation within which a celestial object (the donor) M cannot remain in a stable configuration due to a companion’s tidal field, has been well established when M is in hydrostatic equilibrium and has synchronous rotation in a circular orbit. However, limited analyses exist considering corrections to the Roche limit due to hydrodynamical effects. We fill in the gap by providing a general theoretical framework involving nonlinear hydrodynamics. We consider both exact nonlinear equations derived from an affine model describing incompressible ellipsoids and series-expanded ones that can be calculated for realistic stars and planets. Our formulation addresses the Roche problem in generic orbits and synchronization levels of M, and fully accounts for the history-dependent hydrodynamical effects. We show that, as the orbital eccentricity increases, fluid instability is more likely to develop at the pericenter due to the increased dynamical tide that accumulates over multiple orbits. When M moves in a highly eccentric orbit (with eccentricity around 0.9) and the damping of the fluid is small, the threshold pericenter separation at which mass loss from M can occur can be at least 30% higher than the value predicted for a circular orbit with hydrostatic equilibrium. If only a single passage is considered, however, the threshold separation is 20% smaller than the static limit. The nonlinear interaction at each pericenter passage can also trigger a diffusive fluid evolution inside M even with moderate eccentricities, complementing previous studies of diffusive tides caused by random propagation phases. Our work has broad implications for interacting binaries in eccentric orbits, including migrating gaseous exoplanets, repeated partial tidal disruption events, and more.