Generalized Roche potential for misaligned binary systems - Properties of the critical lobe

The paper considers the Roche potential for binary systems where the stellar rotation axis is not aligned with the orbital revolution axis. It is shown that, as the degree of misalignment varies, internal Lagrangian points and external Lagrangian points may switch their roles. A systematic method to identify the internal Lagrangian point and to calculate the volume of the critical lobe is developed, and numerical results for a wide range of parameters of binary systems with circular orbits are presented. For binary systems with large enough misalignment, discrete changes occur in the topological structure of the equipotential surfaces as the orbital phase varies. The volume of the critical lobe has minima, as a function of orbital phase, at the two instances when the secondary crosses the equatorial plane of the primary. In semidetached systems, mass transfer may be confined to the vicinity of these two instances.