Roche Lobe - Definition of The Roche Lobes

Definition of The Roche Lobes

In a binary system with a circular orbit, it is often useful to describe the system in a coordinate system that rotates along with the objects. In this non-inertial frame, one must consider centrifugal force in addition to gravity. The two together can be described by a potential, so that, for example, the stellar surfaces lie along equipotential surfaces.

Close to each star, surfaces of equal gravitational potential are approximately spherical and concentric with the nearer star. Far from the stellar system, the equipotentials are approximately ellipsoidal and elongated parallel to the axis joining the stellar centers. A critical equipotential intersects itself at the L₁ Lagrangian point of the system, forming a two-lobed figure-of-eight with one of the two stars at the center of each lobe. This critical equipotential defines the Roche lobes.

Where matter moves relative to the co-rotating frame it will seem to be acted upon by a Coriolis force. This is not derivable from the Roche lobe model as the Coriolis force is a non-conservative force (i.e. not representable by a scalar potential).