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Roche lobe

A Roche lobe is one of two volumes of space in a binary star system. These volumes are bounded by a particular surface of equal potential energy. The potential energy is calculated in a frame of reference that corotates with the binary system. Because this frame of reference is a non-inertial frame, the gravitational potentials due to the masses of each of the two stellar nuclei (which vary inversely with distance from the center of each star) must be supplemented by a pseudo-potential corresponding to centrifugal force. This pseudo-potential is proportional to the square of the perpendicular distance from the axis of rotation of the system.

Close to each stellar center the equipotential surfaces 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 center of mass of the system. It is this equipotential which defines the Roche lobes.

Where matter moves relative to the corotating frame it will 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).

See also Roche limit

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