Roche lobe

The Roche lobe is the region around a star in a binary system within which orbiting material is gravitationally bound to that star. It is an approximately tear-drop-shaped region bounded by a critical gravitational equipotential, with the apex of the tear drop pointing towards the other star (the apex is at the L1 Lagrangian point of the system). The Roche lobe is the region around a star in a binary system within which orbiting material is gravitationally bound to that star. It is an approximately tear-drop-shaped region bounded by a critical gravitational equipotential, with the apex of the tear drop pointing towards the other star (the apex is at the L1 Lagrangian point of the system). The Roche lobe is different from the Roche sphere which approximates the gravitational sphere of influence of one astronomical body in the face of perturbations from another heavier body around which it orbits. It is different from the Roche limit which is the distance at which an object held together only by gravity begins to break up due to tidal forces. The Roche lobe, Roche limit and Roche sphere are named after the French astronomer Édouard Roche. 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). In the gravity potential graphics, L1, L2, L3, L4, L5 are in synchronous rotation with the system. Regions of red, orange, yellow, green, light blue and blue are potential arrays from high to low. Red arrows are rotation of the system and black arrows are relative motions of the debris.