Roche lobes

Roche lobe. The Roche lobes of a binary star system form an hour-glass shape. At a, the stars are completely detached. At b, one star fills its Roche lobe and material will stream onto its companion (c). At d, both Roche lobes are filled and the system is a contact binary. In a binary star system, an hourglass-shaped surface on which lie the points where the gravitational force exerted by either star on a small particle is equal. The two segments of the "hourglass" each enclose a region known as a Roche lobe. Between the stars there is a unique location where the two Roche lobes touch: this is the inner Lagrangian point, at which the gravitational force is zero (see illustration (a)). When a star in a close binary system expands during the giant phase of its evolution, it may completely fill its Roche lobe (see illustration (b)); such a system is called semidetached. Matter then streams through the inner Lagrangian point to the other star (see illustration (c)). In a contact binary (see illustration (d)), both stars have completely filled their Roche lobes and mass transfer can occur. This mass transfer is important in dwarf novae, X-ray binaries and Beta Lyrae stars, and in the formation of accretion discs around stars.