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In astronomy, the Roche lobe or Roche limit is defined as the equipotential surface bounding a rotating two body system which passes through the L1 Lagrange point. (To be exact, it is a three body system when you count the test particle) It looks like a figure eight drawn around two massive bodies with the middle of the eight centered on L1, and the top and bottom of the eight passing through the L2 and L3 Lagrange points. All two-body systems have Roche lobes.

An approximate analytic expression for the Roche lobes is

R1 = a × (0.38 + ( 0.2 × log (M1/M2)), R2 = a × (0.38 + ( 0.2 × log (M2/M1)),

where R1 and R2 are the Roche lobe radii, and a is the separation between the two masses M1 and M2.

Roche lobes are particularly important in binary star systems. As the individual stars in the system evolve, their radii increase over time. Eventually, if the radius of one star expands to fill its Roche lobe, mass will start to flow from one star to the other through the "spill point" at L1. The other star will start to gain mass at its partner's expense, which will make it evolve faster. Sometimes, this may make the other star evolve to the point where it overflows its Roche lobe, too, and the system becomes a contact or common envelope binary.

However, in systems where one star is much more massive than the other, it may evolve and die very quickly, forming a system with a normal star and a white dwarf, neutron star, or black hole. In the case of systems with a white dwarf, when the secondary star (the less-evolved one) overflows its Roche lobe, the system can become a cataclysmic variable, a dwarf nova or nova system. Eventually, if the white dwarf gains enough mass from its companion to exceed the Chandrasekhar limit of 1.4 solar masses, it will explode in a Type I supernova. For systems with a neutron star or black hole, Roche lobe overflow by the secondary will result in the formation of a bright, hot accretion disk of matter around the compact object, resulting in an X-ray binary system. Examples of neutron star and black hole X-ray binaries are Scorpius X-1 and Cygnus X-1 respectively.

Taken from my class notes -- memory too hazy to remember sources...

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