Roche lobe

It is an approximately teardrop-shaped region bounded by a critical gravitational equipotential, with the apex of the teardrop 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 a more massive body around which it orbits.

It is also 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.

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.

[2] Where matter moves relative to the co-rotating frame it will seem to be acted upon by a Coriolis force.

It is a gravity cut-off point of the binary star system.

It is the easiest way for the debris to commute between a Hill sphere (an inner circle of blue and light blue) and communal gravity regions (figure-eights of yellow and green in the inner side).

Passing through these two equilibrium points, debris can commute between the external region (figure-eights of yellow and green in the outer side) and the communal gravity region of the binary system.

If the mass ratio of the two stars becomes larger, then the orange, yellow and green regions will become a horseshoe orbit.

In binary evolution this is referred to as mass transfer via Roche-lobe overflow.

While mass transfer from a more massive donor to a less massive accretor generally leads to a shrinking orbit, the reverse causes the orbit to expand (under the assumption of mass and angular-momentum conservation).

To determine the stability of the mass transfer and hence exact fate of the donor star, one needs to take into account how the radius of the donor star and that of its Roche lobe react to the mass loss from the donor; if the star expands faster than its Roche lobe or shrinks less rapidly than its Roche lobe for a prolonged time, mass transfer will be unstable and the donor star may disintegrate.

If the donor star expands less rapidly or shrinks faster than its Roche lobe, mass transfer will generally be stable and may continue for a long time.

Mass transfer due to Roche-lobe overflow is responsible for a number of astronomical phenomena, including Algol systems, recurring novae (binary stars consisting of a red giant and a white dwarf that are sufficiently close that material from the red giant dribbles down onto the white dwarf), X-ray binaries and millisecond pulsars.

Such mass transfer by Roche lobe overflow (RLOF) is further broken down into three distinct cases: The precise shape of the Roche lobe depends on the mass ratio

However, for many purposes it is useful to approximate the Roche lobe as a sphere of the same volume.

The length A is the orbital separation of the system and r1 is the radius of the sphere whose volume approximates the Roche lobe of mass M1.

This is a schematic of a semidetached binary system with the larger component filling its Roche lobe (black line).
A three-dimensional representation of the Roche potential in a binary star with a mass ratio of 2, in the co-rotating frame. The droplet-shaped figures in the equipotential plot at the bottom of the figure define what are considered the Roche lobes of the stars. L 1 , L 2 and L 3 are the Lagrangian points where forces (considered in the rotating frame) cancel out. Mass can flow through the saddle point L 1 from one star to its companion, if the star fills its Roche lobe. [ 1 ]
STL 3D model of the Roche potential of two orbiting bodies, rendered half as a surface and half as a mesh
Potential array
Hill sphere and horseshoe orbit