What is a Roche lobe?

Question

When dealing with Binary systems and their evolution and mass transfers in the systems, why are effective potential and equipotential surfaces point of interest? The one which is called the Roche lobe. How is the effective field at the points on surface and around ? Masses are said to be gravitationally bounded if they are inside these surface what does it mean for them to be gravitationally bounded and what if they go beyond these surfaces and from different region of it ?
How do I mathematically construct one of such surface ?

Comments

Your question is too broad. Try restructuring it to focus on one idea.

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This does not seem to be a question for physicsoverflow but more for physics.stackexchange.com. Do you understand the reasoning for the behavior of a particle in a potential field and when it is bound? The concept of an effective potential? If you understand these concepts, then you can simply see that the Roche potential is the effective potential (gravitational+centrifugal) in the frame corotating with the binary. Since the surface of the star is defined by zero pressure, we can investigate the behavior of the elements of the surface as of free test particles in the effective potential.