RocheLobe

The shape of Roche Lobe vs mass ratio. x direction pointing away from the companion star. y toward orbital motion. z is pointing north.

1. The L1 over separation ratio vs masses ratio (L1.pdf).
2. The ratio of Roche lobe in y/x and z/x to illustrate the shape of the Roche lobe (Ratio.pdf).
3. The location of maximum potential point along y axis in the unit of separation a vs masses ratio (Pot_ymin.pdf).
4. Contour of potential in the x-y plane (potential_xy.pdf).
5. Contour of potential in the x-z plane (potential_xz.pdf).
6. Compare the shape of equal potential surface with a elliptical (Equal_potential_yz.pdf).

Note: The objects are treated as point mass. In reality, the distortion of mass distribution due to the gravitational force of the companion and stellar rotation may deviate the gravitational potential from point mass.

For a study that considered this effect, see Wahl et al. 2020 and the references therein.