We study circumbinary accretion discs in the framework of the restricted three-body problem ( R3Bp ) and via numerically solving the height-integrated equations of viscous hydrodynamics .
Varying the mass ratio of the binary , we find a pronounced change in the behaviour of the disc near mass ratio q \equiv M _ { s } / M _ { p } \sim 0.04 .
For mass ratios above q = 0.04 , solutions for the hydrodynamic flow transition from steady , to strongly-fluctuating ; a narrow annular gap in the surface density around the secondary ’ s orbit changes to a hollow central cavity ; and a spatial symmetry is lost , resulting in a lopsided disc .
This phase transition is coincident with the mass ratio above which stable orbits do not exist around the L4 and L5 equilibrium points of the R3B problem .
Using the DISCO code , we find that for thin discs , for which a gap or cavity can remain open , the mass ratio of the transition is relatively insensitive to disc viscosity and pressure .
The q = 0.04 transition has relevance for the evolution of massive black hole binary+disc systems at the centers of galactic nuclei , as well as for young stellar binaries and possibly planets around brown dwarfs .