1. A supermassive binary immersed in an accretion disc: the case of retrograde rotation Starring: John Papaloizou, Sijme-Jan Paardekooper, Alexander Polnarev and Pavel Ivanov AstroSpace Centre PN Lebedev Physical Institute, DAMTP, University of Cambridge, Queen Mary College, University of London

3. Basic facts and definitions α – is the Shakura-Sunyaev parameter, δ=h/r is the relative disk’s thickness, Σ – disc’s surface density,  - Keplerian angular velocity, ν – disc’s kinematic viscosity, t ν = (α δ 2  ) -1 M – primary mass, m – secondary mass, It is assumed that q=m/M << 1, r p – binary separation distance.

4. The disc’s alignment When q r p may be represented as a sum of the gravitational field of a point source of mass M and a ring of mass m and radius r p.

5. Basic equations

6. ‘Gap’ in the disc

8. Schematic structure of the accretion disc for the case of sufficiently massive secondary m > M d and torque exerted on the binary from the disc side

9. The rate of evolution of the separation distance

10. The orbital evolution rate due to emission of gravitational waves

11. Accretion rate onto the secondary

12. Results Contrary to the case of prograde rotation there is no pronounced central cavity In the disc. Instead the disc consists of two quasi-stationary part, the inner and outer discs, respectively, joined by the gap in the vicinity of perturber. The mass flow through this system is approximately constant. The evolution rate due to interaction with the disc is approximately determined by the ‘accretion’ time scale associated with the perturber. It is smaller than that in prograde case though the difference is typically small. When the evolution is determined by the interaction with the disc the accretion rate onto the perturber is approximately q 1/3 the accretion rate through the disc. However, it can be greatly amplified when the evolution is determined by emission of gravitational waves. This could lead to interesting observational consequences. Note that when binary is very eccentric (e > 0.6-07) and the disc is very thin, the cavity in the disc can, in principle, be formed by Lindblad resonances, which are present in an eccentric binary even in the case of retrograde rotation.