The behaviour of eccentric sub-pc massive black hole binaries embedded in massive discs

Using the 3D smoothed-particle hydrodynamics code <ns0:sc>PHANTOM</ns0:sc>, we investigated the evolution of the orbital properties of massive black hole binaries embedded in massive discs where gravitational instabilities (GIs) triggered by the disc’s self-gravity are the only significant source of angular momentum transport. In particular, we investigated the evolution of binaries with different initial eccentricities of e0 = 0.05, 0.5, 0.8 and mass ratios of q = 0.1, 0.3, 0.9. Previous studies indicate an equilibrium eccentricity of around 0.6 < e < 0.8, where the binary tidal torques and disc self-gravity torque are in dynamical balance. Our simulations suggest that there might not be a universal value of critical eccentricity. We find that binaries that are initially more eccentric attain higher asymptotic eccentricity than more circular ones do. This implies that there is a range of critical eccentricity values that depend on the initial condition and microphysics (initial eccentricity, mass ratio, cooling) of the system. In particular, we find the width of this range to be narrower for more unequal binaries. We furthermore measured preferential accretion on one of the binary components, only finding more accretion onto the primary for the mass ratio q = 0.3 and eccentricity e = 0.8. We discuss how this might have implications for the amplitude of the gravitational wave background detected by pulsar timing array (PTA) experiments. We finally measure the corresponding value of the viscosity parameter α due to GIs in our simulations and discuss how this depends on the binary properties.