Evolution of binary black holes in self gravitating discs: dissecting the torques

We study the interplay between gas accretion and gravity torques in changing a binary elements and its total angular momentum (L) budget. Especially, we analyse the physical origin of the gravity torques (T_g) and their location within the disc. We analyse 3D SPH simulations of the evolution of initially quasi-circular massive black hole binaries (BHBs) residing in the central hollow of massive self-gravitating circumbinary discs. We use different thermodynamics within the cavity and for the numerical size of the black holes to show that (i) the BHB eccentricity growth found previously is a general result, independent of the accretion and the adopted thermodynamics; (ii) the semi-major axis decay depends both on the T_g and on the interplay with the disc-binary L-transfer due to accretion; (iii) the spectral structure of the T_g is predominately caused by disc edge overdensities and spiral arms developing in the body of the disc and, in general, does not reflect directly the period of the binary; (iv) the net T_g changes sign across the BHB corotation radius. We quantify the relative importance of the two, which appear to depend on the thermodynamical properties of the instreaming gas, and which is crucial in assessing the disc-binary L-transfer; (v) the net torque manifests as a purely kinematic (non-resonant) effect as it stems from the cavity, where the material flows in and out in highly eccentric orbits. Both accretion onto the black holes and the interaction with gas streams inside the cavity must be taken into account to assess the fate of the BHB. Moreover, the total torque exerted by the disc affects L(BHB) by changing all the elements (mass, mass ratio, eccentricity, semimajor axis) of the BHB. Common prescriptions equating tidal torque to semi-major axis shrinking might therefore be poor approximations for real astrophysical systems.