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.
