Abstract
We analyse 3D SPH simulations of the evolution of initially quasi-circular
massive black hole binaries (BHBs) residing in the central hollow (cavity) of
self-gravitating circumbinary discs. We perform a set of simulations adopting
different thermodynamics for the gas within the cavity and for the 'numerical
size' of the black holes. We study the interplay between gas accretion and
gravity torques in changing the binary elements (semi-major axis and
eccentricity) and its total angular momentum budget. We pay special attention
to the gravity torques, by analysing their physical origin and location. We
show that (i) the BHB eccentricity grows due to gravity torques from the inner
edge of the disc, independently of the accretion and the adopted
thermodynamics; (ii) the semi-major axis decay depends not only on the gravity
torques but also on their subtle interplay with the disc-binary angular
momentum transfer due to accretion; (iii) the spectral structure of the gravity
torques is predominately caused by disc edge overdensities and spiral arms
developing in the body of the disc; (iv) the net gravity torque changes sign
across the BHB corotation radius: gas inside this radius exerts a net positive
torque, while streams located outside this radius (but within the cavity) exert
a net negative torque. The relative importance of the two might depend on the
thermodynamical properties of the instreaming gas and is crucial in assessing
the disc--binary angular momentum transfer; (v) the net torque manifests as a
purely kinematic effect as it stems from the low density cavity, where the
material flows in and out in highly eccentric orbits. Thus 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 binary.
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