  We present three-dimensional Smoothed Particle Hydrodynamics (SPH)
simulations investigating the dependence of the accretion rate on the disc
thickness around an equal-mass, circular black hole binary system. We find that
for thick/hot discs, with $H/R\gtrsim 0.1$, the binary torque does not prevent
the gas from penetrating the cavity formed in the disc by the binary (in line
with previous investigations). The situation drastically changes for thinner
discs, in this case the mass accretion rate is suppressed, such that only a
fraction (linearly dependent on $H/R$) of the available gas is able to flow
within the cavity and accrete on to the binary. Extrapolating this result to
the cold and thin accretion discs expected around supermassive black hole
binary systems implies that this kind of systems accretes less material than
predicted so far, with consequences not only for the electromagnetic and
gravitational waves emissions during the late inspiral phase but also for the
recoil speed of the black hole formed after binary coalescence, thus
influencing also the evolutionary path both of the binary and of the host
galaxy. Our results, being scale-free, are also applicable to equal mass,
circular binaries of stellar mass black holes, such as the progenitor of the
recently discovered gravitational wave source GW150914.
