Tidal disruptions in circumbinary discs (I): Star formation, dynamics,
  and binary evolution
  In our current interpretation of the hierarchical structure of the universe
it is well established that galaxies collide and merge with each other during
their lifetime. If massive black holes (MBHs) reside in galactic centres, we
expect them to form binaries in galactic nuclei surrounded by a circumbinary
disc. If cooling is efficient enough, the gas in the disc will clump and
trigger stellar formation in situ. In this first paper we address the evolution
of the binary under the influence of the newly formed stars, which form
individually and also clustered. We use SPH techniques to evolve the gas in the
circumbinary disc and to study the phase of star formation. When the amount of
gas in the disc is negligible, we further evolve the system with a
high-accurate direct-summation $N-$body code to follow the evolution of the
stars, the innermost binary and tidal disruption events (TDEs). For this, we
modify the direct N-body code to (i) include treatment of TDEs and to (ii)
include "gas cloud particles" that mimic the gas, so that the stellar clusters
do not disolve when we follow their infall on to the MBHs. We find that the
amount of stars disrupted by either infalling stellar clusters or individual
stars is as large as 10^{-4}/yr per binary, higher than expected for typical
galaxies.
