improve the computational efficiency of the code). Finally, the forth test is that the divergence of the accelerations must be less than zero. This final check ensures that the group of particles is not in the process of being tidally disrupted or bouncing. If all of these tests are passed, the particle becomes a sink and the mass and linear momentum of the neighbors are added to the sink particle.

As the simulation progresses, the sink particles are then allowed to accrete other gas particles that fall within the accretion radius. As in the Bate et al. (1995) prescription, several tests must be passed before any SPH particles can be accreted by the sink. First, it must obviously be bound and moving toward the candidate sink. Second, in the case where there is more than one sink present, it must be more bound to the candidate sink than any other sink in the simulation. Finally, the SPH and sink particles need to be on the same integration time-step (to ensure temporal momentum conservation). Once these conditions are passed, the mass and linear momentum of the SPH particle are added to the sink particle. Note that accretion onto existing sink particles 