Forming Pop III binaries in self-gravitating disks: how to keep the orbital angular momentum

The disk fragmentation is a possible process leading to the formation of Population III stellar binary systems. However, numerical simulations show diverse fates of the fragments; some evolve into stable binaries and others merge away with a central star. To clarify the physics behind such diversity, we perform a series of three dimensional hydrodynamics simulations in a controlled manner. We insert a point particle mimicking a fragment in a self-gravitating disk, where the initial mass and position are free parameters, and follow the orbital evolution for several tens of orbits. The results show great diversity even with such simple experiments. Some particles shortly merge away after migrating inward, but others survive as the migration stalls with the gap-opening in the disk. We find that our results are well interpreted postulating that the orbital angular momentum is extracted by (i) the gravitational torque from the disk spiral structure, and (ii) tidal disruption of a gravitationally-bound envelope around the particle. Our analytic evaluations show the processes (i) and (ii) are effective in an outer and inner part of the disk respectively. There is a window of the gap-opening in the middle, if the envelope mass is sufficiently large. These all agree with our numerical results. We further show that the binaries, which appear for the ``survival'' cases, gradually expand while accreting the disk gas.