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. Our
theoretical framework is freely scalable to be applied for the present-day star
and planet formation.
