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The disk fragmentation is a possible process leading to the formation ofPopulation III stellar binary systems. However, numerical simulations showdiverse fates of the fragments; some evolve into stable binaries and othersmerge away with a central star. To clarify the physics behind such diversity,we perform a series of three dimensional hydrodynamics simulations in acontrolled manner. We insert a point particle mimicking a fragment in aself-gravitating disk, where the initial mass and position are free parameters,and follow the orbital evolution for several tens of orbits. The results showgreat diversity even with such simple experiments. Some particles shortly mergeaway after migrating inward, but others survive as the migration stalls withthe gap-opening in the disk. We find that our results are well interpretedpostulating that the orbital angular momentum is extracted by (i) thegravitational torque from the disk spiral structure, and (ii) tidal disruptionof a gravitationally-bound envelope around the particle. Our analyticevaluations show the processes (i) and (ii) are effective in an outer and innerpart of the disk respectively. There is a window of the gap-opening in themiddle, if the envelope mass is sufficiently large. These all agree with ournumerical results. We further show that the binaries, which appear for the"survival" cases, gradually expand while accreting the disk gas. Ourtheoretical framework is freely scalable to be applied for the present-day starand planet formation.

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