Exponentially Amplified Magnetic Field Eliminates Disk Fragmentation around Population III Protostars

One critical remaining issue that is unclear in the initial mass function of the first (Population III) stars is the final fate of secondary protostars that formed in the accretion disk-specifically, whether they merge or survive. We focus on the magnetic effects on the formation of the first star under a cosmological magnetic field. We perform a suite of ideal magnetohydrodynamic simulations for 1000 yr after the first protostar formation. Instead of the sink particle technique, we employ a stiff equation of state approach to represent the magnetic field structure connecting protostars. Ten years after the first protostar formation in the cloud initialized with B (0) = 10(-20) G at n (0) = 10(4) cm(-3), the magnetic field strength around the protostars has amplified from pico- to kilo-Gauss, which is the same strength as the present-day star. The magnetic field rapidly winds up since the gas in the vicinity of the protostar (<= 10 au) has undergone several tens of orbital rotations in the first decade after protostar formation. As the mass accretion progresses, the vital magnetic field region extends outward, and magnetic braking eliminates the fragmentation of the disk that would happen in an unmagnetized model. On the other hand, assuming a gas cloud with a small angular momentum, this amplification might not work because the rotation would be slower. However, disk fragmentation would not occur in that case. We conclude that the exponential amplification of the cosmological magnetic field strength, about 10(-18) G, eliminates disk fragmentation around Population III protostars.