Jet-driving and fragmentation processes in a collapsing primordial cloud are studied using three-dimensional MHD nested grid simulations. Starting from a rotating magnetized spherical cloud with a number density of nc 103 cm?3, we follow the evolution of the cloud until the adiabatic core (or protostar) formation epoch, nc 1022 cm?3. We calculate 36 models parameterizing the initial magnetic γ0 and rotational β0 energies. The evolution of collapsing primordial clouds is characterized by the ratio of the initial rotational energy to the magnetic energy, γ0/β0. The Lorentz force significantly affects cloud evolution when γ0 β0, while the centrifugal force dominates the Lorentz force when β0 γ0. When the cloud rotates rapidly with an angular velocity of Ω0 10?17(nc/103 cm ?3)2/3 s?1 and β0 γ0, fragmentation occurs before protostar formation, but no jet appears after protostar formation. On the other hand, when the initial cloud has a magnetic field of B0 10?9(nc/103 cm ?3)2/3 G and γ0 β0, a strong jet appears after protostar formation without fragmentation. Our results indicate that Population III protostars frequently show fragmentation and protostellar jets. Population III stars are therefore born as binary or multiple stellar systems; as in present-day star formation, they can drive strong jets that disturb the interstellar medium significantly, and thus they may induce the formation of next-generation stars.
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