Star formation in relic H II regions of the first stars is investigated using magnetohydrodynamical simulations with a nested-grid method that covers 10 orders of magnitude in spatial scale and 20 orders of magnitude in density contrast. Due to larger fraction of H2 and HD molecules, its prestellar thermal evolution is considerably different from that in the first star formation. Reflecting the difference, two hydrostatic cores appear in a nested manner: a protostar is enclosed by a transient hydrostatic core, which appears during the prestellar collapse. If the initial natal core rotates fast at a rate with rotational to gravitational energy ratio β0 ≳ 0.01-0.1, the transient hydrostatic core fragments to 10 M ⊙ subcores at density 109 cm-3. With smaller rotation energy, fragmentation occurs at higher density while a single protostar forms without fragmentation if rotation is extremely slow with β0 ≲ 10-6 to 10-5. If magnetic field is present, these threshold values of β0 are boosted owing to angular momentum transport by the magnetic breaking. Magnetic field also drives the protostellar outflows. With strong magnetic field, two distinct outflows are observed: the slower one emanates from the transient hydrostatic core, while the faster one from the protostar. These flows may affect the final stellar mass by ejecting some of masses in the initial core, and also may play some role in driving and maintenance of interstellar turbulence in young galaxies.
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