Magnetic fields and rotations of protostars

The early evolution of the magnetic field and angular momentum of newly formed protostars are studied, using three-dimensional resistive MHD nested grid simulations. Starting with a Bonnor-Ebert isothermal cloud rotating in a uniform magnetic field, we calculate the cloud evolution from the molecular cloud core (n_c ≃ 10⁴ cm^-3 and r = 4.6 × 10⁵AU, where n_c and r are the central density and radius, respectively) to the stellar core (n_c ≃ 10²² cm^-3;r ∼ 1 R_⊙). The magnetic field strengths at the centers of clouds with the same initial angular momentum but different magnetic field strengths converge to a certain value as the clouds collapse for n_c ≲ 10¹² cm^-3. For 10¹² cm^-3 ≲ n_c ≲ 10¹⁶ cm^-3, ohmic dissipation largely removes the magnetic field from a collapsing cloud core, and the magnetic field lines, which are strongly twisted for n_c ≲ 10¹² cm^-3, are decollimated. The magnetic field lines are twisted and amplified again for n_c ≳ 10¹⁶ cm^-3, because the magnetic field is recoupled with warm gas. Finally, protostars at their formation epoch (n_c ≃ 10²¹ cm^-3) have magnetic fields of ∼0.1 -1 kG, which is comparable to observations. The magnetic field strength of a protostar depends slightly on the angular momentum of the host cloud. A protostar formed from a slowly rotating cloud core has a stronger magnetic field. The evolution of the angular momentum is closely related to the evolution of the magnetic field. The angular momentum in a collapsing cloud is removed by magnetic effects such as magnetic braking, outflow, and jets. The formed protostars have rotation periods of 0.1-2 days at their formation epoch, which is slightly shorter than observations. This indicates that a further removal mechanism for the angular momentum, such as interactions between the protostar and the disk, wind, or jets, is important in the further evolution of protostars.