Evolution of Rotating Molecular Cloud Core with Oblique Magnetic Field
  We studied the collapse of rotating molecular cloud cores with inclined magnetic fields, based on three-dimensional numerical simulations.The numerical simulations start from a rotating Bonnor-Ebert isothermal cloud in a uniform magnetic field. The magnetic field is initially taken to be inclined from the rotation axis. As the cloud collapses, the magnetic field and rotation axis change their directions. When the rotation is slow and the magnetic field is relatively strong, the direction of the rotation axis changes to align with the magnetic field, as shown earlier by Matsumoto & Tomisaka. When the magnetic field is weak and the rotation is relatively fast, the magnetic field inclines to become perpendicular to the rotation axis. In other words, the evolution of the magnetic field and rotation axis depends on the relative strength of the rotation and magnetic field. Magnetic braking acts to align the rotation axis and magnetic field, while the rotation causes the magnetic field to incline through dynamo action. The latter effect dominates the former when the ratio of the angular velocity to the magnetic field is larger than a critical value \Omega_0/ B_0 > 0.39 G^1/2 c_s^-1, where B_0, \Omega_0, G, and c_s^-1 denote the initial magnetic field, initial angular velocity, gravitational constant, and sound speed, respectively. When the rotation is relatively strong, the collapsing cloud forms a disk perpendicular to the rotation axis and the magnetic field becomes nearly parallel to the disk surface in the high density region. A spiral structure appears due to the rotation and the wound-up magnetic field in the disk. 
Masahiro N. Machida, Tomoaki Matsumoto, Tomoyuki Hanawa, Kohji   Tomisaka