The angular momentum problem and magnetic braking - an exact time-dependent solution

A problem in which angular momentum is transported away from a model cloud by hydromagnetic waves is formulated, put in dimensionless form, and solved for the case where the angular-momentum and magnetic-field vectors are mutually perpendicular. Exact time-dependent solutions for the angular velocity of the cloud as a whole and the external medium are obtained, and the magnetic field is determined. Results are presented for four values of the ratio between the densities of the cloud and the external medium. It is concluded that: (1) magnetic braking in the case considered can reduce the angular momentum of an interstellar cloud by at least a few orders of magnitude in a time less than 1 million yr; (2) the efficiency of magnetic braking in this case is much higher than in the case where the angular-momentum and magnetic-field vectors are parallel; and (3) the energy for cosmic-ray acceleration could come from the gravitational potential energy of interstellar clouds.