Angular momentum problem and magnetic braking: An exact, time-dependent solution

A cylindrical cloud of uniform density rho/sub cl/ is imparted an initial angular velocity about its axis of symmetry with respect to the external medium of uniform density rho/sub ext/. A frozen-in magnetic field, initially radial and perpendicular to the axis of symmetry, links the two media. The angular velocity of the cloud is then calculated as a function of time for different ratios rho/sub cl//rho/sub ext/, representing different stages of contraction. Magnetic braking becomes more efficient as rho/sub cl//rho/sub ext/ (the only free parameter in the equations) increases. This is due to a decrease of the cloud's moment of inertia and an increase of the Alfven velocity in the neighborhood of the cloud upon contraction. A cloud with mass 103 M/sub sun/ and density 103 cm-3 which formed in a background field of 3 microgauss reduces its angular momentum by more than two orders of magnitude in less than 106 yr.The angular velocity, the shape of field lines, and the magnetic field of the external medium are calculated as functions of space and time. The initial rotational discontinuity propagates outward, setting into rotational motion matter farther and farther away from the axis. When a moment of inertia comparable to that of the cloud is swept, the cloud's rotation slows down significantly, and vanishes in a relatively short time. Because the magnetic torques exterted on the cloud do not vanish at that instant, however, the cloud reverses its sense of rotation. This can happen several times (depending on rho/sub cl//rho/sub ext/) before the cloud comes to a complete rest with respect to the surrounding medium. Each reversal of rotation sends out a new wave. A steepening of field lines takes place, raising the possibility of magnetic reconnection in the intercloud medium. For cloud densities < or =104 cm-3, cosmic rays of energy up to a few times 1011 eV may be produced in situ in the neighborhoods of clouds