Angular momentum transport and proton-alpha differential streaming in the low-latitude fast solar wind

The Weber & Davis analysis on the angular momentum loss of the Sun is reconsidered for a steady-state solar wind that incorporates alpha particles and flows out of the equatorial plane. Closely following McKenzie et al. (1979), we exploit the fact that ion gyro-frequencies are many orders of magnitude larger than other frequencies in the ion momentum equations. This requires the ion velocity difference to be aligned with the magnetic field. The governing equations are derived from standard transport equations in virtue of this alignment condition. A general analysis, independent from specific energy equations, yields that the magnetic field helps the coronal plasma to achieve an effective corotation out to the Alfvénic radius, where the poloidal Alfvén Mach number M_T equals one. M_T however has to be defined as a composite one by Eq. (11). In a fast solar wind solution along the flux tube which lies at a colatitude of 70° at 1 AU, it is found that the angular momentum loss from the Sun is almost entirely due to magnetic stresses. The proton contribution, which can be as important as the magnetic one in interplanetary space, is canceled by the alpha particles that develop an azimuthal speed in the direction of counter-rotation with the Sun. The Poynting flux associated with the azimuthal components is negligible. Nevertheless, the solar rotation has an appreciable effect in limiting the proton-alpha differential streaming in the fast streams at low latitudes in interplanetary space. However this mechanism alone can not solely account for the Helios observations.