A Generalized Theory for the Evolution of Angular Momentum and Azimuthal Magnetic Fields in the Ecliptic Heliosphere

Abstract:

An analytic, self-consistent, theoretical model for the solar wind is developed that generalizes previous models to include all of the following: conservation of angular
momentum, frozen-in magnetic fields, both radial ($r$) and azimuthal ($\phi$) components of
the magnetic field ($B_r$ and $B_{\phi}$) and velocity ($u_r$ and $v_{\phi}$) from the source surface to $1$ AU, and the detailed tracing back of
observations at $1$ AU to the solar source surface and all intervening $(r,\phi)$. The new model applies near the solar equatorial plane,
assumes constant radial wind speed at each heliolongitude, and enforces corotation at the source surface.
It is shown that the new theoretical model can be reduced to the previous models in the appropriate limits.
We apply the model to two solar rotations of Wind spacecraft data, one near solar minimum (1-27 August 2010) and one near solar maximum (1-27 July 2002).
The model constrains the Alfv\'{e}nic critical radius $r_a$ to typically be less than fifteen solar radii, in agreement with some recent observations.
Values of $v_\phi(r,\phi)$ are predicted
from the model, being always in the sense of corotation but varying in magnitude with $r$ and $\phi$. Reasonable
and self-consistent results are found for $B_r(r,\phi)$, $B_{\phi}(r,\phi)$, $v_{\phi}(r,\phi)$ and $n(r,\phi)$
from the source surface $r_s$ to $1$ AU. Both the azimuthal and radial magnetic fields on the source
surface vary with time by more than an order of magnitude and usually $|B_r(r_s,{\phi}_s)|\geq |B_{\phi}(r_s,{\phi}_s)|$. Typically, though
not always, magnetic contributions to the total angular momentum are small. Interestingly, however, the azimuthal flow velocities observed
at 1 AU are not always in the corotation direction and usually have much larger magnitudes than predicted by the model. Conservation of angular
momentum alone cannot explain these azimuthal velocities. 
Issues regarding the model's applicability appear to be due to the assumptions of corotation and constant wind speed breaking down below the Alfv\'{e}n critical radius.