An equatorial solar wind model with angular momentum conservation and nonradial magnetic fields and flow velocities at an inner boundary

Abstract

AbstractAn 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 (ϕ) components of the magnetic field (Br and Bϕ) and velocity (vr and vϕ) from the inner boundary rs to 1 AU, and the detailed tracing back of observations at 1 AU to the inner boundary and all intervening (r,ϕ). The new model applies near the solar equatorial plane, assumes constant radial wind speed at each heliolongitude, and enforces corotation at the inner boundary. 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 analytically predicts the Alfvénic critical radius ra from the radial Alfvénic Mach number observed at 1 AU. Typically, the values are less than 15 solar radii, in agreement with some recent observations, and vary with longitude. Values of vϕ(r,ϕ) are predicted from the model, being always in the sense of corotation but varying in magnitude with r and ϕ. Reasonable and self‐consistent results are found for Br(r,ϕ), Bϕ(r,ϕ), vϕ(r,ϕ), and n(r,ϕ) from rs to 1 AU. Both the azimuthal and radial magnetic fields at rs vary with time by more than an order of magnitude and usually |Br(rs,ϕs)|≥|Bϕ(rs,ϕs)|. 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 and the standard interpretation involving stream‐stream interactions and dynamical behavior seems reasonable. Issues regarding the model's applicability appear to be due to the assumptions of corotation and constant wind speed breaking down below the Alfvén critical radius.