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

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 (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.

A Generalized Equatorial Model for the Accelerating Solar Wind

“…Section 5 fits the model to data at 1 AU over a solar rotation in order to investigate the predictions for r A (ϕ a , t a ), the electric field in the corotating frame ( ), the intrinsic v ϕ ( r s ,ϕ s , t s ) and B ϕ ( r s ,ϕ s , t s ), and the variations of radial and longitudinal velocity and magnetic field. Section 5.1 shows that the predictions for r A agree well with the observations of DeForest et al () and are semiquantitatively consistent with Tasnim & Cairns's () model. Section 5.2 shows that deviations δ v ϕ ( r s ,ϕ s ) from corotation are generally present and have significant implications.…”

“…Section 5.2 shows that deviations δ v ϕ ( r s ,ϕ s ) from corotation are generally present and have significant implications. It also shows that the predictions for B ϕ ( r s ,ϕ s , t s ) are different from but semiquantitatively consistent with the predictions from previous solar wind models (Schulte in den Bäumen et al, , ; Tasnim & Cairns, ), and it demonstrates that sometimes the predicted values of δ v ϕ ( r s ,ϕ s , t s ) cancel out the azimuthal speed due to corotation. The sudden changes in δ v ϕ are interpreted in terms of converging and diverging flows associated with granulation and supergranulation cells.…”

“…This model is the first analytic theoretical attempt to simultaneously treat the acceleration of the solar wind, permit a deviation from corotation at the inner boundary, include intrinsic nonradial velocity and magnetic field from the inner boundary to 1 AU and beyond, and enforce conservation of angular momentum. It generalizes the existing theoretical solar wind models (Jokipii & Kóta, ; Parker, ; Schulte in den Bäumen et al, , ; Tasnim & Cairns, ; Weber & Davis, ) by relaxing the assumptions of constant radial speed, strong corotation, zero electric field in the corotating frame, and so on. Therefore, this model improves the preceding models, specifically, the new model relaxes the assumptions of purely radial magnetic field (Hu et al, ; Jokipii & Kóta, ; Keppens & Goedbloed, ; Parker, ; Weber & Davis, ) and velocity (Jokipii & Kóta, ; Parker, ; Schulte in den Bäumen et al, , ) at the inner boundary, constant radial speed (Jokipii & Kóta, ; Schulte in den Bäumen et al, , ; Tasnim & Cairns, ; Weber & Davis, ), (Parker, ; Weber & Davis, ), neglect of conservation of angular momentum (Parker, ; Schulte in den Bäumen et al, , ), and an azimuthal flow, which is only due to the corotation of the solar wind (Tasnim & Cairns, ).…”

“…The MHD equation for the conservation of angular momentum including gravity (Tasnim & Cairns, ) in an inertial frame is where ∂ L ⋆ /∂ t is the time derivative of the angular momentum L ⋆ = ρ ( r × v ), and B 2 /2 μ 0 is the magnetic pressure in the corotating frame. We assume that the distribution of particles is sufficiently random that the pressure tensor can be approximated as a scalar pressure P .…”

“…Assuming radially symmetric thermal and magnetic pressures (Tasnim & Cairns, ), becomes …”