Meridional transport of magnetic flux in the solar wind between 1 and 10 AU: A theoretical analysis

Pioneer 10 observations suggest that the mean (longitudinally averaged) solar wind azimuthal field strength, Bϕ, near the ecliptic plane falls off more rapidly with heliocentric distance than would be expected in a classic Parker expansion, showing a deficit of 10-20% (as compared to the projected 1-AU value) by 10 AU. Though this observational interpretation has been challenged by subsequent analyses of Voyager data, it has nevertheless stimulated efforts to explain the inferred deficit on the basis of systematic north-south magnetic pressure gradients generated by the differential spiral wrapping of magnetic field lines in interplanetary space. We reexamine this issue from the theoretical perspective using a three-dimensional MHD nonlinear numerical model for steady, corotating flow. For realistic solar wind parameters we find that a purely axisymmetric expansion is capable of producing sizable magnetic flux deficits only when there are substantial meridional gradients in mean flow conditions localized about the ecliptic plane near the sun. Even then the match between plausible flow states and significant mean Bϕ deficit is achieved over such a limited parameter range that it is unlikely this mechanism alone can produce deficits of the magnitude inferred from the Pioneer data. We present calculations on three-dimensional corotating flows which demonstrate that latitudinal transport of magnetic flux by stream interactions may be an important consideration. For streams having a tilted-dipole geometry we find that deficits in the mean Bϕ of the order of 10% or more at 10 AU are readily produced over a broad range of tilt angles and flow conditions. Both the axisymmetric and stream interaction mechanisms should operate most efficiently and be most prominent observationally in the late declining and minimum phases of the solar cycle, when the solar wind flow is systematically organized with a narrow band of slow flow about the solar equator and fast flow toward the poles. However, it is unlikely that either mechanism would be capable of producing significant deficits under the global flow conditions of the solar cycle epoch (that centered about solar maximum) to which the published Pioneer and Voyager analyses refer. It is furthermore emphasized that deficits in Bϕ do not necessarily imply equivalent transport of magnetic flux and that a substantial portion of apparent Bϕ deficits may be due to the global, nonlinear averaging by stream interactions of the large-scale, correlated variations in flow parameters near the sun.