Modeling the heliolatitudinal gradient of the solar wind parameters with exact MHD solutions

The heliolatitudinal dependence of observations of the solar wind macroscopic quantities such as the averaged proton speed, density and the mass and momentum flux are modeled. The published observations covering the last two and a half solar cycles, are obtained either via the technique of interplanetary scintillations for the last 2 solar cycles (1970-1990), or, from the plasma experiment aboard the ULYSSES spacecraft for the recent period 1990-1994. Exact, two dimensional solutions of the full set of the steady MHD equations are used which are obtained through a nonlinear separation of the variables in the MHD equations. The three parameters emerging from the solutions are fixed from these observations, as well as from observations of the solar rotation. It is found that near solar maximum the solar wind speed is uniformly low, around the 400 km/s over a wide range of latitudes. On the other hand, during solar minimum and the declining phase of the solar activity cycle, there is a strong heliolatitudinal gradient in proton speed between 400-800 from equator to pole. This modeling also agrees with previous findings that the gradient in wind speed with the latitude is offset by a gradient in density such that the mass and momentum flux vary relatively little.