The heliolatitudinal gradient of the solar wind during solar minimum conditions modelled by exact hydrodynamic solutions

The heliolatitudinal dependence of observations of the solar wind macroscopic quantities such as the averaged proton speed and density is modelled during solar minimum conditions when the rotational and magnetic axes roughly coincide. Published observations via the technique of interplanetary scintillations for the previous two solar cycles were used, as well as recent data from the plasma experiment aboard the ULYSSES spacecraft, which also refer to the declining phase of the present solar cycle. A class of exact, two-dimensional solutions of the full set of steady HD equations is used which is obtained analytically through a nonlinear separation of the variables. The three parameters which emerge in these solutions are fixed from such observations, as well as from observations of solar rotation. The solutions are consistent with observational inferrences that during solar minimum and the declining phase of the solar activity cycle, there is a strong heliolatitudinal gradient in rotation averaged proton speed between about 400 - 800 km s(-1) from equator to pole. This modelling 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.