Magnetic collimation of the solar and stellar winds

We resolve the paradox that although magnetic collimation of an isotropic solar wind results in an enhancement of its proton flux along the polar directions, several observations indicate a wind proton flux peaked at the equator. To that goal, we solve the full set of the timedependent MHD equations describing the axisymmetric outflow of plasma from the magnetized and rotating Sun, either in its present form of the solar wind, or, in its earlier form of a protosolar wind. Special attention is directed towards the collimation properties of the solar outflow at large heliocentric distances. For the present day solar wind it is found that the poloidal streamlines and fieldlines are only slightly focused toward the solar poles. However, even such a modest compression of the flow by the azimuthal magnetic field would lead to an increase of the mass flux at the polar axis by about 20% at 1 AU, relatively to its value at the equator, for an initially isotropic at the base wind, contrary to older and recent (Prognoz, Ulysses, SOHO) observations. For the anisotropic in heliolatitude wind with parameters at the base inferred from in situ observations by ULYSSES/SWOOPS and SOHO/CDS the effect of collimation is almost totally compensated by the initial velocity and density anisotropy of the wind. This effect should be taken into account in the interpretation of the recent SOHO observations by the SWAN instrument. Similar simulations have been performed for a fiveand ten-fold increase of the solar angular velocity corresponding presumably to the wind of an earlier phase of our Sun. For such conditions it is found that for initially radial streamlines, the azimuthal magnetic field created by the fast rotation focus them toward the rotation axis and forms a tightly collimated jet.