A Global MHD Model of the Solar Wind: Comparison with Ulysses Data

Arcadi V. Usmanov, Institute of Physics, University of St.-Petersburg, St.-Petersburg 198904, Russia

A global MHD model of the solar wind is developed with the purpose to study the heliospheric structure during Ulysses' fast latitude scan in 1994-1995. Ulysses' observations showed that at that time of solar activity minimum the heliospheric structure was nearly axisymmetric, steady and dominated by fast solar wind except for an equatorial band ~40 deg wide. The fast flows in each hemisphere were found to be relatively structure-free, unipolar and have the opposite magnetic field polarities which corresponded to those observed in the polar coronal holes at the Sun. The important finding of Ulysses was the independence of the radial component of the heliospheric magnetic field on heliolatitude in the fast solar wind. In this work, we make an attempt to reproduce quantitatively these features of Ulysses' observations and, in particular, to simulate the transformation of a dipolar magnetic field near the Sun into a latitude-independent one at large heliocentric distances. We approach numerically the problem of the steady solar wind flow in a dipolar magnetic field geometry. The governing polytropic single-fluid MHD equations are solved self-consistently by using a combination of the time-relaxation numerical technique in the inner computational region (1-20 Rs) and a marching-along-radius numerical method in the region extending out to 5 AU. The equations include the heat and momentum addition terms due to Alfvén waves in the WKB approximation. It is assumed that Alfvén waves propagate outward from the Sun and provide an additional heating and acceleration to the solar wind flow. The boundary conditions are specified at 1 Rs and include the Alfvén wave energy influx in the open magnetic field region. The radial component of the magnetic field is prescribed to have a dipole variation over the base with a peak field strength of 18 G at the poles. We show that the results of our simulation compare favorably with the Ulysses observations.