Comparison of heliospheric in situ data with the quasi-steady solar wind models

The standard theory for the solar-heliospheric magnetic field is the so-called quasi-steady model in which the field is determined by the observed magnetic flux at the photosphere and the balance between magnetic and plasma forces in the corona. In this model, the solar magnetic flux that opens to the heliosphere can increase or decrease as the photospheric flux evolves. The most sophisticated implementation of the quasi-steady theory is the SAIC model, which solves the fully time-dependent 3D MHD equations for the corona and wind until a steady state is achieved. In order to test the quasi-steady theory, we compare the 3D MHD model with observations of the heliospheric flux using multipoint measurements from the VHM instrument on the Ulysses spacecraft from 1991 to 2005 and from magnetic field measurements from various spacecraft at L1 compiled into the OMNI data set from 1976 through 2005. We also compare the observations to the predictions of the potential-field source-surface model, an older and simpler implementation of the quasi-steady theory. During solar maximum, ICMEs significantly disturb the heliospheric magnetic field, making our comparisons difficult. We find that the MHD model compares well with the general trends of the observed heliospheric fluxes. Variations on short timescales, presumably due to local effects, are missed by the model, but the long-term evolution is well matched. The model disagrees with observations most when Ulysses is in slow wind or ICME-related flows. The model underestimates the flux at solar maximum; however, this is to be expected, given the large number of ICMEs in the heliosphere at this time. We discuss the possible sources of discrepancy between the observations and the quasi-steady models.