A Comparison between Global Solar Magnetohydrodynamic and Potential Field Source Surface Model Results

The large-scale, steady-state magnetic field configuration of the solar corona is typically computed using boundary conditions derived from photospheric observations. Two approaches are typically used: (1) potential field source surface (PFSS) models, and (2) the magnetohydrodynamic (MHD) models. The former have the advantage that they are simple to develop and implement, require relatively modest computer resources, and can resolve structure on scales beyond those that can be handled by current MHD models. However, they have been criticized because their basic assumptions are seldom met. Moreover, PFSS models cannot directly incorporate time-dependent phenomena, such as magnetic reconnection, and do not include plasma or its effects. In this study, we assess how well PFSS models can reproduce the large-scale magnetic structure of the corona by making detailed comparisons with MHD solutions at different phases in the solar activity cycle. In particular, we (1) compute the shape of the source surface as inferred from the MHD solutions to assess deviations from sphericity, (2) compare the coronal hole boundaries as determined from the two models, and (3) estimate the effects of nonpotentiality. Our results demonstrate that PFSS solutions often closely match MHD results for configurations based on untwisted coronal fields (i.e., when driven by line-of-sight magnetograms). It remains an open question whether MHD solutions will differ more substantially from PFSS solutions when vector magnetograms are used as boundary conditions. This will be addressed in the near future when vector data from SOLIS, the Solar Dynamics Observatory, and Solar-B become incorporated into the MHD models.