Elliptical Surfaces For The Potential Field Source Surface Model

Abstract:

Knowledge of the magnetic configuration in the lower corona is essential for mapping solar wind parcels to their estimated source regions near the photosphere. The Potential Field Source Surface (PFSS) model has been employed for many decades to obtain an approximate configuration of the magnetic field close to the solar surface (Altschuler & Newkirk, 1969; Schatten et al., 1969). The classical implementation of the PFSS model relies on a spherical boundary condition a few solar radii above the photosphere, the eponymous source surfcace. Although it is the simplest boundary condition, other shapes might be better suited to give an improved representation of the magnetic field (Schulz et al., 1978 & 1997; Levine et al., 1982; Riley et al., 2006).

We developed a finite difference solver that computes the constituting mathematical equation, i.e. Laplace's equation, but which allows prolate or oblate ellipsoids acting as source surfaces (Kruse et al., 2020a). We evaluated these new boundary conditions via ballistic backmapping to the source surface and comparing the predicted with the magnetic field polarity measured by instruments on the Advanced Composition Explorer (ACE) and the twin Solar Terrestrial Relations Observatories (STEREO-A/B) (Kruse et al., 2020b). The results show a slight improvement for oblate elliptical source surfaces during quiet periods of the solar activity cycle compared to the classical spherical boundary.