Potential Field Source Surface Model

Assuming that the coronal magnetic field is potential, if the currents carried by the plasma is negligible, it can be computed by solving the LaPlace's equation, using the observed photospheric magnetic field and assuming all the field to be radial beyond a distance of 2.5 R_sun as boundary conditions. A coronal model of this kind is called Potential Field Source Surface (PFSS) model and has been useful in predicting the observed coronal structures, though discrepancies are significant. The PFSS model was first put forth by Schatten et al. (1969) and independently, by Altschuler and Newkirk (1969). The model has a few free parameters: height of source surface: 2.5 or 2.35_sun, the radius of the inner surface: 1.0 _sun or slightly different, the number of multipole components included in the spherical harmonic expansion of fields, represented by N_max. These three parameters are sensitive factors in computing the coronal features using the PFSS model, with N_max being the most sensitive one. Poduval and Zhao (2004a) computed the locations (&theta, &phi) of the photospheric foot points of coronal sources of solar wind observed near the Earth mapped back to the Sun, for different values of N_max in the potential field calculations, as evident in Thetafig and Phifig below.

The deviations did not show any latitudinal or longitudinal dependencies, instead, they were quite random fluctuations without any systematic variation with N_max and are nearly constant for most locations above N_max = 22. From this study, we estimated that the error or uncertainty in the photospheric foot points of a feature on source surface when traced back along the magnetic field lines can be as high as 60° in longitude and 20° in latitude.