Description
The open flux problem relates to the inconsistencies between the in-situ measurements of the magnetic flux at 1 AU and the estimated magnetic flux propagated from near the Sun surface (typically 2-3 solar radii) to 1 AU. The estimate measure of the flux at 1 AU is larger than the flux estimated from solar modelling, which is not compatible with our understanding of the interplanetary magnetic field. The magnetic flux at 1 AU is obtained by in situ measurements of the magnetic field vector from space missions, whilst the open flux value near the Sun's surface is modelled using photospheric measurements of the magnetic field combined with magnetic field models. One such model is the Potential Field Source Surface (PFSS) model: solving the Laplace equation with boundary conditions provided by the photospheric magnetic field and a source surface. The PFSS model is commonly derived as an expansion into spherical harmonics and a fully open magnetic field at the source surface (no longitudinal and azimuthal components). We here use the properties of the potential field model to study the effect of the spatial resolution and the photospheric maps on the measure of the open flux: we provide a direct measure of the flux at the source surface without computing the potential magnetic field everywhere in the 3D domain. We also show the fluctuations of the open flux to quantify the effects of the open/close field transitions.
