A "breathing" source surface for cycles 23 and 24

The potential field source surface (PFSS) model is used to represent the large-scale geometry of the solar coronal magnetic fields. The height of the source surface in this model can be taken as a free parameter. Previous work suggests that varying the source surface height during periods of solar minimum yields better agreement between PFSS models and the measured magnitude of the interplanetary magnetic field (IMF) open flux at 1 AU-in other words, the source surface "breathes" in and out over the course of the solar cycle. We examine the evolution of open flux during all of cycle 23 and the first part of cycle 24 using photospheric magnetic field maps from the Solar and Heliospheric Observatory's Michelson Doppler Imager and Solar Dynamics Observatory's Helioseismic and Magnetic Imager instruments. We determine the value of source surface height that provides a best fit to the IMF open flux at 1 AU (using the OMNI 2 data set) for the time period 1996-2012. The canonical 2.5 R-s source surface matches the measured IMF open flux during periods of solar maximum but needs to be raised by approximately 15-30% in order to match the measured IMF open flux at the periods of solar minimum.