Solar Magnetism

Home » Research » Solar Magnetism

The Potential-field Source-surface (PFSS) model provides a simple and effective model for the large-scale features of the global coronal magnetic field. To capture large-scale field structure in a model we may assume that the electric currents in the corona do not significantly influence the global field structure. The PFSS model was originally developed by Schatten, Wilcox & Ness (1969) and Altschuler & Newkirk (1969) and refined by Hoeksema (1984) and Wang & Sheeley (1992). The PFSS model gives a reasonable estimate of the coronal field structure because most of the coronal field is approximately Maxwell-stress-free most of the time. There is twisting and shearing in active regions and the solar wind imposes inertial forces on streamers, but ignoring these effects does not fatally undermine the model and in practice the PFSS model compares well with MHD models (Neugebauer et al. 1998, Riley et al. 2006).

The lower-boundary data for the PFSS models are provided by GONG synoptic magnetograms. Full-disk photospheric magnetograms from GONG’s six sites are used to derive maps of the magnetic field over the entire surface of the Sun. These maps are constructed in near-real-time and for integral Carrington rotations. Using these maps as lower boundary data, GONG PFSS models are calculated in near-real-time and for integral Carrington rotations.

The PFSS model includes at its upper boundary an electric current source surface where the field lines are forced to be radial. This models the effect on the field of the outflowing solar wind. Altschuler & Newkirk (1969) deduced from a 1966 eclipse photograph that the source-surface radius is approximately 2.5 solar radii. Hoeksema (1984) compared the observed interplanetary mean field (IMF) with predictions based on PFSS models for different intervals of solar cycle 21 and found similar optimal values for the source-surface radius, 2.5 +/- 0.25 solar radii. Recently Lee et al. (2011) argued based on IMF predictions that the source-surface radius should be lower for the minima of solar cycles 22 and 23. In the models shown here the source surface is fixed at the standard value of 2.5 solar radii. We find that for some rotations, such as this one, the value 2.5 solar radii works as well as any. The model coronal hole distributions and streamer structures (see below) can be compared to STEREO synoptic maps.

Coronal Holes and Streamer Belts

These plots show the large-scale features of the the model, plotted in Carrington coordinates in the left picture and in spherical coordinates in the right picture. In these plots only the tallest closed field lines are shown. All field lines reaching r=2.5R are open by assumption and so the tallest closed field lines are those with vanishing radial component just below r=2.5R. Such field lines separate regions of open and closed magnetic flux and are therefore a useful simple representation of the global magnetic field topology. The field lines plotted all mark boundaries between regions of open and closed field. Regions of open flux are known as coronal holes, whose footprints in the photosphere are represented here by patches of color: green denotes positive coronal holes and red negative. The neutral line, which meanders in a quasi-sinusoidal pattern between about +/- 45 degrees, is drawn in black and may be identified with the equatorial streamer belt. (Click the images for high-resolution versions.)

Open fields

Here we plot open positive (outward from the Sun) flux in green, open negative flux in red, the tallest closed flux trajectories in blue and closed active-region flux in yellow. These fields are plotted over the original synoptic magnetogram, whose flux density is indicated by a grey scale from white (maximum- strength positive flux) to black (maximum-strength negative flux). The open field spreads out to fill the heliosphere at 2.5R.

Ecliptic fields

Shown here are model field lines that are open to the heliosphere at the ecliptic plane. These trajectories are likeliest to channel dangerous energetic particles associated with flares and CMEs towards Earth. Also shown are the associated magnetogram and the polarity inversion line, which divides the lines into same-polarity groups, and coronal holes, which are represented by dots. The polarities of both the open ecliptic-plane flux and the coronal holes are indicated by the same color code: green for positive polarity and red for negative polarity.
A top view of the ecliptic-plane field lines, from above the North pole. Here the expansion of the flux tubes is evident. Positive-polarity field lines and coronal holes are in green and negative-polarity in red. Northerly coronal holes are represented by solid shading and southerly by dots.


Dr. Gordon Petrie
National Solar Observatory

Relevant Publications

Additional Information



[et_pb_divi_related_posts_module admin_label=”Related Posts” _builder_version=”3.1″ orderby=”title” order=”ASC” /]