On the Expansion of Coronal Funnels in the Quiet Sun

Coronal funnels originated from chromospheric networks are key regions of solar wind origin and mass supply to large coronal loops. However, due to the lack of observational coronal magnetic field data, the geometrical and physical properties of coronal funnels can not be obtained through direct observations. Through applying force-free magnetic field extrapolation to a rectangular quiet-Sun region based on the observational MDI magnetogram, the coronal magnetic field up to 40 Mm above the photosphere can be reconstructed. Below 20 Mm, there are over 10 small funnels originating from magnetic networks and expanding with height. The small funnels merge into two big funnels above 20 Mm. For the first time, the height variations of the funnels' cross section areas in the quiet Sun are studied using observational data. The result reveals that coronal funnels expand almost linearly with height above the photosphere in the quiet Sun region. The expansion factor is larger in the lower part of the solar atmosphere than in the upper part. This result has been discussed with regard to 2D modeling of solar wind origin and mass flows in coronal loops. It is also found that the number of closed magnetic field lines decreases exponentially with height.