Zhao et al. have developed a three-layer model of the solar magnetic field to extrapolate the observed photospheric magnetic field into the corona and the inner heliosphere (see Figure 1) (Zhao and Hoeksema, 1995; Zhao, Hoeksema and Rich, 2001). The boundary data used in this model are magnetic 'synoptic chart' (see Figure 2a) or magnetic 'synoptic frame' (see Figure 2b) generated from MDI magnetograms or the magnetograms taken at Wilcox Solar Observatory.
Using this model, Zhao shows that there are two types of large scale closed field regions in solar corona, the helmet streamer that is sandwitched by opposite-polarity coronal holes and the one that is between the like-polarity coronal holes. (Figure 3). Most full-halo CMEs originate in closed field regions between opposite-polarity coronal holes under neutral lines.
This model successfully reproduces the coronal helmet streamer belts between 2.5 and 30.0 solar radii, in good agreement with SOHO/LASCO Carrington maps (see Figure 4a for solar minimum and Figure 4b for solar maximum), suggesting the radial variation in the shape of the streamer belts, and also computes the radial component of the interplanetary magnetic field that matches well with in situ observation (Figure 5).
To understand the physical processes in the initiation and development of CMEs, the phenomena of large-scale ejections of coronal plasma and magnetic field, the time variation of the global distribution of vector magnetic fields in the photosphere is necessary, and desired to be constructed. Assuming that the non-potential field occurs mainly in the active regions with strong field strength, we have tried to construct the Carrington synoptic map for the vector photospheric field by using the observed vector magnetic field in active regions and the three components of the potential field computed on the basis of the synoptic chart of the line-of-sight field (Figure 6 ). Those synoptic charts also enable us to reproduce the global non-linear force free field by means of using the Boundary Element Method suggested by Yan and Sakurai (2000). Comparison of this non-linear force free field (Figure 7 ) and the potential field (Figure 8 ) shows that force free field is evidently sheared while potential field has additional magnetic connectivities between active regions that don't show up in force free field. Observation suggests that those connectivities may not, in fact, exist; instead, there are probably magnetic interfaces between them. This indicates that the vector field is essential to calculate magnetic topological structure and identify magnetic separatrix that are specifically important to understand flares and CMEs as such locations provide suitable conditions for occurence of fast reconnection.
Liu W. is using a 2-D MHD code to study the effects of topology on CME kinematic properties motivated by a new qualitative theory proposed by Low and Zhang (2002). In that theory, normal and inverse topoloy of quiescent prominences are responsible for observed fast and slow CMEs, respectively. Our preliminary numerical results show that the distinct topologies indeed lead to fast and slow initial speeds of CMEs, which supports the theory. Two test cases are studied with Case 1 for normal topology and Case 2 for inverse. Except magnetic topology, all the parameters are set the same for the two cases. The MHD model simulates the response of the corona to a flux rope emerging from the photosphere. The evolution of the magnetic and velocity field is shown in Figure 9 for Case 1 and Figure 10 for Case 2. A comparision of the height-time curves of the two cases shows a higher initial speed for the normal topology ( Figure 11).
Figure 1: The geometry of the current sheet-cource surface model.
Figure 2: a. Magnetic 'synoptic chart' generated from SOHO/MDI magnetograms and WSO magnetograms. A SOHO/MDI synoptic chart (top panel) is smoothed to WSO resolution (middle panel). The bottom panel is the WSO synoptic chart in the same Carrington Rotation. White represents positive polarity and black, negative. The white lines are magnetic neutral lines. b. The top two panels are synoptic charts of Carrington Rotation CR1976 and CR1975. The area marked in a black square in CR1976 is replaced by the magnetogram at the time of interest and a 'synoptic frame' is thus generated ( the third panel),and smoothed ( the last panel).
Figure 3: The top panel shows the distribution of the two kinds of closed field regions near sunspot maximum. There are eleven coronal holes indicated by different colors (Say, the red hole at the leftest and the yellow hole at the rightest). symbole `+' and `-' denote the magnetic polarity of away from and toward the Sun, respectively. The lines made by blue and red segments are closed field lines with their apex lower than 1.25 solar radii. The black lines denote the `neutral line' at 2.5 solar radii where Br = 0. The closed field regions under the neutral lines are helmet streamers sandwiched between opposite polarity. The closed field regions far away from the neutral lines, for example, the one between red and green holes and between red-green and blue holes, occur between like-polarity holes. The middle panel shows the radial variation of the boundary of the closed field regions from 1.0 to 2.5 solar radii. The bottom panel shows the boundary of open field regions at 2.5 solar radial.
Figure 4: Computed neutral line (black lines) and observed helmet streamer belt (from SOHO/LASCO) from 2.5 to 20.0 solar radii. The symbols `+' and `-' denote the magnetic polarity observed near the Earth. They have been shifted 5 days for mapping back to the Sun. The LASCO synoptic maps in left and right columns are obtained using data from east and west limb, respectively. a: near sunspot minimum; b. near sunspot maximum.
Figure 5: The in situ observations of the radial component of the interplanetary magnetic field (IMF) during the year of 1996 (CR1918, near solar minimum) and 1999 (1955, near solar maximum). The black dots denote the daily mean of signed hour-average of the radial IMF. The black lines denote the radial IMF computed at the location of the Earth using the MDI synoptic charts and the three-layer model at the location of the Earth. Here `Polarity match' denotes the ratio of the number of dots when the prediction of polarity is consistent with observation to the total number of dots. The first and second number on the right hand are for daily mean and its 27-day running average. `Strength deviation' is the RMS of the difference between the predicted stength with correct polarity and the observed one.
Figure 6: The left and right panels are the three components of the potential field and the vector magnetic field, respectively. The potential field is calculated from magnetic synoptic chart generated from SOHO/MDI magnetograms. The vector magnetic field synoptic chart at the right panels are created by replacing remapped vector field in active regions taken by magnetographs to the potential field synoptic chart shown in the left panels.
Figure 7-8: Non-linear force-free field calculated from the vector magnetic field synoptic chart using the Boundary Element Method (Yan and Sakurai, 2000) and the potential field, respectively. Evident difference is found and marked by `A'--`F'. Those areas are where the observed vector field replaces the calculated potential field. The force-free field appears sheared in areas `A', `D', `E' and `F'. The potential magnetic field shows additional connectivity in areas `B' and `C', while such connectivities do not show up in force-free field configuration.
Figure 9: The MHD simulation of CMEs with case 1 for normal topology.
Figure 10: The MHD simulation of CMEs with case 2 for inverse topology.
Figure 11: Height-time curve of case1 and case2.