The MDI instrument on SOHO has made 2" full-disk observations of the photospheric field every 96 minutes since May 1996, except for a several-month gap in 1998 and early 1999 caused by problems with the SOHO spacecraft. We are now developing tools to characterize the local variations and relate them to their global effects. The high-cadence high-quality MDI magnetograms can be used to construct the proxy of the global distribution of the stable photospheric magnetic field without any data gap. Using the synoptic MDI maggnetogram map, the KPNO and WSO counterpart can be successfully reproduced. The two types of the proxy of global distribution of the instantaneous photospheric magnetic field and their effects on the model coronal field are analyzed and discussed.
The global distribution of the photospheric magnetic field is necessary for modeling large-scale coronal structures and for understanding large-scale dynamic phenomena. The commonly-used synoptic magnetogram map or the SYNOPTIC CHART is a proxy of the global distribution of the photospheric magnetic field. The synoptic chart is made of central meridian stripes of magnetograms observed over one solar rotation. The Kitt Peak National Observatory (KPNO) and the Wilcox Solar Observatory (WSO) publish the synoptic chart routinely. It is implicitely assumed in the construction of the synoptic chart that the magnetic field is stable over the time interval of one solar rotation. By extrapolating the monthly-stable global photospheric field into the corona, such stable large-scale structure as the base of the heliospheric current sheet and the location of coronal holes have been reproduced using various coronal field models.
Some of large-scale coronal structures, such as X ray arcades and coronal hole boundary, vary on the time scale of one day or less. To model the evolution of such coronal strutures, the proxy of the instantaneous global distribution of the photospheric field at the time of interest, the SYNOPTIC FRAME in what follows, must be constructed.
The MDI instrument on SOHO has made 2" full-disk observations of the photospheric field every 96 minutes. The high cadence, high quality MDI magnetograms may be used to construct the synoptic chart without data gap. The high cadence MDI observations provide the possibility to monitor the change of the photospheric field that is associated with the evolution of large-scale coronal structures. By combining the MDI magnetogram observed at the time of interest and the appropriate synoptic chart two types of the synoptic frame has been constructed. One put the interesting time or Carrington longitude in the center of the synoptic frame. The other put the interesting time at the left part of the synoptic frame, usually located about 60 degrees from the west side of the synoptic frame. The former is often used for modeling coronal structures and the latter for prediction of coronal and interplanetary properties. To be brief, we call them, respectively, the central and left synoptic frames in what follows.
We compare the MDI synoptic chart with the KPNO and WSO synoptic charts in next section. The construction of the central and left synoptic frames and the effect of the different proxy of the global distribution of the photospheric magnetic field on the model coronal field are presented in Section 3.
The synoptic charts or the monthly-stable global distribution of the photospheric magnetic field have been routinely published by KPNO and WSO with grid spacing of 360x180 and 72x30, respectively. They have been widely used to model large-scale coronal structures, though some data gap must be existed due to the bad weather condition.
The MDI instrument on SOHO makes 2" full-disk observations of the photospheric field every 96 minutes. The high-cadence, high-quality MDI magnetograms provide a possibility to construct high-resolution synoptic chart without any data gap. The maps may be used to study the fine structures in the photospheric field and its extrapolation to the corona. Figure 1 displays the synoptic chart with grid spacing of 3240x1080 (top) and 720x360 (bottom) pixels.
By lowering its spatial resolution, the obtained lower-resolution MDI synoptic chart may be compared with the KPNO and WSO synoptic charts. The panels A and D in the top of Figure 2a and Figure 2b are the MDI and KPNO synoptic charts with grid spacing of 1 degree (360x180). The KNPO image has been reconverted to line-of-sight (Bl) from radial component (Br) by Br*COS(\latitude). The two images are saturated at +/- 100 Gausses. The white curves denote the polarity reversal at the spatial resolution of 5 degrees (see Panel B). Panels A and D show that the global polarity structures in MDI and KPNO maps are almost identical, implying that the zero point adjustment in both is consistent. However, the field strength in high latitude in KNPO map appears more homogeneous than what in MDI map. The cause of the difference is the method used to fill out the data at missing pixels. Panels B and E in the middle of Figure 2a and 2b show the difference of the large-scale magnetic structures in low resolution MDI and WSO synoptic charts. They are saturated at the ranges of +/- 5 Gauss and +/- 4 Gauss, respectively. Here the WSO data have been multiplied by 1.8 for the simple correction for the saturation effect in the 5250 A observations. The difference of the polarity (white) reversal lines between the two panels is quite big, suggesting the inconsistence of the zero point adjustment in data reduction. It is found that the average of WSO data over whole solar surface is 0.306477 (0.170265*1.8). Panels C and F in the bottom are obtained after adding 0.383096 (0.306477*5/4) to Panel B and subtracting 0.306477 from Panel E, respectively. The similarity between Panels B and F or between Panels E and C is much improved. Because of the consistence of the zero point adjustment between the MDI and KPNO maps the zero point adjustment in the WSO map is needed to be corrected. The comparison between MDI and WSO maps also shows that the WSO strength is about 2.25 (1.8*5/4) times lower than the low-resolution MDI strength.
In order to compare the magnetic strength among MDO, KPNO and WSO synoptic charts, scatter plots of MDI chart v.s. KPNO and WSO charts are analysed. Figure 3 displays the scatter plots between MDI and KPNO and between MDI and WSO synoptic charts. The consistence between MDI(72x30) and WSO (the bottom-left panel) appears better than others. Before discussion of the inconsistence shown in left column of Figure 3, the cause of the '+' shape structure in top-left panel must be understood. Figure 4 shows the scatter plot between the parts of MDI and KPNO synoptic charts, i.e., MDI(333x180) and KPNO(333x180). Here the longitude for KPNO is fixed from Carrington longitude of 13 to 346, but it is shifted for MDI relative to KPNO data, as shown at the top of each panel. Figure 4a indicates that the longitude or time shift may produce '+' shape structure in scatter plot between synoptic charts, though the '+' shape becomes smallest in the case of no shift. It suggests that the '+' shape may be caused by the data gap existed in KPNO data set and it could be smoothed out in lower resolution data. Figure 5 shows the consistence between KPNO(72x30) and WSO(72x30) and between MDI(72x30) and KPNO(72x30) synoptic charts when the lower-resolution KPNO data are divided by 1.6.
Figure 6 displays the histograms for MDI(360x180), KPNO(360x180), MDI(72x30) and WSO(72x30) synoptic charts. The similar shape of the distribution functions between MDI(360x180) and KPNO(360x180) and between MDI(72x30) and WSO(72x30) synoptic charts implies that the correction for KPNO and for WSO data found above is acceptable.
By combining the high cadence, high quality MDI magnetograms at the time of interest with the appropriate synoptic chart, the synoptic frame, or the proxy of the instantaneous global photospheric field, may be constructed magnetogram map (Zhao, Hoeksema and Scherrer, 1997). Figure 7a and Figure 7b show how to construct the central synoptic frame. Panels A and D are the two synoptic charts being used to obtain the new synoptic chart (Panel B) with its central longitude corresponding to the time of interest. The vertical solid line in Panel A denotes the time of interest: 1997:05:12_06h:54m:03s or CT1922:128. Panel B consists of the part of 0 -- 307 of Panel A and the part of 308 -- 359 of Panel D. The data in the area bordered by the dashed lines are replaced by the approapriate data in the full-disk magnetogram observed at the time of interest. Such obtained Panel E is the proxy of the global photospheric field distribution at the time of 1997:05:12_06h:54m:03s. The magnetic field in Panels A, D, B, and E is the observed line-of-sight component. It is usually assumed that the photospheric field is radial-dominated. The line-of-sight component can thus be converted to radial field, as shown in Panels C of Figure 7. The total flux of the radial field of Panel C may not be zero. To ensure the total magnetic flux over the whole solar surface being zero, the data outside the dashed-line-bordered area is adjusted. Panel F is the radial field distribution after adjustment.
Figure 8a and Figure 8b show how to construct the left synoptic frame. It is the same as Figure 7a and 7b but the time of interest is put at the place 60 degrees from the left side of the synoptic frame. It consists of the part of 68 -- 359 of the CR1922 chart and the part of 0 -- 67 of the CR1921 chart.
Extrapolating sych constructed global photospheric field into the corona using the potential field source-surface model, the foot points of open field lines and the neutral lines can be computed. What is the different effect of the central and left synoptic chart (CSC and LSC), the central and left synoptic frames (CSF and LSF), and the unseen-surface-adjustment central synoptic frame (CVS) on the model coronal magnetic field? Figure 9a displays different foot-point areas (dark regions) of the open field lines obtained by extrapolating the central synoptic chart and the central synoptic frame (Panel C and E of Figure 7). The difference occurs near the boundary of the foot-point areas. The left (right) column shows the field lines closed (open) in the case of CSC but open (closed) in the case of CSF. In other words, The west (east) part of open field region in the case of CSC is smaller (larger) than in the case of CSF. It is caused by different field distribution in the the dashed-line-bordered area. Figure 9b displays the different open field regions obtained using the central and left synoptic charts, showing the effect of the different data used mostly in the unseen solar surface. The number of the different field lines is even greater than the case of the different data in the visible surface. It suggests that using the central synoptic frame may be better than using left synoptic frame for modeling the evolution of coronal strutures. Figure 9c displays no different field lines when using the central synoptic frame and its adjusted version. The grid spacing used in the calculation is 72x30. More different field lines are expected to be existed as the grid spacing increases. This result suggests that the effect of the unseen-surface and whole-surface adjustments on the model coronal field is slight.
The polarity reversal lines or the polarity structures in MDI synoptic chart are the same as in KPNO synoptic chart, suggesting that the zero point adjustment is acceptable in the two data sets. To obtain a consistent scatter plot and similar histograms the KPNO (MDI) data set must be divided (multiplied) by a factor of 1.6. The small '+' shape ocuured in the scatter plot of MDI(360x180) v.s. KPNO(360x180) synoptic chart is caused by the time or longitude shift between the two sets. The shift may be produced by the data gap existed in the KPNO data set.
The low-resolution MDI synoptic chart, MDI(72x30), can match the observed WSO synoptic chart if the WSO synoptic chart is subtracted by its non-zero average. To obtain its histogram similar to the MDI(72x30) histogram the observed WSO data set need to be multiplied by factor of 2.25. This enlargement of the WSO data may be used to improve the prediction of the radial heliospheric magnetic field, better agreeing with the in situ observations at 1 AU.
The difference of the foot-point areas computed using the the central and left synoptic charts and the existense of many different field lines computed using the two sets suggests that the effect of the time variation of the photospheric field over half of solar rotation on the model coronal field can not be neglected. To model the evolution of the large-scale coronal structures it would be better to use the central synoptic frame as an input to coronal models.
The existense of the different field lines computed using the the synoptic frame and the synoptic chart suggests the significance of the effect of the shorter-time variation of the photspheric field on the model coronal field, though it is not obvious in the computed foot-point area of the open field lines.
Comparison of the prediction using various proxy of global distribution of the photospheric magnetic field with the location of coronal holes and heliospheric current sheet may further test the zero point adjustment and the scaling of the magnetic field strength mentioned above, and show the advantage and weakness of these proxy of global distribution of the photospheric magnetic field. The study is in progress.
We would thank
Zhao, X.P., Hoeksema, J.T. and Scherrer, P.H., 1999, J. Geophys. Res., 104, 9735.
