The First Michigan MURI Workshop, Ann Arbor, July 16, 2001.
The Comprehensive Solar-Terrestrial Enviroment Model (COSTEM) consists of a validated set of tightly-couped models describing various regions and/or processes from the Sun through the interplanetary medium to its interaction with the magnetosphere-ionosphere system. The Solar Coronal Model (SCM) describe the magnetic field and plasma in the near-solar region from the photosphere to the Alfven critical point where the magnetic field becomes radial due to the dominated radially pointed solar wind. The Inner Heliospheric Model (IHM) describe the magnetic field and plasma beyond the Alfven critical point.
We have developed a three-layer model of the solar magnetic field to extrapolate the rbserved photospheric magnetic field into the corona and the inner heliosphere (see Figure 0 ). The magnetic field in the solar atmosphere is divided into three layers by two spherical surfaces: the cusp surface and the source surface located, respectively, near the cusp point of coronal helmet streamers and the Alfven critical point. There are a global horizontal electric current flowing near the photosphere and the heliospheric current sheet beyond the cusp surface in the model. The magnetic field lines are assumed to be open over the cusp surface and radial beyond the source surface (Zhao and Hoeksema, 1995; Zhao, Hoeksema and Rich, 2001).
We will present the global distribution of the photospheric magnetic field based on the magnetic field data obtained on the Earth-side of the Sun in the next section. Section 3 displays two kinds of large-scale closed field regions below the cusp surface, that might be the candidate of the source of coronal mass ejections (CMEs). The radial variation of the coronal helmet streamer belt observed by the SOHO/LASCO from 2.5 solar radii to 20.0 solar radii is reproduced using the three-layer model in Section 4. Finally we reproduce the strength as well as the polarity of the interplanetary magnetic field (IMF) observed near the Earth.
To study the time variation of coronal structures over the scale of a day or less we need the instantaneous global distribution of the phtospheric magnetic field. A new type of Carrington synoptic map, the "synoptic frame" has been built up based on the magnetogram at the time of interest and the associated synoptic chart (Zhao, Hoeksema and Scherrer, 1997). Figure 1c explains how to construct the synoptic frame of 2001.05.30_03:12:30 using the magnetogram of 2001.05.30_03:12:30 (CR1976:50) (the bottom panel of Figure 1a) and the synoptic chart of CR1976 (the top panel of Figure 1b). The synoptic frame is used as the proxy of the instantaneous global distribution of the phtospheric magnetic field, and has been used to model the time variation of the coronal hole boundary (Zhao, Hoeksema and Scherrer, 2000), the SXT arcade (Zhao, Hoeksema and Scherrer, 2000), and to predict the IMF polarity and solar wind speed a few days in advance (Arge and Pizzo, 2000).
Coronal mass ejections (CMEs) are believed to be originated in closed field regions having free magnetic energy. Coronal helmet streamers observed in white light are such closed field regions and have been assumed to be the source region of CMEs (Hundhausen, 1993).
The helmet streamers occur between open field regions (coronal holes) having opposite magnetic polarity. Near sunspot minimum, all coronal open field regions occurr in polar regions. All closed field regions occur between north and south polar coronal holes. As sunspot activity increases, coronal holes occur at low latitude as well as high latitude, as shown in Figure 2a . In addition to helmet streamers that form the coronal streeamer belt or the heliospheric current sheet, there are large-scale closed field regions occured between coronal holes having like-polarity, as sketched in Figure 7.1 of Hundhausen's book (1972). Figure 2b shows the cycle change in the distribution of the two kinds of closed field regions from 1997 to 2000. The light blue arrows in the panel of CR1935 point the two kinds of closed field regions. Helmet streamers sandwitched between opposite-polarity open field regions contain odd number bipoles, and the another kind of large-scale closed field regions contain even number bipoles, occuring all activity phases except the minimum phase.
The top panel of Figure 3 shows the distribution of the 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.
We have shown that most of full-halo CMEs originate in closed field regions between opposite-polarity coronal holes under neutral lines. What is the function of the other kind of closed field region for the initiation of CMEs and for the evolution of coronal configuration?
SOHO/LASCO Carrington maps of the corona show the coronal helmet streamer belts between 2.5 and 30.0 solar radii, suggesting the radial variation in the shape of the streamer belts. This variation is associated with non-radial streamers at mid-latitudes. We reproduce the radial variation using the three-layer model and SOHO/MDI data. Figure 4 and Figure 5 show the computed neutral line (black lines) and observed helmet streamer belt 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.
Figure 6 shows the radial variation of the computed neutral lines during different phases of solar cycle.
There have been many studies that attempted to reproduc the structure of the heliospheric current sheet since the early eighties. There are only a few studies to predict the strength of the interplanetary magnetic field.
Figure 7 shows in situ observations of the radial component of the interplanetary magnetic field (IMF) during the year of 1996 (CR1918) and 1999 (1955). The black dots denote the daily mean of signed hour-average of the radial IMF. As shown in ealier papers (Wang snd SAheeley, 1993; Zhao and Hoeksema, 1995), the ambient radial IMF may be obtained by running average of the daily mean over 27 days (the green dots). A 5-day shift is used to map the observations neat 1 AU to the Alfven critical point. 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. It is assumed in the computation that there is no interaction between solar wind flow and the interplanetary magnetic field beyond the Alfven critical point. 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 8a and Figure 8b compare the prediction with observation for 25 years from 1976 to 2000 using WSO synoptic charts. The agreement between prediction and observation both in polarity and strength is pretty good. The agreement may be improved if using more accurate method of mapping rather than simply 5-day shift.
The high quality and high cadence MDI observations of the photospheric magnetic field provide an opportunity of constructing synoptic frames that may be used to produce the time variation of coronal structures over the scale of a day or less.
These predictions of magnetic fields in the corona and inner heliosphere may be used as the initial and/or boundary conditions for the Solar Coronal Model (SCM) and the Inner Heliospheric Model (IHM). The 96-minute synoptic frame may be used in modeling the evolution of large-scale coronal structures.
