In the Chapman and Ferraro [1931] model, the Earth's magnetosphere is closed, and is separated from the solar wind plasmas by a current sheet at the magnetopause. To explain the auroral convection, Dungey [1961] proposed a magnetic merging model producing an open magnetosphere that is accessible to the solar wind plasmas. Polar cap convection is driven by the interplanetary electric fields mapping along the open magnetic field lines to the ionosphere. For a purely southward IMF and no geomagnetic dipole tilt, the model predicts that the ionospheric convection pattern has two symmetric cells with antisunward flow across the central polar cap. A number of authors numerically estimated the polar cap convection by mapping the interplanetary electric fields to the ionosphere for various IMF orientations [e.g., Stern, 1973; Lyons, 1985; Toffoletto and Hill, 1989]. Mechanisms other than the merging that allow the entry of solar wind plasmas into the magnetosphere, include viscous interactions and plasma diffusion [e.g., Axford and Hines, 1961; Eastman et al., 1976]. They also drive the ionospheric convection, but do not provide observed cross polar cap potentials.
The speeds and the directions of the merged flux tube motions along the magnetopause surface are determined by both the magnetosheath plasma flow velocity and the tension of the magnetic field line [e.g., Cowley, 1982; Cowley and Owen, 1989]. Near the subsolar magnetopause, plasma bulk flow in the magnetosheath is very small. Therefore, the j × B force is the dominant term and both IMF By and Bz components have important affects on convection patterns. According to the antiparallel merging hypothesis [Crooker, 1979], dayside merging takes place at the low latitudes near the magnetic equator for negative IMF Bz and at the high latitudes, poleward of the magnetic cusp for positive Bz. In the northern (southern) hemisphere, the merging site shifts to the afternoon (morning) sector for positive IMF By, and vice versa. When IMF By > 0 and Bz < 0, newly merged flux tubes move dawnward (duskward) and tailward in the northern (southern) hemisphere. The resulting ionospheric convection patterns have two asymmetric cells [Heppner and Maynard, 1987]. These asymmetric convection patterns play important roles in creating the magnetic topology of theta auroras.
An issue remains regarding the degree to which the magnetopause is open or closed [e.g., Sonnerup et al., 1981; Eastman and Hones, 1979]. In fact, both conditions may exist simultaneously. The part of the magnetopause where magnetic field lines interconnected to the IMF have been convected is open; otherwise it is closed. Regions within the magnetosphere that map across the magnetopause are open; those that do not are closed. As long as the merging keeps supplying open flux tubes to a given region, it remains open. Reconnection in the tail terminates the extent of the open region. The location and size of merging lines are closely related to the solar wind conditions, such as the IMF orientation and shocked solar wind speed and dynamic pressure, etc., and the orientation of geomagnetic fields. It is likely that the magnetopause is either completely open or partly open and closed, depending on the geometry of the merging lines and the direction of the merged flux tube motion. It could also be completely closed if there were no solar wind conditions that favored merging. A strip of closed flux separating two open regions on the magnetopause surface, associated with a bifurcated polar cap, as proposed by Frank et al. [1982], remains a possibility. The location of the boundary between the open and closed magnetic field lines at any altitude is determined by the mapping of field lines. In the geomagnetic tail, one side of this boundary is the lobe and the other side is the distant plasma sheet. Another possible configuration occurs when only a small portion of the tail side of the magnetopause is open, and the distant plasma sheet expands to high latitudes. Magnetic field lines crossing the ionosphere at high latitudes could therefore map to this region. This configuration can be found during extended northward IMF intervals or during quiet conditions [Hones et al., 1989]. If the IMF By component is large, the distant plasma sheet expands more into the dusk (dawn) side of the lobe for positive (negative) By. The morphology of the highly contracted polar cap suggested by Meng [1981] and Murphree et al. [1982] is an example of this case.
Based on the above arguments, we propose a model of the theta auroras.
Figure 2 and Figure 3 illustrate two examples of theta auroral configurations discussed below.
A time sequence of the magnetopause and magnetosphere configurations in the northern hemisphere is shown from left to right.
Each column contains three sketches for the same time but with different views: from top to bottom, the dayside magnetopause as viewed from the Sun, the polar cap as viewed from above the north pole, and a cross-section of the magnetotail as viewed from the distant tail looking toward the Earth.
During a prolonged period of geomagnetic quiescence, the polar cap contracts and closed magnetic field lines threading the auroral oval and the boundary plasma sheet expand to high magnetic latitudes, as illustrated in Figures 2a and 3a.
Such configurations usually occur for northward IMF conditions when the merging site is at high latitudes, poleward of the cusp.
The ionospheric convection evolves into a four-cell pattern, with two lobe cells within the polar cap for IMF Bz 
By [e.g., Burke et al., 1979; Reiff and Burch, 1985] or a three-cell pattern with only one lobe cell for |By| Bz > 0 [e.g., Crooker, 1979; Reiff and Burch, 1985].
The two viscous-driven cells at the dawn and dusk edges of the polar cap are not shown in the middle panels of Figures 2a and 3a.
As IMF Bz turns negative and/or By changes significantly, the merging line(s) jumps closer to the equator and/or to the other side of the magnetic noon (see the top two panels of Figures 2b and 3b).
Newly merged magnetic flux tubes move along the magnetopause surface in directions determined by magnetic tension.
In the northern hemisphere, they move dawnward (duskward) for positive (negative) By, and vice versa for the southern hemisphere.
In the ionosphere, the convection of the recently opened flux tubes creates a new open region that previously was closed and mapped to the plasma sheet, as illustrated in the middle panels of Figures 2b and 3b.
Between the new open region and the original open region, a closed region remains that maps to the outer boundary of the plasma sheet in the tail (see the bottom panels of Figures 2b and 3b).
As moving newly opened flux tubes in the ionosphere fills the region equatorward of the auroral oval boundary, the closed flux tubes in the high latitude part of the oval become detached and shift poleward.
As long as the open flux continuously fills in the polar cap, the detached closed region shifts farther poleward (see the middle panels of Figures 2c and 3c).
The closed strip, therefore, shows an apparent drift in the direction of IMF By component.
This drift motion is much slower than the convection of the open fluxes.
The history of the poleward moving closed flux tubes ultimately depends on the evolving, merging driven convection pattern.
This in turn is determined by IMF and solar wind plasma conditions.
If the merging line(s) stays about the same, the closed fluxes will gradually join the oval and a polar cap with a totally open region will resume.
On the other hand, if the merging line(s) jumps back to higher latitude and/or to the other side of local noon as the IMF Bz turns northward and/or By changes sign again, the closed flux remains and adjusts to the new convection that results in a polar cap consisting of two open lobes separated by a strip of closed field lines, as shown in Figures 2d and 3d.
This is similar to the polar cap model of Frank et al. [1982] for theta auroras.
The closed field line region bifurcates the two open-field lobes, and maps to the boundary plasma sheet, as shown in the bottom panel of Figures 2d and 3d.
This transient behavior can last for a long period of time and appears to be quasi-stationary, as long as the sequence repeats.
If the IMF remains persistently northward, polar cap configuration becomes similar to that suggested by Kan and Burke [1985].
Otherwise the polar cap eventually returns to one of its normal states, contracted in geomagnetically quiet times and expanded in active times.
For certain IMF configurations, such as positive Bz with |By| Bz, the auroral oval can expand to high magnetic latitudes, resulting in the polar cap morphology described by Meng [1981] and Murphree et al. [1982].
Having the magnetic topology of the theta aurora is not enough to have a visible transpolar arc. A sufficient flux of energetic electrons must precipitate and excite enough atoms in the ionosphere to produce visible emissions. According to the Liouville theorem, electrons at the low altitude have the same distribution as in the high altitude source region. The denser or more energetic the electrons precipitating from the boundary plasma sheet that magnetically connects to the transpolar arc, the more luminous the arc will be.
Please send questions, comments, or suggestions about the paper to:
Shen-Wu Chang
Department of Physics and Astronomy, The University of Iowa, Iowa City, IA 52242
Phone:(319)335-3828; Fax:(319)335-1753;
swc@space-theory.physics.uiowa.edu