Solar concept of flux transport by interchange reconnection applied to the magnetosphere

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi: /2008ja013140, 2008 Solar concept of flux transport by interchange reconnection applied to the magnetosphere V. G. Merkin 1 and N. U. Crooker 1 Received 3 March 2008; revised 6 May 2008; accepted 3 June 2008; published 8 August [1] The traditional concept of steady state convection of magnetic field-line foot points in Earth s ionosphere driven by reconnection between the interplanetary and geomagnetic fields implies that those foot points follow closed contours of circulation. Remote reconnection that occurs when the foot points cross the polar cap boundary controls whether the field lines are open or closed, but the foot points remain firmly rooted to their paths around the closed circulation cells. In steady state MHD models, however, this concept of convection breaks down owing to interchange reconnection between open and closed field lines. In the solar heliospheric community, interchange reconnection has long been understood as a means of flux transport. In the magnetosphere, flux transport by interchange reconnection causes field-line foot points to jump, or saltate, from one side of the polar cap to the other as part of the steady state circulation. We develop a definitive method for identifying interchange reconnection in an MHD model and illustrate the resultant foot point saltation. Citation: Merkin, V. G., and N. U. Crooker (2008), Solar concept of flux transport by interchange reconnection applied to the magnetosphere, J. Geophys. Res., 113,, doi: /2008ja Introduction 1 Center for Space Physics, Boston University, Boston, Massachusetts USA. Copyright 2008 by the American Geophysical Union /08/2008JA [2] The term interchange reconnection means reconnection between an open and a closed field line, as illustrated in Figure 1a where the closed field is a loop with both feet rooted in the Sun. The term was introduced by Crooker et al. [2002] in the course of describing how closed loops in interplanetary coronal mass ejections become open through reconnection with open fields back at the Sun. Closed loops interchange locations in the process, in this case between the heliosphere and the solar atmosphere. In Figure 1a, interchange reconnection at the gray arrows opens the large loop on the right and creates a small loop on the left. Well before it was named, however, interchange reconnection was widely called upon as an explanation for a number of solar processes: the release of plasma from closed loops, for example, in polar jets [Shibata et al., 1992] and at the tips of helmet streamers [Wang et al., 1998, 2000]; the release of energetic particles [e.g., Reames, 2002]; and transport of the feet of open field lines at coronal hole boundaries to maintain their rigid rotation on the differentially rotating solar surface [e.g., Nash et al., 1988; Wang and Sheeley, 1993]. More recently, interchange reconnection has been invoked as a necessary step in the evolution of the solar magnetic field in the course of the solar cycle [e.g., Wang and Sheeley, 2003, 2004] and as the process responsible for mismatches between true polarity reversals and local magnetic field reversals in the heliosphere at sector boundaries [Crooker et al., 2004]. [3] In the model of global circulation of solar fields developed by Fisk [1996], Fisk et al. [1999], and Fisk and Schwadron [2001], interchange reconnection between loops and open fields occurs everywhere on the Sun as a means of open flux transport and dominates transport at low heliomagnetic latitudes where loops are large. Figure 1a illustrates open flux transport from point 1 to point 2 as a consequence of interchange reconnection. The open field line rooted at point 1 interchanges foot points with the far end of the closed loop rooted at point 2. The larger the loop, the greater the distance over which interchange reconnection transports the open field line. Owens et al. [2007] go so far as to suggest that systematic open flux transport by interchange reconnection with the large loops constituting coronal mass ejections may be the means by which the polarity of the polar coronal holes reverses in the course of the solar cycle. [4] In contrast to its wide application in solar and heliospheric physics, until recently interchange reconnection has not been invoked for magnetospheric processes. It has no place in the traditional sequence of reconnection thought to drive magnetospheric convection, where an open geomagnetic field line reconnects only with another of its kind. This is true even in the conceptual models of reconnection poleward of the cusps for northward interplanetary magnetic field (IMF), which afford opportunity for a wider range of reconnection geometries [e.g., Cowley, 1983; Crooker, 1992]. The first instances of interchange reconnection in an MHD simulation of the magnetosphere were reported independently by Tanaka [1999] and by Siscoe and Siebert 1of9

2 Figure 1. Interchange reconnection (a) on the Sun and (b) in the magnetosphere. In each case an open field line reconnects with a closed field line at the gray arrows, transporting the foot point of the open field line from point 1 to point 2. The dashed lines indicate topologies after reconnection. [2003]. They pointed out the occurrence of reconnection between open and closed fields on the flanks of the magnetosphere for simulations in which the IMF had equal northward and east-west components. Watanabe et al. [2004] further analyzed the consequences of reconnection between open and closed fields in the MHD model of Tanaka [1999] and, subsequently, in a model developed at the University of Michigan for northward IMF at solstice [Watanabe et al., 2005]. In both papers, Watanabe et al. [2004, 2005] use conceptual models to explain how reconnection between open and closed fields affects a transport of open flux. In subsequent work, Watanabe et al. [2007] and Watanabe and Sofko [2008] develop these conceptual models in a rigorous way, substantially building upon a long history of null-separator and current-penetration models [e.g., Cowley, 1973; Alekseyev and Belen kaya, 1983; Siscoe, 1988; Crooker et al., 1990; Siscoe et al., 2001], to demonstrate how interchange reconnection, although not by that name, fits into the larger context of familiar reconnection geometries. In particular, they show how the sites of the various types of reconnection on the magnetopause and in the magnetotail map down to the ionosphere. Mapping options for interchange reconnection are numerous and can affect the ionospheric convection pattern in many ways. What controls these options, beyond IMF orientation, is still not understood. [5] Figure 1b illustrates the topology of interchange reconnection in the MHD and conceptual models of the magnetosphere discussed above. Gray arrows mark the interchange reconnection site poleward of the southern cusp. The history of the open field line participating in the interchange reconnection deserves special mention because it departs from expectations for northward IMF discussed as far back as 1963 [Dungey, 1963; Cowley, 1983; Crooker, 1992]. As illustrated by Tanaka [1999] and Watanabe et al. [2004] (and described further in section 2), the field line was not generated by reconnection poleward of the cusp in the Northern Hemisphere, as proposed in the older studies, but rather by reconnection equatorward of the cusp in the Southern Hemisphere, just upstream from the interchange reconnection site on the flanks, where the geocentric solar magnetospheric (GSM) y components of the reconnecting fields are antiparallel (note, the GSM coordinate system is used throughout the paper). In the projection onto the noon midnight meridian plane in Figure 1b, what looks like an overdraped configuration for the open field line results not from what originally was the IMF end of the field line draped over the magnetopause but rather what was originally the geomagnetic end, lying inside the magnetopause. The closed field line that reconnects with the IMF in this projection is on the dayside, not the nightside. It is similar to the dashed dayside field line that forms after interchange reconnection but lies in a different plane. Reconnection poleward of the cusp does occur in the cited simulations but, apparently, only on open tail lobe field lines that feed into the lobe-cell circulation confined to the polar cap. Reconnection poleward of the cusp on nightside closed field lines, as first drawn by Dungey [1963], may be restricted to configurations with strong dipole tilt [e.g., Crooker, 1992; Watanabe et al., 2005, 2006]. The nightside closed field line in Figure 1b participates in interchange reconnection, as shown. Watanabe et al. [2007] and Watanabe and Sofko [2008] describe how the interchange reconnection sequence in Figure 1b and its counterpart in the Northern Hemisphere both occur in three dimensions as part of a steady state circulation pattern. [6] As in Figure 1a, the interchange reconnection in Figure 1b transports the foot point of the open field line from point 1 to point 2. These points can be widely separated. In Figure 1b transport is from the dayside to the nightside of the polar cap. At the same time, the closed loop on the nightside that was rooted at point 2 becomes a closed loop on the dayside rooted at point 1. Thus, the form of flux transport driven by interchange reconnection is considerably different from what is usually envisioned for the magnetosphere. Instead of flowing from one location to another, foot points jump from one location to another. The formal name for this kind of transport is saltation, as 2of9

3 ionosphere that jump from the dayside to the nightside of the polar cap, as shown in Figure 1b. Figure 2. Ionospheric convection pattern in the Northern Hemisphere simulated by the LFM model for the 45 IMF clock angle simulation. In both plots thin solid black lines represent electrostatic potential isocontours, while the thick black dotted line depicts the open-closed boundary. The contours of constant colatitude are separated by 10. The (a) electrostatic potential and (b) total parallel potential drop along the field line traced from the center of the grid cell are color coded. The parallel potential drop is obtained by integrating the electric field along the magnetic field lines upward from the Northern Hemisphere. commonly used in geology to describe the leaping motion of sand carried by wind or pebbles carried by water. [7] Magnetic foot point saltation is the focus of this paper. That it can be part of steady state convection in the magnetosphere was first recognized by Watanabe et al. [2004] in the context of explaining convection patterns for northward IMF. Here we expand upon their work, pointing out that foot point saltation follows from application of the solar concept of interchange reconnection, thus recognizing that interchange reconnection is a universal process. We develop a method for identifying magnetic foot point saltation in an MHD model, specifically, in the Lyon- Fedder-Mobarry (LFM) global MHD model [Lyon et al., 2004]. We show that magnetic field lines advecting smoothly antisunward in the solar wind can have foot points in the 2. Identifying Interchange Reconnection in the LFM Model [8] In this section we present results of an idealized LFM model simulation run with steady IMF and solar wind plasma parameters. In this simulation, the dipole tilt was set to zero, the solar wind velocity had only one component, Vx = 400 km/s, and the IMF had two components, By = 3.5 nt and Bz = 3.5 nt. The simulation was run long enough (a few hours) for the magnetosphere to reach a quasi-steady configuration. The result is the classical ionospheric convection pattern for an IMF jbyj jbzj configuration. Most of the signatures of this pattern in the LFM simulation are similar to the work of Tanaka [1999]. Here we are concerned with one particular signature, interchange reconnection, as discussed in section 1. [9] Figure 2a depicts a snapshot of the simulated ionospheric convection pattern in the Northern Hemisphere. The convection pattern exhibits the main features of a negative By-driven configuration, with a round (positive-potential) cell occupying a major part of the polar cap and a crescent (negative-potential) cell on the duskside. The open-closed boundary is indicated by the set of black dots On Dayside Reconnection [10] It is instructive for understanding dayside reconnection in the LFM simulation to follow the convection path of the ionospheric foot point of a particular magnetic field line in one hemisphere starting from its return motion from the tail along the flanks of the magnetosphere. We will consider only closed field lines that feed into the dayside reconnection site, excluding those populating the lobe cell, which circulates wholly within the volume of open field lines that constitute the polar cap. The dayside reconnection of such high-latitude field lines has been described elsewhere [e.g., Crooker et al., 1998; Tanaka, 1999] and will not be addressed here. We use the fact that the motion of the foot point of the field line in the opposite hemisphere can be readily envisioned by observing its motion in the opposite cell in the same hemisphere mirrored about the x axis (the noon midnight meridian). For instance, consider points marked 1, 2, and 3 in Figure 2a. These are the Northern Hemisphere foot points of a closed field line convecting sunward in the dawnside, round, positive-potential cell. By symmetry, points 1 0,2 0, and 3 0 represent the motion of the opposite ends of field lines 1, 2, and 3 in the dawnside, crescent, positive-potential cell in the Southern Hemisphere. When the field line reaches the flow reversal boundary (points 3 and 3 0, respectively) the flow reverses in both cells, but soon after that the flow in the positive cell reverses its direction again (point 4). In the region between points 4 and 5 (and later) the plasma in the round cell moves in the direction opposite to that of plasma in the crescent cell would convect (points 4 0 and 5 0 are not shown for reasons explained below). This conflict leads to behavior of the simulated plasma which is different from the one reported by Tanaka [1999]. It is clear from Figure 2a that points 3, 4, and 5 lie close to the open-closed boundary. Figure 2b 3of9

4 Figure 3. Schematic drawing of the dayside reconnection leading to the formation of the round cell in both hemispheres. Two scenarios are shown: the one with the X line in the (top) Southern Hemisphere and in the (bottom) Northern Hemisphere. The geometry of field lines is not to scale. The drawings on the left show a closed field line and an IMF field line just before reconnection. The closed field line has one end in the Northern Hemisphere round cell and the other end in the Southern Hemisphere round cell. The thick black circle represents the ionosphere. The drawings on the right show the two open field lines formed after reconnection. For the field lines of type A the ionospheric foot point lies in the same hemisphere as the X line, while for type B field lines the ionospheric foot point lies in the opposite hemisphere. The inset (top, right) shows the orientation of the GSM coordinate system axes along with the IMF direction, the solar wind speed, and the resulting direction of the solar electric field, based on ideal Ohm s law. The direction of the h axis (see Figure 4) is also shown in the lower right corner of Figure 3 (top). demonstrates that field lines traced from these points pass through the diffusion region in the vicinity of the magnetopause, which is indicated by the magnitude of the total (numerical) parallel potential drop along the field line comparable to the electrostatic potential at the foot point of the field line. The effect of this parallel potential drop is that field lines traced from regions 3, 4, and 5 no longer map to points with the same potential in the crescent cell in the opposite hemisphere (this is the reason we do not show points 4 0 and 5 0 ). The ends of these field lines (those that would have been found at points 4 0 and 5 0 on the same equipotential with points 1 0,2 0, and 3 0 had there been no parallel potential drop) slip from the crescent cell to the same (3, 4, and 5) region in the round cell (having the opposite potential) in the opposite hemisphere. Thus, by the time a plasma element convecting beyond point 5 reaches the open-closed boundary, it is connected to a diagonal field line having its foot points in the round cell in both hemispheres. [11] Figure 3 shows a schematic of the subsequent reconnection process. Scenario 1 shows that the reconnection line forms in the Southern Hemisphere. The picture on the left shows the situation before reconnection between a closed field line and an IMF line. Here the closed diagonal field line is formed from a regular dipolar field line connected to the round cell in the Northern Hemisphere and returning from the tail along the dawnside (note that by the time the closed field line participates in reconnection, it is skewed to the duskside). Correspondingly, the picture on the right shows the two open field lines formed after reconnection. Similar to the picture discussed by Tanaka [1999], two types of open field lines are formed (denoted A and B on the right drawing in Figure 3 (top right)): one with its ionospheric foot point lying in the same hemisphere as the X point (A), and one with its ionospheric foot point lying in the opposite hemisphere (B). Note that the symmetry of the problem demands that there exists an identical situation when the reconnection line forms in the Northern Hemisphere. 4of9

5 In such a situation (see Figure 3, bottom), symmetrically identical to the one depicted in Figure 3 (top), the diagonal field line is formed from a field line originally connected to the round cell in the Southern Hemisphere and the crescent cell in the Northern Hemisphere and returning from the tail along the duskside. In this case, a type B open field line would be connected to the IMF in the Northern Hemisphere, while a type A open field line would be connected to the IMF in the Southern Hemisphere. Field lines of type B subsequently participate in interchange reconnection (see section 2.2) in agreement with results of Tanaka [1999]. [12] As already noted, the dayside reconnection picture described above is similar to the one discussed by Tanaka [1999]. However, there is one important difference: only closed field lines, connected to the round cells in both hemispheres, reconnect with the IMF. This has an important implication for the formation of the ionospheric convection pattern; that is, the crescent cells are not formed by reconnection with the IMF. We shall show in section 2.2 that the subject of the crescent cell formation is closely related to the process of interchange reconnection Interchange Reconnection and Crescent Cell Formation [13] We seek a definitive way to demonstrate the existence of the process of interchange reconnection in the simulation. This process invokes reconnection of open field lines, having one end in the solar wind and the other one in the ionosphere, with closed geomagnetic field lines. For flux to be transported by the process of interchange reconnection, the foot point of the closed field line must be spatially separated from the ionospheric foot point of the open field line with which it reconnects. The idealized geometry of our simulation results in the solar wind ends of open field lines being dragged along straight lines parallel to the y = z plane. If such a field line participates in interchange reconnection, its uniform motion in the solar wind will be accompanied by a jump of its ionospheric foot point. In order to verify that this effect does take place in the simulation, we have developed the following technique. We populate the polar cap (the region of open field lines) with points distributed uniformly in the polar (0.3 separation) and azimuthal angle (2 separation). Then we trace magnetic field lines from these foot points to the solar wind. All field lines originating in the northern polar cap trace to the southern hemispace. We trace the field lines beyond the z = 75 R E plane to ensure that their solar wind ends lie beyond the bow shock and travel uniformly antisunward. Finally, we plot a color map of x and y coordinates of the ionospheric foot points of a given field line as a function of this field line s coordinates in the solar wind. [14] The result of this procedure is demonstrated in Figure 4. The two plots show where a field line with given coordinates in the ionosphere maps in the solar wind. In both of these plots the horizontal axis corresponds to the GSM x axis and the vertical axis marks the distance from the y = z plane (see Figure 3 (bottom right) for the orientation of the h axis). The color coding in these plots corresponds to coordinates of the ionospheric foot point of a given field line; the x coordinate for the upper plot, and the y coordinate for the lower one. The small inset plots indicate where a particular field line originates in the ionosphere. [15] Using the plots in Figure 4, one can follow the convection path of the ionospheric foot point of a given field line by making a cut along the x axis and observing how colors change as the solar wind end convects from right to left (antisunward). Such a diagnostic is possible because deep into the solar wind the plasma velocity has only an x component because of the boundary conditions, so a cut along the x axis gives the time history of a particular field line for a steady state configuration. Close examination of these plots shows that most field lines with h > 0 convect smoothly in the ionosphere on closed paths: these are the field lines populating the lobe cell. The ragged upper boundary of the h > 0 region corresponds to field lines convecting very close to the center of the round cell in the ionosphere. The more interesting region is populated with field lines closer to the h = 0 axis and, especially, the h <0 region. Close examination of both Figure 4 and Figure 2a confirms that the crescent cell is not formed by reconnection of the IMF with closed field lines. Open field lines formed by reconnection with the IMF are only those that first appear at the rightmost boundary of the open field line region depicted in Figure 4. It is easy to see that open field lines in the crescent cell are not formed at this boundary by noting that no yellow points appear there in the y coordinate plot (Figure 4, bottom). Rather, the fairly narrow region of yellow color lies near the x axis between approximately 50 and 100 R E. It is this region that maps to the dayside boundary of the crescent cell in the ionosphere, as can be seen by comparing the ionospheric inset to Figure 2a. Therefore, these open field lines are suddenly born inside the open field line region in the solar wind, not at its boundary with the IMF. This is exactly the kind of situation that is expected to occur if interchange reconnection takes place. [16] We can gain more insight into this process by examining the h < 0 portion of the open field line region depicted in Figure 4. This region is characterized by field lines whose ionospheric ends jump between two spatially separated regions while their solar wind ends convect uniformly antisunward, as indicated by the discontinuity in color (Figure 4, top). The rightmost portion of the h <0 region is yellow-orange while the left portion of the region, lying farther along the antisunward direction, is mostly dark blue. The small inset plot shows that the foot points of these field lines in the ionosphere are spatially separated. In fact, they lie on opposite sides of the polar cap. [17] The definitiveness of our conclusion about the existence of interchange reconnection in the simulation is hampered by the fact that the solar wind ends of field lines traced from points distributed uniformly (in polar and azimuthal angles) in the ionosphere are not distributed uniformly in the solar wind, as Figure 4 clearly demonstrates. Thus, the region that we identified as the one of most interest to us (h < 0) is obviously undersampled. In order to overcome this difficulty, we apply, essentially, the inversion of the original technique in just this region. That is, we now uniformly distribute points in the h < 0 part of the h-x plane in the solar wind and trace field lines from there all the way to the ionosphere. The result is shown in Figure 5. Figure 5 (left) shows the map of the solar wind ends of the field lines selected for tracing from the h <0 domain, while Figure 5 (right) shows the map of the 5of9

6 Figure 4. The image of the polar cap in the solar wind. Each point marked with a cross on both plots corresponds to a single field line traced from a given foot point in the Northern Hemisphere. The crosses are colored according to the coordinates of the ionospheric foot point: the x coordinate on the upper plot, and the y coordinate on the lower plot. The small inset plots show the polar cap color on the basis of the same principle. Thus, by matching the color of a given field line in the solar wind and the polar cap one can identify where the field line originates in the ionosphere. The vertical axis on both plots shows the distance from the y = z plane (see Figure 3 for details). corresponding ionospheric ends. For this tracing, the points with x > 0 in the ionosphere are green and those with x <0 in the ionosphere are red. Figure 5 (left) clearly shows that these points form contiguous regions in the solar wind, while Figure 5 (right) clearly shows that their foot points in the ionosphere are spatially separated. The transition from the green to the red region as the solar wind end of the field line convects uniformly antisunward demonstrates unambiguously that the ionospheric foot points saltate from the dayside to the nightside of the polar cap. Since saltation is a defining property of interchange reconnection, we have thus demonstrated that it takes place in the LFM simulation. [18] An important remark is in order here. Although the spacing between points of both colors in Figure 5 (left) is smaller than the grid cell size of our simulation in the region shown, it has no effect on our conclusion about the field line foot point saltation. This conclusion is still valid, but only to within the simulation code resolution. In other words, Figure 5 demonstrates that field lines traced from two contiguous grid cells on either sides of the red-green boundary on the left will trace to the spatially separated green and red regions in the ionosphere depicted on the right. 3. Discussion [19] In the course of demonstrating foot point saltation by interchange reconnection in the LFM model, we have shown that for an IMF with equal northward and dawnward ( y) components, the crescent cell in the usual two-cell convection pattern is not formed by reconnection with the IMF, as is usually assumed. Instead, our diagnostic plots in Figure 4 indicate that the open field lines feeding the crescent cell are suddenly born within rather than at the boundary of the bundle of open field lines extending into the solar wind, a clear signature of interchange reconnection. This result is consistent with the conceptual model of Watanabe et al. [2004] and Watanabe and Sofko [2008], who call this crescent cell the secondary exchange cell, where open field lines are introduced by interchange reconnection and closed field lines are formed by the usual nightside reconnection between open field lines. 6of9

7 Figure 5. (left) The h < 0 portion of the polar cap image in the solar wind as depicted in Figure 4. Here the field lines are traced from points distributed uniformly in the solar wind along the x and h axes (note that only points from which the field lines are successfully traced to the ionosphere are shown, which results in gaps between some of the points). (right) Foot points of these field lines in the northern polar cap. The field lines marked by the red and green crosses originate on the opposite side of the polar cap but map into adjacent regions in the solar wind. [20] The model of Watanabe et al. [2004] and Watanabe and Sofko [2008] also contains a complementary primary exchange cell, where field lines open by the usual IMF reconnection with closed field lines and closed field lines are introduced by the same interchange reconnection that transports open field lines across the polar cap. Thus, their two exchange cells accommodate the simultaneous open and closed flux transport affected by interchange reconnection, as illustrated in Figure 1. Their primary exchange cell is a crescent cell located on the side of the round cell opposite the secondary exchange cell and more toward the dayside. This cell is not apparent, however, in the LFM convection pattern (Figure 2 or Figure 5), where it should appear on the dawnside of the round cell. The parallel electric fields there and resultant field-line slippage discussed in section 2.1 may prevent its formation or preclude its detection. The convection contours in Figure 5 (right), however, suggest that the green open foot points sweep duskward across the dayside of the polar cap close to the boundary and interchange reconnect on the duskside rather than dawnside of the polar cap. This may still be consistent with the conceptual model, since Watanabe and Sofko [2008] point out that the location of interchange reconnection as mapped to the ionosphere along the polar cap boundary can be highly variable, as can the strength of the convection cell that accommodates it. For example, for an IMF with only a y component, Watanabe et al. [2007] describe how a convection cell associated with interchange reconnection can be embedded within the usual crescent cell driven by reconnection with the IMF. The resultant potential is reduced relative to the potential in the conjugate round cell, thus accounting for the difference in potential between the round and crescent cells in the LFM code reported by Crooker et al. [1998]. [21] We note that the interchange reconnection in the primary and secondary exchange cells of Watanabe et al. [2004] and Watanabe and Sofko [2008] may be associated with the unusual equatorward protrusions of the polar cap boundary in the postnoon and premidnight sectors, respectively, as can be seen in Figure 2 and Figure 5. Because the size of these features is comparable to the LFM ionospheric grid resolution, however, we refrain from making any further statements about them. [22] The occurrence of flux transport by interchange reconnection in the magnetosphere raises the question of what transport problem the magnetosphere is solving by this process. In the model of Watanabe et al. [2004], some overdraped field lines form so far down the flank by reconnection with the IMF that they are carried antisunward along the side of the magnetosphere opposite to the bulk of reconnecting fields and thus require transport by interchange reconnection to the other side in the primary exchange cell. This does not appear to be happening in the LFM model presented here. The open flux transport by saltation is primarily from day to night. Figure 5 (right) shows that the green foot points, having been swept from dawn to dusk along the polar cap boundary, saltate to become the red foot points, which are poised to form closed field lines along the length of the nightside polar cap boundary through usual nightside reconnection. Why the green foot points are apparently forced to saltate instead of flow is not clear. [23] What seems like an obvious need for magnetic foot point saltation in the magnetosphere is the dawn dusk movement of the bar in the theta aurora configuration observed during periods of northward IMF when the y component of the IMF is reversing [e.g., Craven et al., 1991]. The bar is a sun-aligned band of aurora that apparently completely spans the usual ring of aurora encircling the polar cap [Frank et al., 1982, 1986]. Particle measurements suggest that the bar occurs on closed field lines, thus bifurcating the polar cap into two separate volumes of open 7of9

8 field lines [e.g., Frank et al., 1986]. Although a contested point [e.g., Lyons, 1985], if true, then the transport of open fields from one volume to the other, as required by the change in volume sizes in response to a changing By, could only be accomplished by field-line saltation over the bar through interchange reconnection. The alternative, convection across the bar and the reconnection it would require, would be inconsistent with the bar-aligned, sunward flows observed there. Watanabe and Sofko [2008] address theta aurora formation with their conceptual model but stop short of splitting the polar cap into two volumes and calling upon interchange reconnection to transport flux. Doing so is far from trivial, however, in the context of the necessarily complicated reconnection geometry of their comprehensive model. 4. Conclusions [24] We have demonstrated that in the LFM MHD model, under steady state conditions, the foot points of open magnetic field lines moving uniformly antisunward in the solar wind can jump, or saltate, between widely separated locations in the ionosphere like grains of sand in the wind. This pattern is contrary to usual expectations that foot points circulate like a fluid in closed convection cells. The foot point saltation is driven by reconnection between overdraped lobe field lines and closed field lines along the flanks of the magnetosphere, as originally proposed by Tanaka [1999] and Watanabe et al. [2004]. We point out that this process is interchange reconnection, a process widely called upon in solar and heliospheric physics as a means of flux transport by foot point saltation, among other properties. That interchange reconnection has been identified in the magnetosphere, as well, classifies it as a universal heliophysical process. [25] Acknowledgments. We thank G. L. Siscoe for suggesting saltation as the appropriate word for magnetic foot point transport driven by interchange reconnection. We also thank J. G. Lyon for providing us with the LFM model simulation data as well as reading the manuscript and providing valuable comments. V.G.M. thanks W. J. Hughes for proofreading the manuscript and suggesting important corrections. This research was supported by the National Science Foundation Agreement ATM , which funds the CISM project of the STC program, with additional support from NSF grant ATM [26] Amitava Bhattacharjee thanks the reviewers for their assistance in evaluating this paper. References Alekseyev, I. I., and E. S. Belen kaya (1983), Electric field in an open model of the magnetosphere, Geomagn. Aeron., 23, Cowley, S. W. H. (1973), A qualitative study of the reconnection between the Earth s magnetic field and an interplanetary field of arbitrary orientation, Radio Sci., 8, , doi: /rs008i011p Cowley, S. W. H. (1983), Interpretation of observed relations between solar wind characteristics and effects at ionospheric altitudes, in High Latitude Space Plasma Physics, edited by B. Hultqvist and T. Hagfors, pp , Springer, New York. Craven, J. D., J. S. Murphree, L. A. Frank, and L. L. Cogger (1991), Simultaneous observations of transpolar arcs in the two polar caps, Geophys. Res. Lett., 18, , doi: /91gl Crooker, N. U. (1992), Reverse convection, J. Geophys. Res., 97, 19,363 19,372, doi: /92ja Crooker, N. U., G. L. Siscoe, and F. R. Toffoletto (1990), A tangent subsolar merging line, J. Geophys. Res., 95, , doi: / JA095iA04p Crooker, N. U., J. G. Lyon, and J. A. Fedder (1998), MHD model merging with IMF B y : Lobe cells, sunward polar cap convection, and overdraped lobes, J. Geophys. Res., 103, Crooker, N. U., J. T. Gosling, and S. W. Kahler (2002), Reducing heliospheric magnetic flux from coronal mass ejections without disconnection, J. Geophys. Res., 107(A2), 1028, doi: /2001ja Crooker, N. U., S. W. Kahler, D. E. Larson, and R. P. Lin (2004), Largescale magnetic field inversions at sector boundaries, J. Geophys. Res., 109, A03108, doi: /2003ja Dungey, J. W. (1963), The structure of the exosphere or adventures in velocity space, in Geophysics: The Earth s Environment, edited by C. DeWitt, J. Hieblot, and A. Lebeau, pp , Gordon and Breach, New York. Fisk, L. A. (1996), Motion of the footpoints of heliospheric magnetic field lines at the Sun: Implications for recurrent energetic particle events at high heliographic latitudes, J. Geophys. Res., 101, 15,547 15,553, doi: /96ja Fisk, L. A., and N. A. Schwadron (2001), The behavior of the open magnetic field of the Sun, Astrophys. J., 560, , doi: / Fisk, L. A., T. H. Zurbuchen, and N. A. Schwadron (1999), On the coronal magnetic field: Consequences of large-scale motion, Astrophys. J., 521, , doi: / Frank, L. A., J. D. Craven, J. L. Burch, and J. D. Winningham (1982), Polar views of the Earth s aurora with Dynamics Explorer, Geophys. Res. Lett., 9, , doi: /gl009i009p Frank, L. A., et al. (1986), The theta aurora, J. Geophys. Res., 91, , doi: /ja091ia03p Lyon, J. G., J. A. Fedder, and C. M. Mobarry (2004), The Lyon-Fedder- Mobarry (LFM) global MHD magnetospheric simulation code, J. Atmos. Sol. Terr. Phys., 66, , doi: /j.jastp Lyons, L. R. (1985), A simple model for polar cap convection patterns and generation of q auroras, J. Geophys. Res., 90, , doi: / JA090iA02p Nash, A. G., Jr., N. R. Sheeley, and Y. -M. Wang (1988), Mechanisms for the rigid rotation of coronal holes, Sol. Phys., 117, , doi: /bf Owens, M. J., N. A. Schwadron, N. U. Crooker, W. J. Hughes, and H. E. Spence (2007), Role of coronal mass ejections in the heliospheric Hale cycle, Geophys. Res. Lett., 34, L06104, doi: /2006gl Reames, D. V. (2002), Magnetic topology of impulsive and gradual solar energetic particle events, Astrophys. J., 571, L63 L66, doi: / Shibata, K., et al. (1992), Observations of X-ray jets with the YOHKOH soft X-ray telescope, Publ. Astron. Soc. Pac., 44, L173 L179. Siscoe, G. L. (1988), The magnetospheric boundary, in Physics of Space Plasmas (1987), edited by T. Chang, G. B. Crew, and J. R. Jasperse, pp. 3 78, Scientific, Cambridge, Mass. Siscoe, G. L., and K. D. Siebert (2003), Local boundary layer properties from non-local processes illustrated by MHD simulations, in Earth s Low-Latitude Boundary Layer, Geophys. Monogr. Ser., vol. 133, edited by P. T. Newell and T. Onsager, pp , AGU, Washington, D. C. Siscoe, G. L., G. M. Erickson, B. U. Ö. Sonnerup, N. C. Maynard, K. D. Siebert, D. R. Weimer, and W. W. White (2001), Global role of E 2 in magnetopause reconnection: An explicit demonstration, J. Geophys. Res., 106, 13,015 13,022, doi: /2000ja Tanaka, T. (1999), Configuration of the magnetosphere-ionosphere convection system under northward IMF conditions with nonzero IMF B y, J. Geophys. Res., 104, 14,683 14,690, doi: /1999ja Wang, Y.-M., and N. R. Sheeley Jr. (1993), Understanding the rotation of coronal holes, Astrophys. J., 414, , doi: / Wang, Y.-M., and N. R. Sheeley Jr. (2003), On the topological evolution of the coronal magnetic field during the solar cycle, Astrophys. J., 599, , doi: / Wang, Y.-M., and N. R. Sheeley Jr. (2004), Foot point switching and the evolution of coronal holes, Astrophys. J., 612, , doi: / Wang, Y.-M., N. R. Sheeley Jr., J. H. Walters, G. E. Brueckner, R. A. Howard, D. J. Michels, P. L. Lamy, R. Schwenn, and G. M. Simnett (1998), Origin of streamer material in the outer corona, Astrophys. J., 498, L165 L168, doi: / Wang, Y.-M., N. R. Sheeley Jr., D. G. Socker, R. A. Howard, and N. B. Rich (2000), The dynamical nature of coronal streamers, J. Geophys. Res., 105, 25,133 25,142, doi: /2000ja Watanabe, M., and G. J. Sofko (2008), Synthesis of various ionospheric convection patterns for IMF B y -dominated periods: Split crescent cells, exchange cells, and theta aurora formation, J. Geophys. Res., doi: /2007ja012868, in press. Watanabe, M., G. J. Sofko, D. A. André, T. Tanaka, and M. R. Hairston (2004), Polar cap bifurcation during steady-state northward interplanetary magnetic field with jbyj Bz, J. Geophys. Res., 109, A01215, doi: /2003ja Watanabe, M., K. Kabin, G. J. Sofko, R. Rankin, T. I. Gombosi, A. J. Ridley, and C. R. Clauer (2005), Internal reconnection for northward 8of9

9 interplanetary magnetic field, J. Geophys. Res., 110, A06210, doi: / 2004JA Watanabe, M., G. J. Sofko, D. A. André, J. M. Ruohoniemi, M. R. Hairston, and K. Kabin (2006), Ionospheric signatures of internal reconnection for northward interplanetary magnetic field: Observation of reciprocal cells and magnetosheath ion precipitation, J. Geophys. Res., 111, A06201, doi: /2005ja Watanabe, M., G. J. Sofko, K. Kabin, R. Rankin, A. J. Ridley, C. R. Clauer, and T. I. Gombosi (2007), Origin of the interhemispheric potential mismatch of merging cells for interplanetary magnetic field By-dominated periods, J. Geophys. Res., 112, A10205, doi: /2006ja N. U. Crooker and V. G. Merkin, Center for Space Physics, Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA. 9of9