Magnetopause erosion: A global view from MHD simulation

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A6, 1235, doi: /2002ja009564, 2003 Magnetopause erosion: A global view from MHD simulation M. Wiltberger High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado, USA R. E. Lopez Department of Physics, University of Texas at El Paso, El Paso, Texas, USA J. G. Lyon Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire, USA Received 28 June 2002; revised 26 November 2002; accepted 30 January 2003; published 13 June [1] In this paper we use a global magnetohydrodynamic simulation of the magnetosphere to examine the behavior of the magnetopause position when the interplanetary magnetic field suddenly changes from northward to southward. The inward motion of the magnetopause under the influence of a southward IMF is generally referred to as magnetopause erosion. Physical models to explain erosion have been proposed, notably the onion peeling model, a model based on the effects of fringe fields from the Region 1 Birkeland currents and the nightside cross-tail current. The simulation shows behavior consistent with aspects of these models, but it also shows behavior that is most consistent with the major driver of erosion being the growth of the nightside cross-tail current. In particular, the simulation exhibits a marked delay between the arrival of the southward IMF at the magnetopause and the inward motion of the magnetopause. We attribute this delay to the delay in the growth of the nightside current system in response to the southward turning of the IMF. INDEX TERMS: 2753 Magnetospheric Physics: Numerical modeling; 2724 Magnetospheric Physics: Magnetopause, cusp, and boundary layers; 2740 Magnetospheric Physics: Magnetospheric configuration and dynamics; 2708 Magnetospheric Physics: Current systems (2409); 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions; KEYWORDS: magnetospheric simulation, magnetopause erosion, MHD simulation Citation: Wiltberger, M., R. E. Lopez, and J. G. Lyon, Magnetopause erosion: A global view from MHD simulation, J. Geophys. Res., 108(A6), 1235, doi: /2002ja009564, Introduction [2] The shape and location of the boundary of the magnetosphere, the magnetopause, is determined through a complex interaction between the solar wind, the Earth s magnetic field, and the internal magnetospheric currents. At the most basic level, control of the magnetopause location is physically explained by requiring force balance at the boundary between the solar wind dynamic pressure and the magnetospheric magnetic pressure [Martyn, 1951; Spreiter and Stahara, 1985]. The shape of the magnetopause away from the subsolar point is controlled by the angle between the solar wind flow and the normal of the magnetopause surface [Ferraro, 1960]. The statistical work done by Fairfield [1971] confirmed the general shape and location of magnetopause predicted by the application of this fundamental plasma physics principle but also reported several instances when the shape deviated from being controlled entirely by the solar wind dynamic pressure. The solar wind magnetic field also plays a critical role in magnetopause shape and position. Copyright 2003 by the American Geophysical Union /03/2002JA [3] The inward motion, or erosion, of the subsolar magnetopause location from the force balance predictions was first noted by Aubry et al. [1970], who also observed an outward motion of the magnetopause in the magnetotail. This fact led to magnetopause models that depend on both solar wind dynamic pressure and magnetic field, such as Roelof and Sibeck [1993]. The work of Petrinec and Russell [1993] showed that the subsolar magnetopause location moved inward from the simple pressure balance position for southward IMF B z but was independent of IMF B z northward. Shue et al. [2001] conducted a careful comparison between models and observations to qualitatively determine that the dependence of magnetopause erosion on IMF B z is nonlinear and includes a saturation at highly negative values. The dependence of the magnetopause location and shape on IMF B z has been included in the modern class of magnetopause models [Shue et al., 2000, and references therein]. The models assume a functional form for the magnetopause which is parameterized in terms of the solar wind dynamic pressure and IMF B z to fit the observation of a large number of magnetopause crossings. [4] While the modern models can predict the magnetopause location with considerable reliability, they do not provide a physical explanation of the dependence of mag- SMP 8-1

2 SMP 8-2 WILTBERGER ET AL.: MHD SIMULATION OF MAGNETOPAUSE EROSION netopause shape and location on IMF B z. Over the years a variety of physical theories have been put forward to explain the physics of subsolar magnetopause erosion as well as its change in shape. The two main categories are the qualitative onion peel model and a model that relies on the effects of fringe fields from magnetospheric current systems. It is important to note that these two categories are really nearly equivalent descriptions using the different paradigms of magnetospheric physics described by Parker [1996]. The onion peel model reflects the ~v~b paradigm, while the fringe field model uses the ~E~j paradigm. [5] As explained by Sibeck et al. [1991], the onion peel model argues that dayside merging caused by a southward IMF results in a transport of magnetic flux away from the merging line near the subsolar magnetopause. Newly merged flux is dragged by the magnetosheath flow to the nightside, adding to the magnetotail flux. Thus layers of magnetic flux are peeled off the dayside and transported to the nightside. A delay in the return of flux from the nightside results in the earthward motion of the dayside magnetopause. [6] This qualitative model also predicts the outward motion of the nightside portion of the magnetopause since the increased magnetic flux in the magnetotail results in an expansion of the magnetotail. The magnetotail magnetic field also increases, since the increase in the flaring angle results in a greater solar wind dynamic pressure being applied at the near-earth nightside boundary. This model also predicts a slight outward motion of the magnetopause for northward IMF since the reconnection site moves into the high-latitude cusps on the nightside. [7] Maltsev and Lyatsky [1975] developed a model which accounts for the erosion of the magnetopause by considering the effects of the region 1 Birkeland (R1) currents on the dayside magnetic field. The R1 currents are increased during southward IMF and the fringe fields produced by this current system results in a reduction of the magnetic field on the dayside. Since the dayside magnetic field is reduced, the force balance requirements naturally result in an inward motion of the dayside magnetopause. Similarly, the region 1 currents increase the nightside magnetic field. This would result in increased flaring on the nightside, just as in the onion peel model. Later work by Maltsev et al. [1996] extended this model to consider the effects of the growth of the cross-tail current. Maltsev et al. [1996] argued that the fringe field of the nightside cross-tail current was in fact the greatest contributor to the reduction in the dayside flux. [8] In this paper we begin by briefly discussing the Lyon- Fedder-Mobarry (LFM) global magnetohydrodynamic simulation which we use to simulate a magnetopause erosion event. Next, we present the results from the LFM simulation of a transition from northward IMF to southward IMF without changing the solar wind dynamic pressure. These simulation results are then compared to the observations of magnetopause erosion and discussed in the context of the onion peel and fringe-field current models. 2. Code Description [9] The LFM consists of two linked simulations [Fedder et al., 1995a; Fedder and Lyon, 1995; Mobarry et al., 1996] for modeling the interaction of the solar wind, the magnetosphere, and the ionosphere. The ideal magnetohydrodynamic MHD equations [Chen, 1984], numerically solved by the partial donor method [Hain, 1977, 1987], are used to model solar wind and magnetospheric plasmas. The ionosphere is simulated by solving a height integrated current continuity equation that has been coupled via empirical relationships to the magnetospheric simulation. [10] The MHD equations are solved in a region containing the solar wind and the magnetosphere. For the results discussed in this paper this region is essentially a large cylinder 100 R E in radius and 380 R E long. The X axis extends from the front boundary at X =30R E to back boundary X = 350 R E. The computational grid for the LFM has been adapted to place optimal resolution regions known a priori to be important, e.g., the magnetopause, magnetotail, etc. Figure 1 shows the computational grid for the equatorial plane in the near-earth region which includes the magnetopause and bow shock. Cells in the magnetopause region are approximately 0.25 R E long and cells in the solar wind are typically between 1.0 R E and 1.5 R E. [11] Although we are solving the ideal MHD equations, which are nondissipative, in the magnetosphere the effects of finite cell size produces a numerical proxy for magnetic reconnection. The merging of magnetic fields occurs when oppositely directed magnetic fields are convected into a computation cell and the numerical averaging within the cell results in annihilation of the magnetic flux. The resulting numerical resistivity is important only in regions where this forced reconnection situation scenario is possible. The work of Fedder and Lyon [1987] and Fedder et al. [1995a] showed that the subsequent rate of reconnection is largely controlled by the physical boundary conditions rather than the numerical method. In terms of the magnetosphere-ionosphere current system, the solar wind provides the driving voltage and the ionospheric conductivity controls the magnitude of the ionospheric dissipation, which is the dominant load in the system. In the case of magnetopause reconnection the ionospheric conductivity controls the reconnection rate by regulating the size of flux tubes as they enter the bow reconnection line and the strength of the region 1 current systems. We see little variation in the cross polar cap potential, which is an indirect measure of the global reconnection rate, with increased resolution, leading us to conclude that the grid resolution is not controlling the rate of reconnection. [12] The code uses the solar wind, taken either from in situ observations or from an idealized solar wind input, to determine the boundary conditions along the outer edges of the computational domain. A simple supersonic outflow condition is used at the back boundary, which has been located far enough downstream so that the plasma is once again super-alfvenic, and thus it is impossible for effects at the boundary to affect the upstream plasma. The inner boundary of the simulation is set at a geocentric sphere of 3.0 R E where the magnetospheric solution is matched to the ionospheric simulation. [13] An ionospheric simulation supplies the inner boundary condition for the MHD solution in the magnetosphere. The solution in the ionosphere is done by integrating the conservation of current equation over the height of the

3 WILTBERGER ET AL.: MHD SIMULATION OF MAGNETOPAUSE EROSION SMP 8-3 Figure 1. The near-earth portion of the computational grid for the LFM in the XY plane. The a priori knowledge of the magnetosphere has been used to create a grid with finer resolution in the near-earth region than in the solar wind. Typical resolution inside 10 R e is approximately 0.25 R e. ionosphere to obtain a two dimensional potential equation for magnetosphere-ionosphere coupling, r? ~J? ¼r? r? ¼ ~J ~ b; where ~J? is the height integrated current perpendicular to the magnetic field, is the ionospheric potential, is the height integrated anisotropic conductivity tensor. We have used ~J? ¼ ~E as the Ohm s law to obtain the relationship between in the field aligned currents (FAC) and the ionospheric potential in equation (1). The numerical solution for the ionospheric parameters strongly depends on the height-integrated conductivity tensor. This tensor ð1þ includes empirical models for the effects of solar UV ionization and electron precipitation. The detailed empirical model for calculating the anisotropic conductivity tensor in the LFM is presented by Fedder et al. [1995b]. [14] As previously mentioned, the inner boundary of the MHD domain was placed at 3.0 R E. This is routinely done owing to the rapid, proportional to r 3, increase in the Alfvén velocity as the altitude decreases, which would lead to very short time steps if the boundary was extended further down. The field-aligned currents are determined at the inner magnetospheric boundary and are then mapped instantaneously along dipole field lines to the ionosphere. The ionospheric solution for ~E is then mapped back to this boundary

4 SMP 8-4 WILTBERGER ET AL.: MHD SIMULATION OF MAGNETOPAUSE EROSION Figure 2. The solar wind configuration for the magnetopause erosion study. All parameters besides the IMF B Z are held at constant values. IMF B Z changes from southward to northward at 0300 UT and returns southward at 0600 UT. and used to define the boundary condition for the plasma velocity via 3. Simulation Results ~v ¼ ð rþ ~B : ð2þ B 2 [15] In order to create an optimal simulation for studying the magnetopause erosion process within the LFM, we chose to create an idealized solar wind configuration containing only a southward turning of the IMF. As can be seen in Figure 2, we have set a constant solar wind velocity and density of 400 [km/s] and 5 [#/cm 3 ] respectively. In addition, the only variation of the IMF occurs in B Z which is held at 5 [nt] for the first 3 hours of the simulation and then turned northward to 5 [nt] for the next three hours. At 0600 UT the IMF returns 5 [nt] and remains at this value for the remainder of the simulation. A second simulation was run with the same conditions until 0600 UT at which point IMF B Z was set to 10 [nt]. During the time interval around the southward turning, approximately 0555 UT to 0645 UT, the frequency of data dumps from the simulation was increased from approximately once per minute to approximately once every 8 seconds. [16] Figures 3 and 4 shows a series of frames of three parameters in the equatorial plane of the magnetosphere during magnetopause erosion interval. In the left column the equatorial cut plane of the magnetosphere with the log of the plasma density is displayed. The center column shows B Z in the equatorial cut plane. The difference between B Z at the current time and the value at 0555 UT on the equatorial cut plane is shown in the right column. Each column visualizes the same region, 20 R E < XY <20R E, from the same location. [17] The first row of Figure 3 shows the configuration of the magnetosphere at 0555 UT, just prior to the arrival of the southward turning at the Earth. The density frame shows a well-defined dayside magnetopause, magnetosheath, and bow shock. Along the X axis the magnetopause is at 10.5 R E and the bow shock is located at 14 R E. The center, B Z, frame shows a strong northward B Z inside the bow shock and the southward turning front at approximately 18.5 R E. The B Z difference frame in the right column shows a value of zero everywhere since this is the time step that will be subtracted from all future time frames. [18] Although the north-south transition front reaches X =0R E at 0600 UT, it is not until 0605 UT that the southward IMF reaches the dayside magnetopause because of the slower flow in the magnetosheath. Row two of Figure 3 shows the state of the magnetosphere at 0608 UT. The density frames shows that the magnetopause has moved slightly sunward and become more sharply defined. Both the B Z and the B Z difference frames show the southward IMF filling the entire magnetosheath. In addition, the B Z difference frame shows that the field inside the magnetosphere remains nearly the same as prior to the arrival of the southward IMF with a few significant exceptions. The magnetic field inside a pie-shaped wedge centered around the Earth-Sun line and extending from the inner boundary of the simulation out toward the magnetopause is beginning to show a small difference in field strength. This reduction in field strength is largest nearest the Earth. [19] The configuration of the magnetosphere at 0615 UT is shown in the bottom row of Figure 3. The density edge of the magnetosheath remains well defined in the dayside magnetosphere with the subsolar point at X = 10.5 R E. The earthward edge of the magnetosheath has been pushed sunward toward near X =11R E along the Earth-Sun line. In the B Z difference frame we see that the field depletion wedge has increased in strength and expanded to cover the majority of the dayside magnetosphere. In addition, a significant field enhancement can be seen along the earthward edge of the magnetosheath along the leading edge of the field depletion wedge within the magnetosphere. Within the field depletion wedge, a wedge of density depletion can be seen forming near the simulation boundary. This density reduction wedge expands radially outward in local time but never reaches the local time extent of the field depletion. [20] At 0620 UT the magnetopause begins to erode earthward, and by 0625 UT it has clearly eroded inward to approximately X = 9.75 R E, as can been seen by the density frame of row 1 in Figure 4. This subsolar distance remains nearly constant for the next 6 min. The field depletion wedge has expanded into the nightside with a new stronger depletion wedge clearly evident on the dayside originating from the simulation boundary. The field enhancement along the leading edge of the depletion layer near the magnetopause has been almost completely removed. The earthward edge of the magnetosheath in the B Z and density frames are in much closer agreement than at 0615 UT. [21] Around 0631 UT the magnetopause begins to erode further earthward. It stabilizes with the magnetopause along the X axis at 9.5 R E at 0633 UT as is depicted in row two of Figure 4. The density frame shows that while the density depletion wedge has remained constrained in local time it has extended to the magnetopause. There is also significant depletion of density along the earthward edge of the magnetopause for approximately 50% of the dayside magnetopause. The B Z and B Z difference frames show a close

5 WILTBERGER ET AL.: MHD SIMULATION OF MAGNETOPAUSE EROSION SMP 8-5 Figure 3. Frames from the visualizations showing Log(n) (left column), Bz (center column), and Bz(t) Bz(t = 0555) (right column), in the equatorial plane. agreement between the density and B Z locations of the magnetopause including excellent tracking of B Z and density just prior to +Y axis. [22] The final erosion configuration at 0645 UT is shown in row three of Figure 4. The magnetopause has remained fixed with the X axis crossing still occurring at 9.5 R E. The size of the density depletion zone has also remained nearly constant, but the decrease has continued. In addition to the depletion of the magnetic field on the dayside, a significant ring of depletion is clearly evident on the nightside. [23] In Figure 5 the behavior of the magnetic field along the Earth-Sun line is examined in more detail than visualizations allow. In the upper panel the value of jbj at locations from X =9.0R E to X =6.0R E in 1.0 R E steps are plotted. The arrival time of the southward IMF at the Earth is shown with the solid line at 0600 UT. The bottom panel shows the difference between the field at 0555 UT and the value at the current time. A careful examination of the visualizations shows that the southward IMF doesn t reach the magnetopause until 0605 UT, but the field within the magnetosphere shows a global response when the IMF change reaches the Earth maybe even a minute or two prior. The bottom panel clearly shows the compression of the magnetic field between 0608 UT and 0616 UT. A second compression is also evident between 0624 UT and 0630 UT. [24] The coupling between the ionosphere and the magnetosphere during the erosion interval is examined in

6 SMP 8-6 WILTBERGER ET AL.: MHD SIMULATION OF MAGNETOPAUSE EROSION Figure 4. Frames from the visualizations showing Log(n) (left column), Bz (center column), and Bz(t) Bz(t = 0625) (right column), in the equatorial plane. Figure 6. The top panel in Figure 6 shows the cross polar cap potential, the middle panel shows the magnitude of the FAC on the dusk and dawn sides of the ionosphere, and the bottom panel shows the polar cap flux. The solid line in all three panels is at 0600 UT, the time at which the transition from northward to southward IMF passes through X =0R E. The polar cap area begins to increase in size at 0605 which is marked with the dash dot line in Figure 6. The dotted line at 0607 UT marks the time at which the current system begins its transition from the NBZ current system into a classic region 1 Birkeland current system. In the polar cap potential we see a slight reduction in the potential as the magnitude of the FAC system is reduced during the transition from NBZ to R1. The rate of increase in polar cap area during the first five minutes is faster than the steady rate of increase seen after the dashed line at 0610 in Figure 6. The polar cap potential reaches a saturation value at 0623 UT which is marked by the long dashed line. [25] The last output from the simulation that we wish to investigate is the effect of the nightside cross-tail current system. Figure 7 shows the perturbation in the Bz component of the magnetic field at midnight at various radial distances. This perturbation is produced by the fringing field of the nightside cross-tail current. The arrival of the southward IMF on the dayside is marked by the vertical line on

7 WILTBERGER ET AL.: MHD SIMULATION OF MAGNETOPAUSE EROSION SMP 8-7 Figure 5. The top panel in this figure shows the magnitude of the magnetic field along the X axis and the bottom panel shows the difference between the current time and the value at 0555 UT. In each panel the solid line is at X =6R E, the dotted line is at X =7R E, the dashed line is at X =8R E, and the dash dot line is at X =9R E. The solid vertical line is at 0600 UT reflecting the time the IMF transition passes through X =0R E. Figure 7. The top panel in this figure shows the magnitude of the magnetic field along the X axis and the bottom panel shows the difference between the current time and the value at 0555 UT. In each panel the solid line is at X = 6 R E, the dotted line is at X = 7 R E, the dashed line is at X = 8 R E, and the dash dot line is at X = 9 R E. The solid vertical line is at 0600 UT reflecting the time the IMF transition passes through X =0R E. the plot. The nightside field is not significantly modified until about 20 min after the southward IMF arrives at the magnetopause. Figure 6. The top panel is the cross polar cap potential in kv. The middle panel is the magnitude of the FAC in the dawnside (solid line) and the duskside (long dashed line) in MA. In the bottom panel the open polar cap flux in arbitrary units is plotted. The lines extending through all three panels mark significant times in the ionospheric response. The exact time of each line is indicated by the key inset on the right hand side of the bottom panel. 4. Discussion and Conclusions [26] In the previous section we reported the results from the LFM simulation of the southward turning in a concise and factual manner without providing a physical interpretation of the results. Here we argue that the erosion of the magnetopause is a two stage process which reflects significant coupling between the magnetosphere and the ionosphere. In addition, we will compare the results of the simulation with the predictions of the region 1 fringe field model as well as the onion peel model. [27] While we did not show frames from the visualization of the simulation at 0605 UT, we stated that the southward IMF reached the magnetopause at that time. The statement is supported by the growth in the polar cap area which also begins at 0605 UT. The calculation of the open/closed boundary (polar cap area) only depends upon the topological connection of the field lines. This connection changes instantaneously as reconnection occurs on the magnetopause. The polar cap area begins to increase rapidly at this time as reconnection at the magnetopause begins to create open magnetic flux tubes. The ionosphere does not respond to the arrival of southward IMF at the magnetopause until 1.5 min later, when Alfven or fast mode signals have had a chance to propagate from the magnetopause to the ionosphere. If we double this response time we can estimate that the dayside reconnection site does not experience the effects of magnetosphere ionosphere coupling until 0608 UT. The growth rate of the polar cap area begins to slow down around this time and reaches its steady value at 0610 UT as is clearly illustrated by Figure 6. Early results from instantaneous measurements of the polar cap area calculated from the VIS images of the auroral ionosphere also show this two stage behavior in the polar cap area [Sigwarth et al., 2002]. [28] We believe that this early behavior is a clear illustration of the effect of ionospheric conductivity on the rate of dayside reconnection. During the initial growth of the polar cap, the magnetopause is essentially uncoupled from the ionosphere and the reconnection is very similar to the reconnection somewhat earlier in the magnetosheath between the new southward IMF and remnant northward field. The effect of ionospheric conductance is to partially freeze the foot points of the magnetospheric field lines. This freezing, through the medium of the reflected Alfven wave

8 SMP 8-8 WILTBERGER ET AL.: MHD SIMULATION OF MAGNETOPAUSE EROSION from the ionosphere, increases the inward directed curvature force at the magnetopause. The increased curvature force slows the inflow of flux into the reconnection region. [29] The outward motion of the magnetopause that begins around 0615 UT and precedes the 0620 UT erosion of the magnetopause occurs approximately 5 min after the reconnection rate has saturated. This outward motion of the magnetopause prior to erosion is not part of either the R1 fringe field or onion peel models of magnetopause erosion. While not shown here, a simulation with 10 nt IMF B Z shows similar behavior with a smaller outward motion occurring within a few minutes of the initial magnetosphere-ionosphere coupling lag. This outward motion is approximately 0.3 R E, which is near the cell size at that location and may just be a numerical artifact. Higherresolution simulations need to be conducted to determine the physical significance of this feature in the motion of the magnetopause. [30] Each visualization of the magnetosphere shows magnetopause erosion beginning around 0620 UT and the magnetopause reaches its new quasi-steady location at 0630 UT. The earthward motion of the dayside magnetopause precedes the saturation of the polar cap potential by 3 min. The nearly 15 min delay between arrival of southward IMF at the magnetopause and erosion of the dayside magnetopause is not consistent with the onion peel model of magnetopause erosion. In the onion peel model it is imbalance between the onset of reconnection and transport of flux tubes from the dayside and the return of flux tube from the nightside which causes magnetopause erosion. If this were the case in the simulation we would expect to see the magnetopause eroding during the period prior to the saturation of the polar cap potential as the magnetospheric and ionospheric convection is building up to the newly required rate for these solar wind conditions. [31] The R1 fringe field model predicts a reduction in the magnetic field on the dayside within the wedge of the current system. Our simulation results do show a reduction in the magnetic field strength in a wedge centered along the Earth-Sun line. The reduction occurs at each location simultaneously after the initial increase in magnetic field. This result is consistent with the fringing field of the R1 currents. However, the delay in magnetopause erosion after the arrival of southward IMF is not consistent with this model. One question that could be asked is Is the delay real? We are unaware of such a delay being reported in the literature. Detection of the delay in magnetopause erosion after the arrival of southward IMF at the magnetopause will be a significant observational challenge given the difficulties in determining the exact time of arrival of southward IMF from remote solar wind monitors. In addition, in order to detect this significant feature of simulation results in the observations we will need periods with clear southward turnings and steady solar wind conditions. We are currently beginning an exhaustive search for events which meet these criteria to use as drivers for further simulations. [32] Whether the delay is real or not, it does occur in the simulation, and we believe that an explanation exists that is consistent with the results of Maltsev et al. [1996]. That study concluded that an increasing nightside cross-tail current is the most important factor weakening the dayside magnetic field. Our results show that a noticeable effect of the nightside currents on the magnetic field is delayed by about 20 min relative to the arrival of the southward IMF on the dayside. Therefore if the major reduction in the dayside field (which leads to the inward motion of the magnetopause under constant pressure balance) is accomplished by the growth of the nightside currents, we would expect exactly the delay that was observed in the erosion. This delay is consistent with earlier studies using the same simulation code Lyon et al. [1998]; Lopez et al. [1999] that investigated the relative delays between the arrival of the southward IMF, the equatorward motion of the open-closed field line boundary at noon, the onset of the reconfiguration of the polar cap potential, and the equatorward motion of the open-closed field line boundary at midnight. The first three phenomena are essentially simultaneous on the timescale of a few minutes, while the latter was delayed by min. Therefore we take our result as evidence that the major part of the erosion of the magnetopause is related to the growth of the nightside cross-tail current system. [33] In summary, the LFM simulations of the magnetopause erosion require the development of new physical explanation. The simulation results clearly show a two stage growth of polar cap area which is seen in observations and a reflection of the control of magnetosphere-ionosphere coupling on the dayside reconnection rate. We also find that the inward motion of the magnetopause is largely controlled by the growth of the nightside cross-tail current system. [34] Acknowledgments. We thank NCSA for the computational resources used to complete the simulation. This work was supported by the NASA Sun-Earth Connection Theory Program under grant NAG Additional support was provided by NSF grant ATM [35] Lou-Chuang Lee thanks Y. P. Maltsev and another reviewer for their assistance in evaluating this paper. References Aubry, M. P., C. 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Elphinstone, Global numerical simulation of the growth phase and the expansion onset for substorm observed by Viking, J. Geophys. Res., 100, 19,083, 1995b. Ferraro, V. C. A., An approximate method of estimating the size and shape of the stationary hollow carved out in a neutral ionized stream of corpuscles impinging on the geomagnetic field, J. Geophys. Res., 65, , Hain, K., Behavior of ionized plasma in the high latitude topside ionosphere, NRL Memo. Rep., 3713, 1, Hain, K., The partial donor method, J. Comput. Phys, 73, 131, Lopez, R. E., M. Wiltberger, J. G. Lyon, C. C. Goodrich, and K. Papadopoulos, Mhd simulations of the response of the high-latitude potential patters and polar cap boundaries to sudden southward turnings of the interplanetary magnetic field, Geophys. Res. Lett., 26, , Lyon, J., R. E. Lopez, C. Goodrich, M. Wiltberger, and K. Papadopoulos, Simulation of the March 9, 1995 substorm: Auroral brightening and the onset of lobe reconnection, Geophys. Res. 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9 WILTBERGER ET AL.: MHD SIMULATION OF MAGNETOPAUSE EROSION SMP 8-9 Maltsev, Y. P., A. A. Arykov, E. G. Belova, B. B. Gvozdevssky, and V. V. Safargaleev, Magnetic flux redistribution in the storm time magnetosphere, J. Geophys. Res., 101, , Martyn, D. F., The theory of magnetic storms and auroras, Nature, 167, 92 94, Mobarry, C., J. A. Fedder, and J. G. Lyon, Equatorial plasma convection from global simulations of the Earth s magnetosphere, J. Geophys. Res, 101, 7859, Parker, E. N., The alternative paradigm for magnetospheric physics, J. Geophys. Res., 101, 10,587 10,625, Petrinec, S. M., and C. T. Russell, External and internal influences on the size of the dayside terrestrial magnetosphere, Geophys. Res. Let., 20, , Roelof, E. C., and D. G. Sibeck, Magnetopause shape as a bivariate function of interplanetary magnetic field bz and solar wind dynamic pressure, J. Geophys. Res., 98, , Shue, J. H., P. Song, C. T. Russell, J. K. Chao, and Y. H. Yang, Toward predicting the position of the magnetopause within geosynchronous orbit, J. Geophys. Res., 105, , Shue, J. H., P. Song, C. T. Russell, M. F. Thomsen, and S. M. Petrinec, Dependence of magntopause erosion on southward interplanetary magnetic field, J. Geophys. Res., 106, 18,777 18,788, Sibeck, D. G., R. E. Lopez, and E. C. Roelof, Solar wind control of magnetopause shape, location, and motion, J. Geophys. Res., 96, , Sigwarth, J. B., N. J. Fox, and L. A. Frank, Efficiency of dayside magnetic merging of the solar wind and the magnetosphere, Eos Trans. AGU, 83, Spring Meet. Suppl., Abstract SM42D-01, Spreiter, J. R., and S. S. Stahara, Magnetohydrodynamic theories for planetary bow waves, in Collisional Heliosphere: Reviews of Recent Research, Geophys. Monogr. Ser., vol. 37, edited by B. T. Tsurutani, pp , AGU, Washington, D. C., R. E. Lopez, University of Texas at El Paso, Department of Physics, El Paso, TX 79968, USA. (relopez@utep.edu) J. G. Lyon, Dartmouth College, Department of Physics and Astronomy, 6127 Wilder Laboratory, Hanover, NH 03755, USA. (lyon@tinman. dartmouth.edu) M. Wiltberger, National Center for Atmospheric Research, High Altitude Observatory, 3450 Mitchell Lane, Boulder, CO 80301, USA. (wiltbemj@ ucar.edu)