Saturation of the ionospheric polar cap potential during the October November 2003 superstorms

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110,, doi: /2004ja010864, 2005 Saturation of the ionospheric polar cap potential during the October November 2003 superstorms Marc R. Hairston and Kelly Ann Drake Center for Space Sciences, University of Texas at Dallas, Richardson, Texas, USA Ruth Skoug Los Alamos National Laboratory, Los Alamos, New Mexico, USA Received 25 October 2004; revised 18 March 2005; accepted 29 March 2005; published 28 July [1] The question of whether the cross polar cap potential drop in the Earth s ionosphere saturates under conditions of extreme electric field in the solar wind has been tested observationally during the past several years. The challenge to proving the existence of this phenomenon is that periods of such extreme electric fields in the solar wind are relatively rare. The three superstorms of October and November 2003 provided ideal cases for testing this idea. We first review the earlier evidence of the saturation seen by the DMSP-F13 spacecraft during the 31 March 2001 superstorm and other storm events during the time period. Then we present observations from the DMSP-F13 spacecraft during the October and November 2003 superstorms that show definite evidence of this saturation. In addition, some of the electric fields during these superstorms were almost twice as large as the largest fields previously studied, thus increasing the range of our sample set and further increasing our confidence in the existence of the saturation phenomenon. The data are compared with the saturated potentials predicted by the Hill-Siscoe model to test its validity. The DMSP measurements indicate that the saturation limit of the cross polar cap is about 260 kv. Citation: Hairston, M. R., K. A. Drake, and R. Skoug (2005), Saturation of the ionospheric polar cap potential during the October November 2003 superstorms, J. Geophys. Res., 110,, doi: /2004ja Introduction [2] The connection between the solar wind drivers, the interplanetary magnetic field (IMF) and the solar wind ram pressure, with the electric fields and convection patterns in Earth s polar ionosphere has been studied extensively for the past 2 decades and, for the southward IMF conditions, is very well understood [e.g., Heelis, 1984; Heppner and Maynard, 1987; Richmond and Kamide, 1998; Rich and Hairston, 1994; Weimer, 1995; 1996; Boyle et al., 1997; Ruohoniemi and Baker, 1998, and references therein]. As the IMF flows past the Earth, a cross-magnetospheric electric field is generated along the magnetopause. During southward IMF conditions the IMF couples directly with the Earth s magnetosphere and thus part of this electric field maps down to the polar ionosphere. This creates the cross polar cap potential in the ionosphere which can be directly measured by satellite and radar observations [Hairston and Heelis, 1996; Greenwald et al., 1995]. As the solar wind velocity and/ or the magnitude of the southward component of the IMF increases, then this cross-magnetospheric electric field increases, so in turn the ionospheric cross polar cap potential should also increase. Copyright 2005 by the American Geophysical Union /05/2004JA010864$09.00 [3] Work by several researchers [e.g., Reiff and Luhman, 1986; Weimer, 1995, 1996] comparing the observed polar cap potential to the solar wind conditions resulted in a series of empirical relationships where the polar cap potential is a linear function of the solar wind speed and the magnitude of the z-component of the IMF. In the most thorough analysis comparing 3 1/2 years of Defense Meteorological Satellite Program (DMSP) observations of the polar cap potential to solar wind parameters, Boyle et al. [1997] obtained the following best empirical fit: % B ¼ 10 4 v 2 SW þ 11:7 B sin3 ðq=2þ; ð1þ where % B is the ionospheric polar cap potential in kv, v SW is the solar wind speed in km/s, B is the y-z plane component of the IMF field in nt, and q is the clock angle of the IMF in the y-z plane where 0 is northward and 180 is southward. [4] Hill et al. [1976] and later Hill [1984] predicted that once the induced electric field from the solar wind reached a certain magnitude the ionospheric potential would stop increasing and saturate. In this model the solar windinduced region 1 currents in the magnetosphere would create a magnetic field that opposes the Earth s dipole field, effectively reducing the amount of magnetic flux available on the dayside magnetopause for reconnection with the IMF. In effect, the magnetosphere would reach a point 1of12

2 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 where no matter how large the solar wind electric field became, there would be no more magnetic flux available in the magnetosphere to reconnect with the increased flux in the solar wind, thus the magnitude of the polar cap potential could not increase any further. The difficulty in testing this model is that such saturation only occurs under extreme solar wind conditions. Under nominal conditions, even during routine magnetic storms, the polar cap potential responds linearly to the increase in the magnitude of the solar wind induced electric field. Boyle et al. [1997] checked their data set of DMSP observations for any evidence of saturation but found none. However, because of the severe restrictions they placed on their data to ensure the IMF was steady for an extended time period, the highest solar wind electric field they observed was about 8 mv/m. Also, their data set did not include any periods of extremely high solar wind velocities that might have exhibited the saturation effect. [5] Early efforts using limited data sets of polar cap potentials potential measurements from AE-C, AE-D, S3-2, and S3-3 spacecraft performed by Reiff et al. [1981], Cowley [1984], and Reiff and Luhman [1986] showed some indication of possible saturation. Later efforts to test the idea of saturation using larger and better data sets were done by Russell et al. [2001] and Shepherd et al. [2002]. Russell et al. [2001] used the AMIE procedure based on magnetometer, spacecraft, and radar observations from five large storms to calculate the polar cap potential. These events included periods where the solar wind electric field data reached 10 mv/m and indicated saturation beginning to occur at this point. Shepherd et al. [2002] looked at 3 years of SuperDARN data and the inferred polar cap potential based on these observations. Their work (see specifically Figure 4 in the work of Shepherd et al. [2002]) covered data for solar wind electric fields of up to 110 kv/r E (17.27 mv/m) and showed evidence of saturation beginning with solar wind electric fields as small as 20 kv/r E (3.14 mv/m) and showed no potentials larger than 120 kv. However there was some ambiguity about these results which will be discussed in more detail in the final section of this paper. [6] Hill et al. [1976] and Hill [1984] only gave the form of a function where the polar cap potential would saturate. Siscoe et al. [2002] expanded on Hill s idea to formulate an exact prediction of the polar cap potential as a function of the solar wind parameters and the ionospheric Pedersen conductivity. The saturation formula given by Siscoe et al. is Fpc ¼ 57:6 E sw P 1=3 sw P 1=2 D4=3 FðÞ q sw D þ 0:0125 xse sw FðÞ q where % pc is the polar cap potential in kv, E SW is the solar wind electric field (E SW = jv SW B SW j), P SW is the ram pressure exerted by the solar wind in npa (P SW = r SW v 2 SW ), D is the strength of the Earth s dipole field normalized to 1 for the present value, F(q) is a function of the clock angle of the IMF to account for the geometry of reconnection (here F(q) =sin 2 (q2), i.e. F(q) = 0 for IMF northward and 1 for IMF southward), x is a dimensionless coefficient between 3 and 4 that depends on the geometry of currents in the ionosphere [Crooker and Siscoe, 1981], and S is the heightintegrated Pedersen ionospheric conductivity (assumed to ð2þ be uniform throughout the polar region for simplicity s sake) measured in S. From MHD simulations, Siscoe et al. obtained the relation x ¼ 4:45 1:08 log ðs=1sþ ð3þ to compute the value of the x coefficient to use in the formula. They compared the predictions from this formula with polar cap potentials generated from an MHD simulation and found a good agreement. It should be noted that all the variables in equation (2) can be measured directly except for the Pedersen conductivity, so the analysis presented here will use nominal values of 5 and 10 S for the conductivity. From here on, equation (2) will be referred to as the Hill-Siscoe model and equation (1) will be referred to as the Boyle formula. Siscoe et al. [2004] expanded on this work in an attempt to test four explanations (including the Hill-Siscoe model above) of the causes of saturation. They showed all four were consistent with current observations and models but could not specifically rule out any of them at this point. 2. Previous Work With DMSP [7] The DMSP satellites are in polar orbits with periods between 100 and 105 min. In general there are two to four operational satellites at all times situated in two orbital orientations: LT (essentially dawn-dusk) and LT. The two-cell distribution of potential during southward IMF conditions is such that generally the spacecraft in the dawn-dusk orientation passes closest to the absolute maximum and minimum of the potential. Thus for analysis of the cross polar cap potential we restrict ourselves to using data from the dawn-dusk DMSP satellite: F13. Each DMSP spacecraft carries a Special Sensor Ions, Electrons, and Scintillation (SSIES) package which measures several parameters of the thermal plasma including the bulk ion velocity. Combining the cross-track ion flow with the magnetic field data, we calculate the electric field parallel to the spacecraft s track. Starting at the subauroral region on one end of the spacecraft s polar pass and going to the other side, we integrate the electric field along the track to get the electrostatic potential. Because of changes in flow pattern during the time of the pass (generally about 15 to 20 min) the integrated potential rarely returns to zero at the far end of the path. This remaining potential at the end of the pass (called the offset) is redistributed linearly across all the potential data to force both ends to zero. The difference between the maximum and minimum potential in this corrected set of data is what we use as the observed potential drop and one half of the offset is what we use as the uncertainty of the potential drop. Under nominal ionospheric conditions there a period each day from roughly 0200 to 0800 UT where the magnetic dipole is tilted furthest away from the spacecraft s ground track and the spacecraft only skims the edges of the potential distribution pattern. During storm times the polar cap expands equatorward enough that a substantial part of the pattern is still observed by the spacecraft passes between 0200 and 0800 UT. Still, there is the uncertainty about how close the spacecraft did or did not come to the true maximum and minimum of the potential, so for our analysis we prefer to use passes from 2of12

3 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Figure 1. Adapted from Figure 3 from Hairston et al. [2003], this figure shows the data from the six prime DMSP passes during the 31 March 2001 storm. The observed potentials are plotted as a function of the solar wind electric field and demonstrate that the potential saturates under conditions of large electric fields in the solar wind. The straight line labeled % B is the predicted potential from the Boyle formula, while the two curves labeled % H-S are the predicted potential from the Hill-Siscoe model using the nominal values of 2 = 5 and 10 S. the other times of the day when there is greater confidence that the observed potential drop is very close to the actual potential drop. A more complete description of this analysis is given by Hairston and Heelis [1996] and Hairston et al. [1998]. [8] The superstorm of 31 March 2001 provided an excellent chance to use the DMSP observations to test for the existence of cross polar cap potential saturation. During the period from 1300 UT to 2200 UT on that date the IMF was strongly southward with B Z (in GSM coordinates) changing slowly from 30 to 20 nt. During this period, DMSP-F13 made six southern polar passes that were very close to the magnetic pole. The proximity to the pole ensures that the observed potential difference was close to the true cross polar cap potential and the repeated passes demonstrated that the observed patterns were stable and not transitory. A full report of this work was presented by Hairston et al. [2003], and Figure 1 here is an adaptation of Figure 3 from that paper. We plotted the observed potential drops as a function of the corresponding observed solar wind electric field (E SW = v B). The vertical bars on the data points show the uncertainty of the observed potentials based on the offset described above. The straight line labeled % B is the potential predicted by the Boyle formula, while the two curved lines are the Hill-Siscoe model predictions for 2 = 5 and 10 S. The range of the solar wind induced electric field during this event extends to just over 20 mv/m. The observed potentials show that even after accounting for the uncertainty of the measurements, they have definitely saturated far below where the levels where the linear predictions of Boyle et al. [1997] would place them. As pointed out above, all of the data used in the Boyle model occurred when the solar wind electric field was less than 8 mv/m. Examining the Boyle and Hill-Siscoe model predictions in Figure 1 shows that they generally overlap in the region below 8 mv/m. Thus the Boyle formula for the polar cap potential is valid for the vast majority of the time when solar wind conditions are nominal and the solar wind electric field is <8 mv/m. It should be emphasized here that the line for the Boyle formula plotted here and in the subsequent figures is a simplification where the values for the solar wind velocity and are set to constants using their averaged values for that period and only the value of the solar wind electric field is changed. This is done not as an exact comparison of the observations to the Boyle formula but as a first-order guide to show the difference between the observed saturated potentials and the magnitude of the potentials were they to increase linearly with the solar wind electric field. [9] After this work was complete we undertook a search for further passes which occurred during extreme solar wind conditions. We first searched the ACE database for periods when the IMF was strongly southward (B Z < 20 nt) and steady for 1 or more hours. In the period from 1998 through early 2002 we identified about 50 possible events. We then examined the DMSP-F13 database to see if there were any usable passes that occurred during these events. We discarded all events where no DMSP-F13 polar passes overlapped a period where E R > 8 mv/m or where there were only skimmer passes. After this we were left with 22 passes from eight events that should show evidence of saturation. Figure 2 is a plot of these passes along with the original six passes from the 31 March 2001 storm (noted by the letters on the figure) in the same format as Figure 1 but with one significant difference. The x-axis now shows E R, the reconnection electric field in the solar wind, here defined as E R = E SW sin 2 (q/2), where q is the same clock angle as in equations (1) and (2). This takes into account the reconnection factor of the IMF, since obviously a 10 mv/m electric field in the solar wind would have very different results if the IMF orientation was completely north versus completely south. For the 31 March 2001 storm the IMF was almost completely southward during the six polar passes, so for that event E R E SW, but this was not the case for many of the new passes. Thus we rescaled the solar wind electric field to make the comparisons valid. [10] Out of the 22 new passes, three of them were passes where DMSP barely reached 75 magnetic latitude. Normally, these would be discarded as skimmer passes with small observed potentials as described above; however, these three occurred during major storms when the polar cap had expanded significantly equatorward. Thus these three DMSP passes crossed enough of the potential distribution to measure large potential drops ranging from 134 to 218.kV. Because these passes tracked so far from the locations of the true maximum and minimum, we know that the true potential drops were larger than the observed drops, but we have no way of definitively calculating the magnitude of those true potential drops. However, scaling the size of the standard potential distribution up to the size of the patterns measured by the endpoints of these DMSP passes and then comparing the potential along the track with the total potential in the scaled up pattern shows that an increase of 20% would be a reasonable estimate. Thus we plot these three passes on Figure 2 using potentials 20% greater than the measured potential drops and denote these passes by plotting their error bars with dotted lines. For the upper error bar on these three passes we used one-half of the 3of12

4 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Figure 2. Plot of the same six data points along with data from an additional 22 DMSP passes during the time period that also show evidence of saturation. The line showing the predicted potential from the Boyle formulation (here labeled % B ) and the predicted potential from the Hill-Siscoe model (using nominal values of 2 = 5 and 10 S) based on the 31 March 2001 conditions are included as a baseline. offset, thus matching all the other passes plotted here. However, for these three passes we extended the lower error bar down to the original measured potential to include the actual observation and to show the wider range of uncertainty. The first one (at E R = mv/m, extrapolated potential = 161 kv) falls in the middle of several closely spaced points and is difficult to see. The second one (at E R = mv/m; extrapolated potential = 203 kv) is easier to see and, because of its small offset relative to the 20% correction, the location of data point is very asymmetric relative to the error bars. The third point is clearly visible on the far right of the figure. This pass occurred between 0457 and 0524 UT on 4 May 1998 during a period when B Z = 31 nt. Although DMSP-F13 did not go above magnetic latitude, it still observed a potential drop of kv and that is plotted here at 262 kv to include the estimated 20% extra potential. This was only one of these additional 18 passes where the E R value exceeded the highest value from the earlier 31 March 2001 event, so it is particularly frustrating that the true potential for this pass is so uncertain. While the true potentials of these three points could be larger than the values plotted here, anything over 30% larger is unrealistic, and even were the true potential that large it would still be much smaller than the expected potential from the linear Boyle model. Even after including this extra estimated potential, these three data points still appear to fall within the range described by the rest of the data points. [11] In the plot we have left the predicted line from the Boyle formulation and the two Hill-Siscoe model prediction curves based on the 31 March 2001 storm conditions to serve as a baseline. The figure shows the observed potentials as a function of the reconnection electric field in the solar wind (which depends on the solar wind velocity, IMF magnitude, and clock angle) but the Hill-Siscoe model predicted potential curves also depend on the ram pressure (which depends on the solar wind density and the solar wind velocity), the Pedersen conductivity, as well as an extra term of the sine of the clock angle. Varying the average solar wind velocity and clock angle would slightly change the slope and intercept of the line from the Boyle formulation. Likewise, varying the pressure, conductivity, and clock angle would move the curves of the Hill-Siscoe model up and down. Thus a range of nominal values for these variables would not produce a single line but a set of Hill-Siscoe curves forming a band on the plot. Mixing these observations from several different events occurring under different solar wind conditions would not result in a set of points forming a line; rather such data would form a band of points. This is exactly what we see in the data shown in Figure 2: a band of points that show clear evidence of saturation. 3. Data From the October and November 2003 Superstorms [12] The three superstorms of October and November 2003 served as ideal tests for the Hill-Siscoe model. In the space of 3 days we almost doubled the number of passes in the data set and extended the range of the reconnection electric field in the solar wind from just over 20 mv/m to almost 40 mv/m. We start by examining the solar wind data for the October storms. The superstorm of October 2003 was actually two sequential storms caused by two separate coronal mass ejections (CME). Figure 3 shows the data from ACE during this period and a more complete description of this data set is given by Skoug et al. [2004]. The most outstanding feature of the first storm was the solar 4of12

5 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Figure 3. This figures shows the solar wind density, solar wind velocity, and the B Y and B Z components (in GSM coordinates) of the IMF observed by the ACE spacecraft during the October 2003 CMEs. Note that the heavy trace in the density panel between the vertical bars at 0600 UT on 29 October and 0400 UT on 30 October represents the substitution of GEOTAIL density data for the suspect ACE density data during this period. The short horizontal dashes in bottom panel denote the times corresponding to the DMSP polar passes used in this study. The letters denote whether the pass was a Northern or Southern Hemisphere pass. wind speed (second panel) which exceeded 2000 km/s for a period starting at 0759 UT after the first shock passed the ACE spacecraft at about 0620 UT on 29 October. This is only the second time solar winds speeds in excess of 2000 km/s have been directly observed (the other was observed on 4 5 August 1972 by Prognoz 2 and HEOS 2), though there are several storms from the 19th and earlier 20th centuries (such as the Carrington event of 1859) where such high speeds can be inferred [Skoug et al., 2004]. The top panel in Figure 3 shows the solar wind ion density observed by the Solar Wind Electron Proton Alpha Monitor (SWE- PAM) instrument on board the ACE spacecraft. Normally, SWEPAM measures the solar wind speed and ion density every 64 s in its track mode and every 33 min it takes one measurement in a search mode. However, from 1241 UT on 28 October to 0051 UT on 31 October the penetrating radiation from the energetic particles caused the tracking algorithm to fail. Thus during this period only the 33-min resolution search mode data were usable. Also, during the period from 0600 UT on 29 October to 0400 UT on 30 October the calculated ion densities from SWEPAM appear to be too low. Comparing the densities calculated from ACE to the electron densities calculated from the Plasma Wave Instrument (PWI) later on Geotail (200 R E further downstream) show good agreement until 0600 UT on 29 October at ACE. After this time the corresponding Geotail densities are 2 to 5 times higher. Although the exact cause of this disagreement is unknown, it was determined that the Geotail plasma density data were less uncertain than the ACE density data, while the solar wind velocity calculations from ACE remained valid for this period [Skoug et al., 2004]. Thus the region bounded by vertical bars and plotted with a heavy line on the top panel of Figure 3 denotes the period where Geotail data rather than ACE data are used for the solar wind density (after being timeshifted forward to account to the transit time from ACE to the position of Geotail.) After 0400 UT on 30 October, Geotail was in the magnetotail, so after that time we revert to using the ACE density data. At 1100 UT on 31 October Geotail reemerged from the magnetotail (during the recovery phase of the second storm), and the density measurements between it and ACE once again agreed. So from 0400 UT 30 October to 1100 UT 31 October there is no independent check on the quality of the ACE density calculations. However, we believe the data became more reliable toward the end of this period as the storm recovery progressed [Skoug et al., 2004]. [13] It is clear from the Geotail data that there was an enhancement in the density just after the shock passed ACE. The bottom two panels show the B Y and B Z components (in 5of12

6 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Figure 4. This figure shows the history of the potentials observed by DMSP-F13 during the October 2003 superstorms. The solid line traces the potentials observed in the northern polar passes and the dashed line traces the potentials observed in the southern polar passes. the GSM coordinate system) of the IMF measured by the magnetometer on board ACE. The two shocks from the two sequential CMEs can clearly be seen in the data in Figure 3. The first shock arrived at ACE at 0558 UT on 29 October based on the variability of IMF data. At the next SWEPAM observation at 0620 there is a sudden increase in the solar wind speed in the top panel of Figure 3 and the ACE plasma density (not shown here). The second shock arrived at ACE at 1630 UT on 30 October and again is shown by the increase in the solar wind speed and the variability of the magnetic field components; however, there is no appreciable increase in the solar wind ion density. It is not clear why there was no increase in the density following the second shock. It could be there was an increase, but the density algorithm on SWEPAM was still failing and did not properly detect it. Or the SWEPAM data could be accurate, indicating that the first shock had swept most of the plasma out ahead of it, and there simply was not enough plasma remaining behind for the second shock to create a density pulse. [14] The IMF oscillated sharply between north and south for the first few hours after the first shock, then turned steadily northward at 0841 UT on 29 October, and stayed steadily northward until 1746 UT. After that time the IMF turned strongly southward (B Z ranging from 27 to 10 nt) for nearly 9 hours until 0238 UT on 30 October. This extended period of strong steady southward IMF provided the ideal conditions for DMSP observations of the saturated potential. After 0238 UT the IMF turned moderately northward (B Z +10 nt) and the storm recovery began. At about 1630 UT the second shock reached ACE and after a short period of northward IMF B Z turned southward ( 5 to 15 nt) for about 30 min. B Z then hovered around zero until about 1820 UT when it turned strongly southward ( 20 to 35 nt) for about 4 hours. Again the conditions during this period of steady southward IMF were ideal for testing the saturation model. After this period B Z oscillated between northward and southward periods for the next 4 hours. [15] During this period the DMSP-F13 spacecraft made a polar pass every 51 min and measured the potential drop along its track during each of these passes. Figure 4 shows the history of the potential observation for the 3-day period of October. Because of the offset of the Earth s magnetic dipole the spacecraft crosses a different part of the potential distribution in each hemisphere, thus seeing different observed potential drops even when the pattern is the same. If all the potential measurements are plotted sequentially, this creates an artifact where the potential appears to jump back and forth between each hemisphere s measurement. Instead, as in Figure 4, we connect all the Northern Hemisphere measurements sequentially (the solid line) and connect all the Southern Hemisphere measurements sequentially (the dashed line). This gives two different lines that clearly trend with each other rather than matching each other exactly. In Figure 4 we can trace the history of the two storms quite clearly. There is a sharp jump to 160 kv during the northern pass centered on 0643 UT as a response to the initial shock and the strong negative B Y and southward B Z immediately after the shock. Note that this huge potential occurs during the time when DMSP would normally only skim the polar cap region. After that the potential decreases to lower values (70 to 100 kv), corresponding to the 6of12

7 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Figure 5. Plot of the observed potentials versus the reconnection electric field in the solar wind for the first superstorm during October The eight passes with the highest confidence level are denoted by small boxes around the data points. The line for the predicted potential from the Boyle formulation (% B ) and two representative Hill-Siscoe model curves are presented using the averaged values of other parameters during this period. The averaged parameters during this period were V SW = ± km/s; P = ± npa; F(q) = ± following period of northward IMF. During the period from 1500 UT to 0300 UT on 30 October there are large potentials (most passes between 150 and 225 kv) measured in both hemispheres. A period of small potentials follow from 0300 UT to 1700 UT corresponding to the period of small magnitudes of the IMF. From 1700 UT to 0100 UT there is a second set of large potentials (most between 150 and 210 kv) in response to the second shock and the period of southward IMF following that. After that the potential returns to nominal values for the remainder of 31 October. A plot of the potentials from DMSP-F15 for this period (not shown) demonstrates a similar history. However, since the orbit orientation of F15 is local time, its path does not get as close to the true potential maximum and minimum as F13 s path does, and it observed smaller potentials than F13 did. The largest potential drops measured by F15 were kv during the first storm and kv during the second storm. [16] For the analysis, we selected all the DMSP passes during these storms with potentials greater than 140 kv resulting in 20 passes. In Figure 3 we have placed horizontal bars on the bottom panel (B Z ) showing the times of these 20 passes relative to the solar wind inputs, after having timeshifted them appropriately. The amount of time shifting was done individually for each pass and was based on the transit time of the solar wind from ACE to the magnetopause using the corresponding solar wind speed and then adding an additional 10 min to account for the response time of the ionosphere. Because of the different solar wind conditions, primarily the different densities and ram pressures leading to different predictions for the Hill-Siscoe model, we chose to plot these data in two groups, one for each storm. Figure 5 shows the data for the 13 passes from the first storm using the same format as Figure 2 where the observed potential and uncertainty are plotted against the reconnection electric field in the solar wind. The prediction for the Boyle formula and the two Hill-Siscoe curves (for S = 5 and 10 S) are also plotted on the figure. These predictions are based on the following averages for the periods of the twelve passes: V SW = ± km/s; P = ± npa; F(q) = ± The data points cover the reconnection electric field range from 7.73 to mv/m with the highest measured potential being 225 kv. The data clearly show the saturation effect compared to the prediction of the Boyle formula. The seven data points with a box around the central point denote the seven polar passes occurring between 2000 UT 29 October and 0135 UT 30 October which corresponds to the period in Figure 3 of 1927 UT to 0101 UT at ACE, a time of steady strong B Z negative and B Y positive conditions. Thus these are the points in which we have the highest confidence. The fact that all of these seven high-confidence points fall below the Hill-Siscoe curve for S = 10 S indicates that the overall average conductivity during these passes was greater than 10 S. However, it should be noted that since the pressures here are based on the extrapolated densities from the Geotail, the accuracy of the Hill-Siscoe curves on this plot are somewhat uncertain. [17] In Figure 6 we plot the data from the seven DMSP passes picked from the second storm. Here the Boyle formula and the Hill-Siscoe curves are calculated using these averages from the periods of these passes: V SW = ± km/s; P = ± npa; F(q) = ± 7of12

8 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Figure 6. This figure follows the format of Figure 5 in plotting the observed potentials vs. the reconnection electric field in the solar wind for the second superstorm during October The four passes with the highest confidence level are denoted by small boxes around the data points. The averaged parameters during this period were V SW = ± km/s; P = ± npa; F(q) = ± The slight increase in the average velocity causes the line for the Boyle formula to move slightly upward. Meanwhile, the decrease in the pressure causes the two Hill- Siscoe curves to migrate significantly downward relative to their locations in Figure 5. Here the data points for the reconnection electric field range from 7.74 mv/m all the way to mv/m, with the highest measured potential being kv. Again the data clearly show saturation. The fact that three of these points are above 35 mv/m, nearly twice as large as the highest electric field prior to these storms, yet still show no significant increase in their potential serve as conclusive evidence for the reality of the saturation of the potential. In fact, the four passes in which we have the highest confidence are the four data points farthest to the right in Figure 6. They correspond to the period of steady strong southward IMF between 1832 UT and 2130 UT at ACE in Figure 3. This time five of the seven points appear to trend about the S = 10 S Hill-Siscoe curve, while the remaining two indicate a lower conductivity. Again, it should be noted that the density data for this period comes from ACE during the period while Geotail was in the magnetotail. As stated above, there is some uncertainty about the quality of the plasma density data during this period. However, we feel the quality of the SWEPAM data improved as the event progressed, so we are fairly certain about the position of the Hill-Siscoe curves for this period. [18] Twenty-two days after the first superstorm hit the Earth, another large CME from that same active site on the sun struck the Earth on 20 November This time the CME did not swamp the SWEPAM, so there is high confidence in all of the solar wind density and velocity data for this event. Figure 7 show the solar wind data for this event in the same format as Figure 3. There are several major differences between this event and the two October CMEs. First the velocity increase is not as dramatic as the two shocks in October, but is more in line with a typical shock jumping from roughly 440 to 620 km/s. Second, the solar wind densities are much higher this time after the shock, sometimes going over 30 protons/cc. Third, the magnetic fields are much larger in magnitude. After the shock arrived, B Z oscillated between north and south for about 90 min, then spent about 50 min strongly northward (ranging from 13 to 37 nt). At 1059 UT B Z turned sharply southward and began a 12-hour period when it remained strongly southward. B Z reached a minimum of 53 nt at 1435 UT then slowly increased to about 10 nt over the next 9 hours. This extended period of strongly southward IMF provided us with 12 more passes occurring during large solar wind electric fields where the potential should saturate. As in Figure 3 the times of 12 passes are denoted by the locations of the horizontal bars on the bottom panel (B Z ). As before, the passes have been shifted forward in time so that they match the solar wind conditions that were in effect at the time of that DMSP polar pass. [19] Figure 8 shows the history of the observed potentials for November in the same format as Figure 4. Again, the Northern and Southern Hemisphere histories trend along without matching each other exactly. The potential sharply increases after about 1200 UT to over 200 kv. It reaches a maximum of 224 kv during the UT southern pass (corresponding to the conditions in the solar wind just before B Z reached its minimum), then slowly decreased over the next 8 hours. Again the measured potentials from DMSP-F15 (not shown) mirror this history but do not 8of12

9 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Figure 7. Plot of the solar wind parameters measured by the ACE spacecraft during the 20 November 2003 superstorm in the same format as Figure 3. go as high as F13 with the largest F15 potential being kv. [20] Figure 9 shows the observed potentials for these 12 passes plotted against the corresponding reconnection electric field in the solar wind that was driving the magnetosphere during that pass. Like Figures 5 and 6, the line for the Boyle formula and the two curves for the Hill-Siscoe model (S = 5 and 10 S) are also shown on the plot. The averaged values of the solar wind parameters that were used in calculating these were: V SW = ± km/s; P = ± npa; F(q) = ± The lower solar wind speed significantly reduces the value of the intercept in the Boyle formula line compared with Figures 5 and 6. This time the reconnection electric field in the solar wind ranges from 9.61 to mv/m while the highest potential was the kv pass mentioned above. While the range of data is not as great as the range during the earlier storms, these data do help fill in the middle region of the reconnection electric field. Again, it is obvious that the potentials have saturated even as the electric field increases. 4. Discussion and Conclusions [21] If there were any residual doubt about the reality of the saturation of the potential, the evidence from these superstorms should finally put that to rest. Figure 10 combines all the data from Figures 2, 5, 6, and 9 to show the complete set of all 50 passes. We now have observations under solar wind electric field conditions almost all the way out to 40 mv/m, about 2 1/2 times further out than the data set in the work of Shepherd et al. [2002], which previously had the largest coverage. All the data show clear evidence of saturation for conditions where the reconnection electric field in the solar wind is above about 8 mv/m. [22] The next question is: what is the maximum value of the saturated potential? Although the theoretical value under 9of12

10 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Figure 8. Plot of the potentials observed by DMSP-F13 during the November 2003 superstorm in the same format as Figure 4. the Hill-Siscoe model varies with the size of the electric field, the ram pressure, and the Pedersen conductivity, it appears from these data that the maximum saturation potential during these large storms is generally somewhere between 160 and 250 kv. It should noted here that while these results agree with the results of Shepherd et al. [2002] to the extent that saturation exists and begins to manifest itself when the solar wind electric field becomes large, their work showed no potentials above 120 kv. While this may appear to establish a value for the saturation potential that differs from ours, it is actually an artifact of the restriction of the SuperDARN observation to latitudes greater than 60 magnetic latitude. Under disturbed storm conditions such as these where the convection pattern has expanded well below 60 magnetic latitude, SuperDARN is unable to image the entire convection pattern, so their observed potential drop is likely less than the true potential (J. M. Ruohoniemi, personal communication, 2004). As to the size of the maximum saturation potential, we have searched the entire database of DMSP-F8 ( ) and F13 (1994 present) which are the two dawn-dusk DMSP spacecraft. Out of the roughly 170,000+ polar passes from these two spacecraft, there are only 27 passes where the observed potential drop exceeded 200 kv. Two passes tied for highest observed potential of 258 kv, one during the 31 March 2001 storm and the other during the 10 April 1990 storm. (Unfortunately, there were no solar wind data during the April 1990 event.) This points out two facts: first that it is unlikely that we will ever observe potential drop much (if any) in excess of 260 kv and second, how extremely rarely these superstorm conditions occur. [23] We wish to point out two future avenues of research. First, there is the question of the Pedersen conductivity term in the Hill-Siscoe model. While all the other terms in equation (2) can be measured directly, the Pedersen conductivity cannot. Thus for any given polar pass, we can solve for this one remaining free variable to obtain the Hill- Siscoe prediction of the Pedersen conductivity, and while that result may fall within the range of nominal values for the conductivity, without a way to test independently for the Figure 9. Plot of the observed potentials versus the reconnection electric field in the solar wind for the November 2003 superstorm in the same format as Figures 5 and 6. The averaged parameters during this period were V SW = ± km/s; P = ± npa; F(q) = ± of 12

11 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Figure 10. Combination of all the data points from Figures 2, 5, 6, and 9 to give the entire set of 50 points showing saturation during the 1998 through 2003 period. actual magnitude of the conductivity, there is no way to determine conclusively if the Hill-Siscoe model is valid or not. Although there is no way to directly measure the conductivity over the entire polar cap, the AMIE procedure can produce a map of predicted conductivities based on observations from ground magnetometers, radars, and satellite observations [Lu et al., 2001]. We are currently conducting a study of the AMIE results from the October and November 2003 superstorms to compare the predicted Hill-Siscoe conductivities with the AMIE derived conductivities. The results of this study will be the subject of a future paper. Second, we have focused on the extremes of the solar wind to find if the saturation phenomenon existed or not. As a result, we have ignored all the data from the middle region where the solar wind reconnection electric field is between 4 and 8 mv/m. Since there are more data available as the electric field decreases, we should be able to examine that subset of the database to determine clearly where the turnover occurs between the simple linear function obtained by Boyle et al. [1997] and the saturated region of the Hill-Siscoe model. Such a study is part of our future plans for research. [24] Last, it should be noted that despite all the discussions of the uncertainty in the October ACE density data, this has no real effect on the argument for saturation. The E R versus observed potential plots are not affected by this uncertainty; only the position of the prediction curve of the Hill-Siscoe model are affected. Thus the uncertainly of the densities only affects the question of whether the Hill- Siscoe model is the correct description of saturation, not whether the saturation phenomenon itself is occurring. [25] Acknowledgments. We thank the ACE magnetometer group and Charles Smith at UNH for the magnetometer data used in this work. We also thank K. Ishisaka, H Kojima, H. Matsumoto, and T. Terasawa for providing us with the electron density data from Geotail. The first author would like to thank J. Kozyra, M. Liemohn, G. Siscoe, T. Hill, and J. M. Ruohoniemi for their encouragement and discussions about this work. Work at the University of Texas at Dallas was done under the grants NSF ATM and NASA NAG Work at Los Alamos was performed under the auspices of the U. S. Department of Energy, with financial support from the NASA ACE program. [26] Arthur Richmond thanks George Siscoe and another reviewer for their assistance in evaluating this paper. References Boyle, C. B., P. H. Reiff, and M. R. 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12 HAIRSTON ET AL.: POTENTIAL SATURATION DURING OCT NOV 2003 Ruohoniemi, J. M., and K. B. Baker (1998), Large-scale imaging of highlatitude convection with Super Dual Auroral Radar Network HF radar observation, J. Geophys. Res., 103, 20,797. Russell, C. T., J. G. Luhmann, and G. Lu (2001), Nonlinear response of the polar ionosphere to large values of the interplanetary electric field, J. Geophys. Res., 106, 18,495. Shepherd, S. G., R. A. Greenwald, and J. M. Ruohoniemi (2002), Cross polar cap potentials measured with SuperDARN during quasi-steady solar wind and IMF conditions, J. Geophys. Res., 107(A7), 1094, doi: /2001ja Siscoe, G. L., G. M. Erickson, B. U. O. Sonnerup, N. C. Maynard, J. A. Schoendorf, K. D. Siebert, D. R. Weimer, W. W. White, and G. R. Wilson (2002), Region 1 current-voltage relation: Test of Hill model, saturation, and dipole-strength scaling, J. Geophys. Res., 107(A6), 1075, doi: /2001ja Siscoe, G., J. Raeder, and A. J. Ridley (2004), Transpolar potential saturation models compared, J. Geophys. Res., 109, A09203, doi: / 2003JA Skoug, R. M., J. T. Gosling, J. T. Steinberg, D. J. McComas, C. W. Smith, N. F. Ness, Q. Hu, and L. F. Burlaga (2004), Extremely high speed solar wind: October 2003, J. Geophys. Res., 109, A09102, doi: / 2004JA Weimer, D. R. (1995), Models of high-latitude electric potentials derived with a least error fit of spherical harmonic coefficients, J. Geophys. Res., 100, 19,595. Weimer, D. R. (1996), A flexible, IMF dependent model of high-latitude electric potentials having space weather applications, Geophys. Res. Lett., 23, K. A. Drake and M. R. Hairston, Center for Space Sciences, University of Texas at Dallas, P. O. Box , MS FO22, 2601 North Floyd Road, Richardson, TX , USA. (hairston@utdallas.edu) R. Skoug, Space Science and Applications, Los Alamos National Laboratory, Group ISR-1, MS D466, Los Alamos, NM, 87545, USA. 12 of 12