Temporal structure of the fast convective flow in the plasma sheet: Comparison between observations and two-fluid simulations

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2003ja010002, 2004 Temporal structure of the fast convective flow in the plasma sheet: Comparison between observations and two-fluid simulations Shin-ichi Ohtani Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA Michael A. Shay Institute for Research in Electronic and Applied Physics, University of Maryland, College Park, Maryland, USA Toshifumi Mukai Institute for Space and Astronautical Science, Japan Aerospace Exploration Science, Sagamihara, Japan Received 24 April 2003; revised 4 January 2004; accepted 15 January 2004; published 18 March [1] The present study examines the temporal structure of the fast flow in the plasma sheet using both observations and simulations. The data analysis part adopts the strictest criterion ever for the satellite location so that selected flows are mostly convective. From Geotail measurements at X > 31 R E, 818 earthward-flow and 290 tailward-flow events are selected. Superposed epoch analyses are conducted with two different reference times: the start of the fast flow and the time of a sharp change in the B z component. The results are summarized as follows: (1) The magnetic field becomes dipolar in the course of the fast earthward flow; (2) Sharp dipolarization tends to be preceded by a transient decrease in B Z, which starts along with the fast flow and is accompanied by an increase in the plasma density; (3) The corresponding signatures, albeit less clear, can also be found for the tailward flow; (4) Whereas the plasma density decreases in association with the fast flow irrespective of the flow direction (though, more gradually for the tailward flow), the ion temperature increases for the earthward flow and decreases for the tailward flow; (5) The plasma and total pressures decrease in the course of the fast flow, suggesting the reduction of the lobe field strength; (6) In general, magnetic field and plasma parameters change more gradually in time for the tailward flow than for the earthward flow. Those characteristics of the fast flow can be found irrespective of the X distance, even though the ambient magnetic field and plasma vary significantly between X = 5 and 31 R E. The near-earth reconnection is inferred to be the responsible mechanism for most, if not all, flow events, and the difference between the earthward and tailward flows presumably reflects difference in downstream conditions. On the earthward side of the reconnection site, the flow needs to proceed against the rigid terrestrial magnetic field, whereas on the tailward side the flow does not have any obstruction once reconnection reaches the lobe magnetic field. This idea is consistent with the change of the magnetic inclination, which suggests that the plasma sheet becomes thicker and thinner in the course of the earthward and tailward flows, respectively. These observational results are compared with fast plasma flows modeled by two-fluid simulations of magnetic reconnection. A focus is placed on the reduction of B Z prior to dipolarization for the earthward flow (the precursory B Z increase for the tailward flow) since this is the new finding owing to our strict condition for the convective flow. It is found that the fragmentation of the current sheet and the formation of multiple neutral lines create signatures similar to the satellite observations. After multiple X lines form, one of them dominates and establishes the overall flow pattern associated with reconnection. Magnetic islands formed between the X lines are swept downstream by the reconnection process. The signature of this earthward convection of a magnetic island past a satellite at rest in the magnetotail is a strongly bipolar signature in B z with a sudden enhancement in the density: B z spikes negative and then positive in rapid succession, with a maximum in the density between these two spikes. It is therefore suggested that the temporal structure of Copyright 2004 by the American Geophysical Union /04/2003JA010002$ of16

2 the observed fast plasma flows contains information directly linked to their genesis. INDEX TERMS: 2764 Magnetospheric Physics: Plasma sheet; 2760 Magnetospheric Physics: Plasma convection; 2744 Magnetospheric Physics: Magnetotail; 2753 Magnetospheric Physics: Numerical modeling; 2788 Magnetospheric Physics: Storms and substorms Citation: Ohtani, S., M. A. Shay, and T. Mukai (2004), Temporal structure of the fast convective flow in the plasma sheet: Comparison between observations and two-fluid simulations, J. Geophys. Res., 109,, doi: /2003ja Introduction [2] Fast flow in the plasma sheet is considered to be one of the manifestations of near-earth reconnection. The direction (earthward/tailward) of the convection flow and the orientation (northward/southward) of the accompanying magnetic field have been used for diagnosing the location of a NENL relative to the spacecraft [e.g., Hones, 1977]. Recent analyses of Geotail observations [Nagai et al., 1998; Machida et al., 1999] have revealed that around substorm onsets, tailward convection flows are observed mostly beyond 22 R E, whereas within 30 R E from the Earth, earthward convection flows are observed more frequently than tailward flows. These results suggest that the NENL tends to be formed between X = 22 and 30 R E. The overall distribution of the flow direction also shows an enhancement of the occurrence of tailward flows beyond X = 25 R E [Paterson et al., 1998]. The result of those Geotail studies are also consistent with the earlier reports of the predominant occurrence of earthward flows at X > 20 R E [Cattell and Mozer, 1984; Baumjohann et al., 1989]. [3] Because of its plausible association with near-earth reconnection, these fast flows have been studied in terms of substorm initiation [Sergeev et al., 1995; Shiokawa et al., 1998; Nagai et al., 1998, Miyashita et al., 2003]. However, the generation of a fast flow does not necessarily lead to a global substorm [Lyons et al., 1999; Ieda et al., 2001; Ohtani et al., 2002a, 2002b], and the role of fast plasma flows in the substorm trigger is still controversial. On the other hand, it is accepted widely, if not unanimously [see Paterson et al., 1998, 1999], that fast flows play a significant role in the plasma sheet convection despite its infrequent occurrence [Angelopoulos et al., 1994, 1999]. Thus there is no doubt that fast plasma flows are one of the most important features of magnetotail physics. [4] In order to understand the general characteristics of fast plasma flows, superposed epoch analyses have been carried out for timescales of a few tens of minutes [Angelopoulos et al., 1992; Tu et al., 2000; Schödel et al., 2001]. Whereas these studies set reference times based on the flow velocity [Angelopoulos et al., 1992] or the electric field [Tu et al., 2000; Schödel et al., 2001], some events give the impression that the changes of plasma parameters such as the plasma density are better correlated with the change of the magnetic field [see, e.g., Fairfield et al., 1999, Figure 7]. In fact, fast plasma flows are occasionally observed along with a systematic change of the magnetic field, which can be interpreted in terms of the passage of a magnetic flux rope, and a few studies conducted superposed epoch analyses of the fast flow targeting such a feature [Baker et al., 1987; Slavin et al., 1995, 2003]. It is also interesting that a sharp increase in B Z associated with a fast earthward flow is sometimes preceded by a transient decrease [Slavin et al., 2003; see also of Lyons et al., 1999, Figure 11] as was found for dipolarization events in the geosynchronous region [Ohtani et al., 1992; Erickson et al., 2000]. Those internal structures are possibly averaged out if the superposition timing is based on the flow velocity. [5] If fast earthward flows are created by near-earth reconnection, corresponding features should also be found for fast tailward flows since the reconnection creates flows in both directions. On the other hand, the magnetic configurations on the earthward and tailward sides of a neutral line are quite different. Whereas the earthward flow is likely to be decelerated by the stronger magnetic field as it approaches the near-earth region [Haerendel, 1992; Shiokawa et al., 1998], the tailward flow does not have any such obstruction once reconnection reaches the lobe magnetic field and the field line becomes detached from the Earth. Thus the structure of the tailward flow may not be the mirror image of the structure of the earthward flow, and a comparative study of the earthward and tailward fast flows should be useful for understanding the generation and development of these fast flows. [6] In the present study we examine fast flows in the plasma sheet by statistically examining events observed by the Geotail satellite as well as by carrying out two-fluid simulations of magnetic reconnection. In section 2 we briefly describe the Geotail data set and the event selection. We select fast plasma flows perpendicular to the local magnetic field observed inside the plasma sheet. In section 3 we conduct superposed epoch analyses for the earthward and tailward flows with two different reference times; one is based on the flow velocity and another based on the magnetic field change. In section 4 we conduct two-fluid simulations of reconnection and compare the modeled fast flow with observations. The results of the superposed epoch analysis and the two-fluid simulation are discussed in section 5, section 6 is a summary. 2. Data Set and Event Selection [7] The GEOTAIL satellite was launched in July 1992 into an orbit with the initial apogee at 210 R E from the earth. The apogee was lowered down to 50 R E in mid November 1994 and then to 30 R E in February The perigee distance was lowered from 10 R E to 9 R E in The orbital inclination has been set at 7 to the ecliptic plane. [8] The present study uses data acquired from the magnetic field (MGF) [Kokubun et al., 1994] and the Low Energy Particle (LEP) instruments [Mukai et al., 1994] from October 1993 to July The magnetic field data are averaged every 12 s. The LEP instrument (LEP-EA) measures fluxes of ions with energies up to 40 kev. We use 12-s plasma moments such as density, flow velocity, and tem- 2of16

3 perature. Other plasma parameters such as ion pressure and plasma beta are calculated from the moment data. We adopt the geocentric solar magnetospheric (GSM) coordinate system for presenting the magnetic field and flow velocity. [9] First we decomposed the plasma flow velocity into components parallel and perpendicular to the local magnetic field and then selected intervals when the absolute value of the X component of the perpendicular flow velocity, V?, X, exceeded 300 km/s; this velocity threshold is the same as that adopted by recent studies [Paterson et al., 1998; Angelopoulos et al., 1999]. Compared to earlier studies, which used the X component of the total velocity, the present study therefore tends to select fast convection flows in the plasma sheet. The ion beta, b i, the ratio of the ion thermal pressure to the magnetic pressure, is required to be higher than 0.5. If these conditions are satisfied at a certain data point and there is no such data point during the preceding 15-min interval, that point is selected as a mark of an event candidate. Finally we require that b i be higher than 0.5 for the 10-min interval before the point when jv?, X j was below 200 km/s for the last time before rising above 300 km/s (this timing will be used as one of the references for superposed epoch analyses in section 3). We adopted this last condition so that the superposed signatures are not affected by sudden changes of plasma and magnetic field parameters at spacecraft crossings from the tail lobe to the plasma sheet and vice versa. [10] Figure 1 shows the positions of the Geotail spacecraft for earthward (Figure 1a) and tailward (Figure 1b) fast flow events in the GSM X-Y plane aberrated by 4. Inthe following we examine events that took place at 31 < X GSMA < 5 R E and jy GSMA j <15R E, in the area shown by the dashed rectangle. Here our event list includes 818 earthward flow events and 290 tailward flow events in total. There are more events near the apogee distance of the recent Geotail orbit because the satellite spends more time there. There are significantly more earthward flow events than tailward flow events, which is consistent with the results of the previous studies [e.g., Paterson et al., 1999; Angelopoulos et al., 1999]. [11] It should be useful to examine the characteristics of our event set for distinguishing the present study from superposed epoch analyses reported before. For this purpose we created three different event sets from 12-s Geotail measurements made at 31 < X GSMA < 5 R E and jy GSMA j <15R E, the area we selected for the present study. Those data sets are (1) all data points with V X > 300 km/s and b i > 0.5, (2) all data points with V?, X > 300 km/ s and b i > 0.5, and (3) the representative data points of our selected events, that is, data points with V?,X > 300 km/s following a minimum 10-min interval of b i > 0.5 and separated by at least 15 min from the last time V?, X exceeded 300 km/s. The total number of data points are 88,898 (71,988/16,910 for earthward/tailward flows), 30,204 (24,573/5631), and 1108 (818/290) for event sets 1 3, respectively. The event number ratios of tail flows to all flow events are 19%, 19%, and 26% for event sets 1 3, respectively. Since our event selection requires that the spacecraft stay in the plasma sheet before the flow arrival, the larger percentage of tailward flows in event set 3 suggests that the plasma sheet tends to be either thicker or more stable before the tailward flow than before the earthward flow. Figure 1. Geotail positions in the aberrated X-Y GSM plane for (a) earthward flow and (b) tailward flow events observed during October 1993 July The present study examines 818 earthward flow and 290 tailward flow events that occurred at 31 < X GSMA < 5 R E and jy GSMA j <15R E, the area shown by the dashed rectangle. [12] Figure 2a shows histograms of V X (= V?, X + V k, X ) for those three event sets. Here the number of data points in each velocity bin is divided by the total number of data points in each data set. Event sets 1 3 are denoted by dashed lines, thin solid lines, and thick solid lines, respectively. Event set 1 has cutoffs at V X = 300 and 300 km/s, which is due to the event selection. V?, X and V k,x tend to have the same sign, and therefore the relative ratio of large velocity events is higher for event set 2 than for event set 1. Occasional occurrence of oppositely directed parallel and perpendicular flow components explains events at jv?, X j < 300 km/s. In event set 3, the occurrence of extremely fast flows is far less frequent. This is simply because this event set consists of velocities exceeding 300 kms/s for the first time in each event; it is highly likely that higher velocities are observed after such reference times. Thus this result does not mean that the superposed epoch analysis we describe later is biased to slower flows. 3of16

4 tailward flows (defined based on V X ), respectively, in the same format as Figure 2a. For event set 1, the flow tends to be field-aligned. It is found that jv?, X j < jv k, X j for 60 and 62% of earthward and tailward flows, respectively, in that event set. In contrast, for event set 2, which requires jv?, X j > 300 km/s, jv?, X j > jv k, X j for the majority of events, 68% of earthward flows and 85% of tailward flows. In other words, although the criterion for b i, b i > 0.5, is rather popular for selecting flows in the plasma sheet, it is obviously not strict enough for selecting convective flows; see also Pertrukovich et al. [2001, Figures 1 and 2], who examined in more detail the dependence of q VB on b i for fast earthward flows. For event set 3, the preference for the convective flow is even more overwhelming; jv?, X j > jv k, X j for 97 and 94% of earthward and tailward flows, respectively. This can be attributed to our requirement for b i to be continuously higher than 0.5 for 10 min before the event. This additional selection criterion presumably requires that the spacecraft stay close to the center of the plasma sheet and therefore the observed flow is most likely convective. It is therefore expected that the present superposed epoch analysis will shed new light on the fast convection flow in the plasma sheet, which has not been specifically targeted in previous studies. 3. Observations [14] In this section we examine how magnetic field and plasma parameters change in association with the fast plasma flow. Superposed epoch analyses are conducted separately for the entire earthward and tailward flow events as well as for events in different ranges of the X distance. We also adopt two different reference times: one refers to the start of the fast flow, and the other refers to the time of a sharp change of the B Z component. Figure 2. Histograms of (a) V X (= V?, X + V k, X ), q VB for (b) earthward and (c) tailward flows for event sets 1(dashed), 2(thin solid) and 3 (thick solid). See section 2 for details. [13] What is physically more important is the flow direction relative to the local magnetic field. Here we define q VB as the angle between the flow velocity and the local magnetic field. No distinction is made for the direction of the magnetic field; for example, q VB =0 is zero for both completely parallel and antiparallel plasma flows, and for q VB = 45, jv?, X j = jv k, X j. Figures 2b and 2c show the histograms of q VB for earthward and 3.1. Earthward Flows [15] Figure 3 shows the stack plots of various magnetic field and plasma parameters superposed for the all earthward flows observed at 31 < X GSMA < 5 R E. The resolution of the superposed data is 12 s, the same as that of the original data, and the median, rather than mean, values are used throughout the paper so that the result won t be affected by extreme cases. The horizontal axis covers the 20-min interval centered at T 0V, which is defined as the time jv?, X j was below 200 km/s for the last time before it exceeded 300 km/s; the absolute value of V?, X is used for the definition so that it can also be applied later to the tailward flow. V?; X starts to increase a few minutes before T V (= T T 0V ) = 0, when it increases sharply (Figure 3a); here the overline denotes the superposed value of the quantity. Then V?; X decays gradually. The X component of the absolute value of the parallel flow velocity, V k; X, is comparable to, or is larger than, V?; X both before and after the fast flow. During the fast flow interval, however, V?; X dominates V k;x. [16] Figure 3b plots three magnetic field components. For the X and Y components, their absolute values are plotted. B Z starts to increase around the start of the fast flow and after overshooting, it stays at levels higher than the previous 4of16

5 Figure 3. Various magnetic field and plasma parameters superposed over the 818 fast earthward flow events. The start of the fast flow (T 0V ; see the text for the definition) is used as a reference time. t v = T T 0V. levels. That is, the local magnetic field dipolarizes. jb X j is larger than B Z, suggesting that the spacecraft stays in the plasma sheet (because it is required by our selection criterion) but off the neutral sheet or even close to the plasma sheet boundary layer. jb X j deceases in association with the fast flow, and then it recovers to the same level as B Z. Thus according the magnetic inclination, B Z = jb X j,the spacecraft is closer to the neutral sheet after the fast flow than before, and it is even more so during the interval of the fast flow. This is intriguing especially because we require that the spacecraft stay in the plasma sheet before the arrival of the fast flow (section 2), but no condition is adopted for the spacecraft location after the fast flow. The present result implies that the plasma sheet expands in the course of the fast flow, and it may become thickest temporarily during the fast flow interval. A small peak of jb Y j associated with the fast flow suggests that our event set includes earthward-moving flux rope events, which has guiding magnetic field [Slavin et al., 2003]. We note that the minimum value of b i is 4.0 (Figure 3f ), significantly higher than 0.5, the criterion we adopted, and therefore those magnetic features should not depend sensitively on our selection of minimum b i. [17] The plasma density N (Figure 3c) and ion temperature T i (Figure 3d) decreases and increases, respectively, around t v = 0. The decrease in N overcompensates for the increase in T i resulting in the decrease in the ion pressure P i (Figure 3e); here P i is obtained by superposing P i of each event rather than multiplying N and T i. The total pressure P t also decreases, which we define as the sum of the magnetic pressure and 1.15 times the ion pressure assuming the electron temperature to be 15% of the ion temperature [Slavin et al., 1985; Baumjohann et al., 1989]. Since the force balance must hold between the plasma sheet and the tail lobe, the decrease in P t indicates that the lobe magnetic field decreases, which suggests the reduction of the tail current intensity. The idea is consistent with the dipolarization of the local magnetic field in the plasma sheet. The value of b i decreased in the course of the fast flow (Figure 3f ); note that the decrease in P t can be attributed mostly to the decrease in P i. [18] Figure 4 is the same as Figure 3 except for a reference time. The reference time used here, T 0B, is defined for each event as the start time of the sharpest increase in B Z over three data-point intervals (36 s) within the 4-min interval centered at T 0V. Thus T 0B may be regarded as a reference time for the magnetic reconfiguration associated with the fast flow. The peaks of V?;X are lower than 300 km/s, the criterion for our event selection, because V?, X takes its maximum at different times relative to T 0B in different events. [19] The most noticable feature in B Z (Figure 4b), compared to Figure 3b, is the transient decrease in B Z just prior to the sharp increase. The magnitude of the decrease, as well as that of the overshoot, is larger than the magnitude of the net increase in B Z. Interestingly, V?;X starts to increase a few minutes before T 0B. Another feature that can be seen in Figure 4 but not in Figure 3 is the transient increase in N preceding its sharp decrease at T 0B, which is presumably related to the decrease in B Z. The most noticable increase in T i takes place within 1 min from T 0B. This increase appears to correspond to the increase in B Z. In contrast, in Figure 3, the increase in T i is not so confined around T 0V. It is therefore inferred that the changes of the ion density and temperature are related more closely to the magnetic reconfiguration than to the change of the flow velocity. Overall decreases in P i and P t can be easily recognized. P t peaks slightly after T 0B owing to the enhanced magnetic pressure associated with the sharp increase in B Z. The change of b i is almost the mirror image of that of B Z. [20] In Figure 5 we examine the characteristics of the fast earthward flows for five different ranges of X GSMA listed in Figure 5a with the numbers of events in parentheses. Here again T 0B is taken as a reference time. The plots are less smooth because of smaller numbers of events especially for near-earth events. For each X GSMA range, B Z decreases transiently prior to a sharp increase, and the flow starts to develop a few minutes before T 0B. B Z is larger closer to the 5of16

6 fluctuate significantly and do not follow the systematic trends obtained by superposition (Figure 4). The peak-topeak amplitude of fluctuations often becomes of the same order as the average value of the quantity itself, but such variations are averaged out in the superposed signature. These fluctuations can be attributed partly to temporal variations of the fast flow and partly to satellite motion relative to a plasma sheet structure Tailward Flows [22] Figure 7 shows stack plots of the data for the 290 fast tailward flow events superposed using the reference time T 0V. This figure may be regarded as a counterpart of Figure 3. V?;X, which exceeds V k;x in magnitude around its peak, starts to decrease a few minutes prior to T 0V, when it decreases sharply followed by a gradual increase (Figure 7a). B Z decreases in association with the fast tailward flow, which, however, stays around the zero level Figure 4. The same as Figure 3 except that the start of a main B Z increase (T 0B ; see the text for the definition) is used as a reference time. t b = T T 0B. Earth, which reflects the tail magnetic configuration. Such X dependence can also be found for the plasma density and the ion and total pressures. Since there are significantly more events farther away from the Earth, at 31 < X GSMA < 20 R E, the superposed signatures shown in Figure 4 are weighed by distant events. It is also interesting that closer to the Earth, the peak of V?;X is lower, and V?;X returns to the previous levels more quickly. In other words, the duration of the fast flow is shorter in the near-earth region. [21] To confirm that this precursory decrease in B Z is not an artifact of our definition of T 0B as a reference time, we visually inspected all events and selected 6 events for quick examination. Figure 6 plots V?, X, B Z, and N for each event. V?, X starts to increase almost at the same time as B Z starts to decrease. N tends to increase in association with the B Z decrease, which, however, is not always very clear (see Figures 5b and 5d). Once the flow starts, all quantities Figure 5. Results of the superposed epoch analysis for fast earthward flow events observed in various ranges of X GSMA. Those X GSMA ranges are listed in Figure 5a along with the numbers of events in the parentheses. T 0B is used as a reference time. 6of16

7 Figure 6. Six examples of fast earthward flow events in which B Z decreased transiently just prior to a sharp increase. In the bottom panel of each event, B Z is hatched, whereas N is plotted by the gray line with labels on the right axis. and then increases. Though, we emphasize that what is shown in Figure 7 is the average feature, and in individual events B Z turns negative very often but at different times relative to T 0V. [23] jb X j is significantly larger than B Z throughout the interval. jb X j decreases in association with the fast flow, and then it recovers reaching levels higher than before the arrival of the fast flow. In contrast, B Z decreases in the course of the fast flow. Although it recovers later, the net change of B Z is negative. Thus in terms of the magnetic inclination, the spacecraft tends to be located farther off the neutral sheet, therefore the plasma sheet is thinner, after the fast flow. This is in contrast with the fast earthward flow, for which the plasma sheet thickens. During the interval of the fast tailward flow, jb Y j increases by a factor of more than two and becomes a dominant component. That is, the flux 7of16

8 The sharp decrease in B Z is preceded by a transient increase, which starts simultaneously or slightly after the start of the decrease in V?;X. B Z becomes negative at its minimum, and then it recovers gradually. These features appear to correspond to what we found for the earthward flow in Figure 4. However, N tends to decrease gradually for the tailward flow, whereas for the earthward flow, it increases in association with the precursory B Z change. [26] It is also worth mentioning that this bimodal variation of B Z as well as the accompanying peak of jb Y j is very similar to what has been reported for the plasmoid/flux rope in the distant tail [Baker et al., 1987; Slavin et al., 1995]. However, farther down the tail, the duration of the magnetic variation is much longer (15 min) and the fast velocity lasts even longer. [27] We conducted superposed epoch analyses for different ranges of X GSMA using T 0B as a reference time. The result is shown in Figure 9 in the same format as Figure 5. Figure 7. Various magnetic field and plasma parameters superposed over the 290 fast tailward flow events. T 0V is used as a reference time. rope like feature is more manifest for the tailward flow than for the earthward flow. [24] There are some differences as well as similarities between the earthward flow and the tailward flow regarding the variations of the density, temperature, and pressures. The decrease in N, which is also observed for the earthward flow, is more gradual for the tailward flow. Most noticeably, for the tailward flow, T i increases gradually before the peak of V?;X and then decreases equally gradually; for the earthward flow, in contrast, T i tends to increase, rather than decrease, in the course of the fast flow. The decrease in b i is more significant for the tailward flow than for the earthward flow. [25] We define T 0B for the tailward flow in the same way as we did for the earthward flow except that T 0B marks the start of the sharpest decrease, rather than increase, in B z. Figure 8 shows the result of the superposed epoch analysis. Figure 8. The same as Figure 7 except that the start of a sharp decrease in B Z (T 0B ) is used as a reference time. 8of16

9 negative at several data points, but in other events B Z stayed positive or became negative outside of the interval of the tailward flow. The tailward flow accompanied by positive B Z does not exclude reconnection from the list of candidates for its generation mechanism; at the leading edge of a plasmoid, B Z is positive and the flow is directed tailward. However, it is not straightforward to explain why such a structure tends to be observed closer to the Earth. Schödel et al. [2001] found that the occurrence frequency of enhancement of eastward electric field with positive B Z, which corresponds to the tailward flow, actually tends to increase toward the Earth. They suggested a few possible mechanisms such as the vortex motion of plasma, overshooting of the flow braking, and the bubble-related velocity shear. The return flow of a fast earthward flow is also a possible explanation for such a tailward flow [Lui et al., 1999]. Figure 9. Results of the superposed epoch analysis for fast tailward flow events observed in various ranges of X GSMA. Those X GSMA ranges are listed in Figure 9a along with the numbers of events in the parentheses. T 0B is used as a reference time. We can find basic features we found in Figure 8 although the plots are less smooth owing to the smaller numbers of events. There are three points worth noting. First, closer to the Earth, the maximum tailward velocity ( V?;X ) is smaller and the duration of the fast tailward flow is shorter. This suggests that the tailward flow is more shortlived closer to the Earth as we found for the earthward flow. Second, the increase in B Z prior to the sharp decrease cannot be identified for 20 < X GSMA < 5 R E, whereas it is most manifest in the farthest X GSMA range ( 31 < X GSMA < 25 R E ). Finally, for 20 < X GSMA < 5 R E, B Z stays positive except at a single data point, where it becomes barely negative, 0.8 nt. The negative excursion of B Z is unambiguous farther down the tail. [28] Motivated by this last point, we visually inspected the plots of individual events observed at 20 < X GSMA < 5 R E. It was found that in some events B Z clearly turned 4. Two-Fluid Simulations [29] Magnetic reconnection is a very compelling candidate for producing the fast plasma flows measured in the magnetotail. In order to determine if the key signatures of this superposed epoch study can be reproduced by reconnection, we simulated an idealized reconnection process using two-fluid simulations and examined virtual satellite data. The simulations are very simplistic: the plasma is isothermal, there is no equilibrium B z, the system is symmetric in the X direction, and there are no kinetic effects included in the physical equations. However, even with these limitations, these simulations reproduce the bipolar B z signature and the associated density enhancement observed in the superposed epoch study Simulation Code and Initial Conditions [30] This study was performed using the two-fluid F3D code, which is fully parallelized for the largest available computational platforms using 2-D domain composition with Message Passing Interface (MPI). The Hall equations stepped forward in ¼ r J i ¼ r ðj i J i =NÞþJ B T rn ð2þ ¼ re 0 E 0 ¼ J N B0 J i N B ð3þ ð4þ B 0 ¼ 1 d 2 e r2 B; J ¼rB; ð5þ where J i ion flux, V e = 1 N (J i J) = electron velocity, d e = c/w pe, and T T i + T e = total temperature. Time has been normalized to t 0 = 1 i =(eb 0 /m i c) 1, with B 0 chosen as the initial lobe magnetic pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi field. Length has been normalized to L 0 = c/w pi = c m i = ð4pn 0 e 2 Þ, with N 0 equal to the initial current sheet density minus the lobe density. The velocities 9of16

10 therefore are normalized to the Alfvén velocity. We also assume quasineutrality: N i N e. In these simulations we have taken the isothermal approximation with T = 1.0 so that the sound speed equals the Alfvén speed. In order to prevent energy buildup at the grid scale, we have included fourth order r 4 dissipation in each of the equations. [31] The above equations form a closed set. In Ohm s law in equation (4) the J/N B 0 produces the Hall effect and introduces the scale length c/w pi into the equations. The electron inertia, or electron mass, in Ohm s law manifests itself through the term proportional to d 2 e in the pffiffiffiffiffiffiffiffiffiffiffiffi definition of B 0. In normalized coordinates, d e is equal to m e =m i and is treated as a spatially constant free parameter. At the end of each time step, B is unfolded from B 0 using fast Fourier transforms. [32] The electron to ion mass ratio, m e /m i, is chosen to be 1/25, making c/w pe = 0.2. The simulation domain consists of (n x, n z ) = (2048, 1024) grid points with the physical size (L x, L z ) = (204.8, 102.4), giving a grid scale of 0.1. The boundary conditions are periodic in both directions with boundaries at (x, z) =(±L x /2, ± L z /2). The result that we will show in section 4.2 is not affected by this boundary condition; for an interval we examine, flows ejected in the opposite directions by reconnection have not met yet each other. [33] The initial equilibrium consists of a double current sheet with the following magnetic field: B x ð L z =2 Z 0Þ ¼ tanh½ðz þ L z =4Þ=w 0 Š; and B x ð0 Z L z =2Þ ¼ tanh½ðz L z =4Þ=w 0 Š; where w 0 = 1.0. The density outside of the current sheets is N lobe = 1.0, and rises to 1.5 at the center of the current sheets in such a way as to balance magnetic pressure. All of the initial current is carried by the electrons and the ions are initially at rest. A small magnetic perturbation is added to the system to produce x-lines at (X, Z) =(±L x /4, L z /4). Small random perturbations with j f Bj max and ~J ion max are added to ensure symmetry breaking at the X line Simulation Results [34] As the reconnection process begins and the current sheet thins due to the seed X line, it becomes tearing-mode unstable due to the electron inertia effects in Ohm s law. The tearing instability causes the sheet to break apart into several magnetic islands separated by distinct X lines. This fragmentation of the current sheet has been seen in numerous studies of reconnection [e.g., Büchner et al., 1998; Hesse et al., 1998; Karimabadi et al., 1999; Krauss-Vargan and Omidi, 1995; Kuznetsova et al., 2001; Ma and Bhattacharjee, 1999]. An example of one of these secondary X lines is shown in Figure 10, which shows distributions of J y in gray scale with contours of the magnetic potential for four different times during the simulation. The same gray scale is used for all panels, only magnetic potentials within the current sheet are shown, and the data has been shifted so that the primary X line is initially located at (X, Z) = (10, 0). B x < 0 below the current sheet Figure 10. X-Z distribution of J Y at t = 120, 150, 180, 210. Contours of the Y component of the magnetic potential with the same increment for the four panels have been added. The magnetic field is directed in the positive and negative X directions above and below the neutral sheet, respectively. Note that each panel shows a portion of the entire simulation frame. and B x > 0 above the current sheet. Note that only a small portion of the entire simulation is shown. [35] At t = 120 the current sheet has already fragmented into multiple X lines. The primary X line is located at X =10 and a secondary X line is located at around X = 34. There are two additional secondary X lines located beyond X = 0 to the right of the panel. By t = 150 (Figure 10b), the X line at X = 10 has begun to dominate the global structure and its outflows along X are already beginning to sweep the secondary X line at X 38 downstream in the positive X direction. The motion of this X line to the left accelerates and by t = 210 it has been swept beyond the left boundary of the panel. [36] The convergent flows generated by these two X lines produces a significant enhancement of the density. Figure 11 shows the distribution of the plasma density along with magnetic flux contours within the current sheet at t = 150. The aspect ratio of the figure has been stretched to highlight details in the current sheet. There is a strong density peak in the magnetic island created by the two X lines at X 38 and X 10. [37] The passage of this secondary X line and its associated magnetic island generates a clear signature in virtual 10 of 16

11 generated by the global reconnection process. As this flow burst slams into the unmoving initial current sheet plasma, the magnetic island squashes down, significantly enhancing B z. This compression continues as the island is convected away from the dominant X line at x 10, which is why the negative B z spike in Figure 12b becomes more intense but of shorter duration at the virtual satellite farthest from the X line. Figure 11. X-Z distribution of the plasma density at t = 150. Plotted by gray lines are contours of the Y component of the vector potential. satellites located at X = 42.4 and 52.4, which are marked by solid circles in Figure 10. Figure 12 shows V ix, B z, and N versus time at those two locations. Since both virtual satellites are located in the symmetry plane at the center of the current sheet, V ix is perpendicular to the local magnetic field. Both see qualitatively similar phenomena: As the plasma flow gradually accelerates, the slowly increasing B z suddenly dips strongly negative and then becomes positive, and at the same time there is a sudden spike in the density. After reaching its peak, B z decreases to its asymptotic positive value. At the satellite farther from the X line, the strong negative B z spike becomes more intense but of shorter duration. [38] The relationship between these virtual satellite signatures and the 2-D plasma structure associated with reconnection is as follows. In Figure 12 the gradual increase in B z and V ix at the early stage can be attributed to the initial development of magnetic reconnection. The fracturing of the current sheet into multiple X lines creates multiple magnetic islands and several regions of negative and positive B z. Each of these X lines generates its own set of flows which are superimposed on the global X line flow structure created by the dominant X line at x 10. The convergence of these flows at the center of each magnetic island creates a strong density enhancement there. One of these magnetic islands is clearly shown in Figure 11. Note again that B x > 0 above the current sheet and B x < 0 below the current sheet. As the magnetic island located at 38 x 10 sweeps to the left past the satellite, B z will change from negative to positive with a density maximum at the center of the island where B z 0. In addition, while B z < 0, the flow perturbation from the secondary X line is in the opposite direction from the global reconnection flows, and therefore V ix in Figure 12a shows a transient decrease correlated with the negative B z spike. After this magnetic island has swept past the satellite, V x, B z, and N asymptote to the relatively steady values associated with large scale quasi-steady reconnection: V ix 1, B z 1/10, and N is some intermediate value between the lobe and initial current sheet density. [39] The large value of jb z j inside of the magnetic island relative to the asymptotic value of about 1/10 is due to the compression of the island from two different processes: One, the convergent flows of the multiple X lines naturally compresses the magnetic islands. Two, this island in Figure 11 is on the downstream edge of the fast flow burst 5. Discussion 5.1. Comparison of Earthward and Tailward Flows [40] The result of the superposed epoch analysis shows that B Z increases and decreases in association with the fast earthward and tailward flows, respectively. At first glance, these magnetic variations appear to suggest that magnetic configurations associated with the fast earthward and tailward flows are mirror images of each other as one might expect from reconnection in a slab current configuration. Though, more careful inspection reveals that this is actually not the case. For the earthward flow, B Z is positive before the arrival of the flow and it is larger after the flow. For the tailward flow, B Z is also positive before the flow arrival, and after a transient negative excursion it returns positive but stays at levels lower than the precursory levels. This fact strongly suggests that the net change of the equatorial field strength is positive for the earthward flow, whereas it is negative for the tailward flow. The decrease in B Z associated with the tailward flow may be interpreted in terms of the thinning of the plasma sheet after the release of a plasmoid, which is often envisioned as retreat of a Figure 12. Time variations of V X, B Z, and N for the interval of t = 110 to 250 at X = 42.4 and of 16

12 near-earth neutral line [Hones, 1977]. The thinning of the plasma sheet after the tailward flow is also suggested by the change of the magnetic inclination (section 3.2). For the earthward flow, in contrast, the plasma sheet is inferred to become thicker (section 3.1). [41] T i tends to increase in the course of the earthward flow. For the tailward flow, however, T i tends to increase until the peak of V?;X and then to decrease equally gradually. This difference may be related to the aforementioned net change of B Z associated with each flow. If ions undergo an acceleration process that is controlled by the equatorial magnetic field strength such as the betatron acceleration, the difference in the T i signatures is qualitatively consistent with the fact that B Z increases and decreases in the course of the earthward and tailward flows, respectively. Though, obviously we need to take into account the transport of particles for addressing the issue quantitatively, which, however, is beyond the scope of the present study. [42] The changes of T i and N are more abrupt for the earthward flow, and they are correlated better with the magnetic reconfiguration than with the change of the flow velocity. On the other hand, the gradual decrease in N for the tailward flow appears to be irrelevant to the magnetic change. This contrast may be attributed to different physical conditions surrounding the flow. As the earthward flow approaches the Earth, the ambient magnetic field gets stronger, and the flow is decelerated [Haerendel, 1992; Shiokawa et al., 1998]. Thus it is expected that the associated structure gets confined in the X direction as the flow proceeds, and consequently at a given point, variations of plasma and magnetic field may be observed to be abrupt and correlated. There is no corresponding obstacle for the tailward flow. On the contrary, if the fast tailward flow is associated with the release of a plasmoid, its spatial structure possibly becomes more gradual as the plasmoid expands, which is consistent with the gradual changes of N and T i for the tailward flow Comparison Between Observations and Simulations [43] As examined in section 4, the two-fluid simulations show that the fragmentation of the current sheet and the resultant multiple X lines lead to the formation of magnetic islands. Such formation of multiple neutral lines in the magnetotail has been suggested based on ion distributions observed in the plasma sheet after the passage of a plasmoid [Mukai et al., 1998]. Multiple reconnection has also been addressed as the cause of flux transfer events observed in the dayside magnetosphere [Lee and Fu, 1986; Fu and Lee, 1986], which are widely considered to be flux ropes. Likewise, because of a finite Y component of the tail magnetic field, a structure resulting from multiple reconnection in the magnetotail would also be a flux rope rather than a magnetic island [Hughes and Sibeck, 1987]. Nevertheless, the overall structure of the simulated magnetic island seems to be consistent at least qualitatively with the magnetic variation we found for the fast plasma flow in section 3. Specifically, on the two ends of a magnetic island, the magnetic field perpendicular to the current sheet points in opposite directions. As this magnetic island convects Earthward past a satellite, B Z will show a transient negative excursion followed by a major increase, as was found in section 3.1. [44] A rough comparison between the physical length scales in the simulation and the observations can also be made. Examining Figure 4, the decrease in B Z just before dipolarization has a time duration of about 30 s. Assuming that this structure is propagating at 100 km/s (Figure 5), its spatial scale is estimated at 3000 km or about 0.5 R E.On the other hand, the half width of the magnetic island in Figure 11 is about 10 c/w pi, which corresponds to about 1 R E for a density of 0.2 cm 3. Note that these scales are much shorter than the size of the plasmoid/flux rope observed in the distant tail; a propagation velocity of 300 km/s for a duration of 15 min [Slavin et al., 1995] corresponds to a spatial scale of 45 R E. [45] Comparing velocities is much more difficult because they depend on nonlocal magnetic field parameters which are not available at the location of the satellite: the outflows from idealized reconnection events scale like the Alfvén speed in the region just upstream from the X line [Vasyliunas, 1975]. Depending on whether plasma sheet or lobe magnetic fields are reconnecting, the reconnection Alfvén speed can vary from 500 to 3000 km/s using B = 10 to 20 nt and n = 0.2 to 0.02 cm 3. Clearly the average velocities from the superposed epoch study are significantly less than those expected from a simple reconnection scaling, which may be explained in terms of the deceleration of the fast plasma flow owing to global geometry effects (section 1). Note also that the individual events from Figure 6 show peak flow bursts of up to 800 km/s, and in some cases flow bursts in the magnetotail exceeds 1000 km/s. Therefore averaging of the velocities in the superposed epoch study may also be responsible. [46] There are other differences that deserve close attention. The most obvious difference is that the flow velocity increases continuously in the simulation, whereas the observed fast flow is transient. This implies that if the fast flow is created by reconnection, reconnection operates for only a limited time. This is not surprising, however, because the total magnetic flux carried by a single fast flow can be significant despite its short duration [Angelopoulos et al., 1994, 1999]. Exactly what would cause reconnection to stop so suddenly is an outstanding issue at present. [47] There is another difference associated with the density variation. The superposed profile of N obtained for earthward flows (Figure 4) shows a transient enhancement followed by a sharp density decrease. On the other hand, the modeled density decrease is much more gradual than the preceding density enhancement. One possible reason for this difference is that the time profile of the density variation may depend on the distance from the reconnection site. That is, as a sparse plasma ejected from the primary reconnection catches up the magnetic island, a density decrease at its trailing edge gets confined in space, which is therefore observed as a sharper temporal decrease. Another possible explanation for this difference is due to the large density difference between the central plasma sheet and the lobes. The sudden density drop may be observed as the origin of the arrival plasma changes from the plasma sheet to the tail lobe (more likely, a mixture of plasma sheet and lobe plasma). In the simulations, however, the density drop from the plasma sheet to the lobes is only 50%. [48] Regarding the density profile, it is also worth mentioning that the simulation predicts that the density peaks at 12 of 16

13 the reversal of the sign of B Z, whereas the result of the superposed epoch analysis shows that the density peak coincides with the minimum of B Z (Figure 4), which can also be confirmed for some, but not all, individual events (Figure 6). More interestingly, N and B Z tend to change out of phase not only at the very beginning (as identified by the B Z reduction) but also throughout events (Figure 6). In other words, the observation suggests that N and B Z change in such a way that they are proxies of the plasma pressure and magnetic pressure, respectively, and those pressures keep force balance by themselves. In contrast, in the simulation, the density (plasma pressure) enhancement inside the magnetic island is balanced with the magnetic tension, rather than, the magnetic pressure. It is therefore possible that the fast flow is modified as it propagates farther, which may be tested in the future by following the flow for a much longer length. [49] The most interesting difference between the observed and simulated features is the profile of the B Z variation. The superposed B Z signature never becomes negative before the main dipolarization. Although B Z becomes negative in some events (see Figure 5a), we found such events are a minority. On the other hand, B Z becomes inevitably negative at the leading edge of the earthward-moving magnetic island. If a current flowing along its core is somehow shunted, the magnetic island (or flux rope) is annihilated, which likely creates a region of weak magnetic field just on the earthward side of the region of strong northward B Z. [50] Interestingly, Slavin et al. [2003] have found that for earthward-moving flux ropes observed in the near-earth plasma sheet, the northward magnetic flux exceeds the southward magnetic flux, although they are ideally considered to balance. They suggested the southward-directed magnetic flux dissipates quickly as it pushes against the northward geomagnetic field in the near-earth region; they called this process re-reconnection. Thus it is also possible that the decrease in B Z observed prior to dipolarization may be a remnant feature of the flux ropes. [51] If the B Z decrease observed prior to the main dipolarization is indeed created by the fragmentation of the current and the generation of magnetic islands, the result of the present study implies that the formation of multiple neutral lines is not unusual. Such a conclusion is not surprising considering that the thickness of the tail current sheet can decrease below 1 R E far outside of geosynchronous altitude before substorm onsets [e.g., Sanny et al., 1994] and that the plasma sheet is highly turbulent [e.g., Borovsky et al., 1997]. [52] Here events shown in Figure 6 can be attributed to the formation of a dominant neutral line with a single secondary neutral line on its earthward side. On the other hand, sharp dipolarization events without such a precursory B Z decrease, which are observed at least equally frequently, may indicate either that only one neutral line is formed or that the most Earthward neutral line becomes dominant. When a dominant neutral line grows in the middle of many neutral lines, the resultant plasma flow structure could be very complex; however, it is also possible that many smallscale reconnection (tearing) vortices coalesce into a coherent structure such as a plasmoid [Hoshino et al., 1994]. Caution needs to be exercised also because spacecraft motion relative to a structure can cause additional complexity of observed signatures. [53] Recently, Hashimoto et al. [2004] conducted a 3-D MHD simulation of reconnection with a guiding field. The result shows that the flow distribution in the Y-Z plane is skewed from the Z axis so that the guiding field line in front of the flow jet is bent, and it has a negative B Z component at the center of the plasma sheet. This could be an alternative explanation of the precursory B Z reduction, and a detailed comparison with the observation is the subject of our future study Connection to Near-Earth Signatures [54] In section 3.1 we found that the transient decrease in B Z just prior to sudden dipolarization is a common feature for earthward fast flows. It is likely that this B Z decrease was averaged out in the past superposed epoch analyses of the fast earthward flow [Angelopoulos et al., 1992; Schödel et al., 2001] because those studies set the epoch time based on the profile of the flow velocity or the electric field. Another possibility is that events with this B z decrease are confined near the neutral sheet and therefore would comprise much higher percentage of the total events in this study, since we specifically selected events in which the spacecraft stayed in the plasma sheet (section 2). The feature was observed irrespective of the distance from the Earth (Figure 5), and the corresponding signature was found for the tailward flow (Figures 8 and 9). It is therefore inferred that this precursory decrease in B Z is related to the generation process of the fast flow, and in fact, we found in section 4 that a similar feature can be reproduced by multiple reconnection. [55] On the other hand, a feature similar to this precursory decrease in B Z has been reported previously by Ohtani et al. [1991, 1992], who examined dipolarization events observed by the AMPTE/CCE satellite within 8.8 R E from the Earth. The associated anisotropy of energetic ion fluxes indicates that the source current is located on the tailward side of the spacecraft, which strongly suggests that the decrease in B Z is caused by the sudden intensification of the tail current; thus it was often called explosive growth phase. Such an exponential intensification of the tail current before its disruption was also suggested based on in situ measurements of energetic particles [Ohtani et al., 2000]. A similar feature was reproduced by a Hall MHD simulation [Ma and Bhattacharjee, 1996], which showed that as the current sheet becomes thinner than the ion skin depth, the intensification of the current changes from a sluggish linear phase to a rapid nonlinear phase. [56] The precursory decrease in B Z examined in the present study is accompanied by the earthward fast flow and is therefore a propagating signature. This is consistent with the fact that the feature identified as the explosive growth phase tends to be observed in association with the earthward propagation of dipolarization in the geosynchronous region [Ohtani, 1998]. A similar feature can also be found in the result of a hybrid simulation [Hesse et al., 1998], which reveals that the tail current intensifies at the leading edge of the B Z enhancement associated with the earthward flow. Thus it is tempting to regard the precursory B Z decrease observed by Geotail as the same as was observed in the geosynchronous region. In fact, some events were observed in the same X GSMA distance range as the AMPTE/CCE events (Figure 1). 13 of 16