Total pressure variations in the magnetotail as a function of the position and the substorm magnitude

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2003ja010196, 2004 Total pressure variations in the magnetotail as a function of the position and the substorm magnitude R. Yamaguchi, 1,2 H. Kawano, 3 S. Ohtani, 4 S. Kokubun, 5 and K. Yumoto 3 Received 16 August 2003; revised 29 December 2003; accepted 16 January 2004; published 11 March [1] The present study investigates the energy storage and release processes of substorms as a function of both position and substorm intensity in a model-independent manner. As an index of the substorm intensity, we use the amplitude of the positive bay observed at middle and low latitudes. As an index of the energy storage and release in the magnetotail, we use the total pressure measured by Geotail. We have performed a superposed epoch analysis of the total pressure for each substorm group binned in terms of the position and the substorm intensity. We have found that (1) both the magnitude and the increasing rate of the total pressure (i.e., energy density) in the near-tail region ( 15 R E <X GSM < 6 R E and 8 R E <Y GSM <8 R E ) are highly correlated with the substorm intensity, while those in the midtail ( 25 R E <X GSM < 15 R E and 10 R E <Y GSM <10 R E ) are not correlated with the substorm intensity. We have also found that (2) the start of the energy release of small substorms in the near-tail region tends to be delayed from the first Pi2 onset. INDEX TERMS: 2788 Magnetospheric Physics: Storms and substorms; 2740 Magnetospheric Physics: Magnetospheric configuration and dynamics; 2744 Magnetospheric Physics: Magnetotail; 2764 Magnetospheric Physics: Plasma sheet; 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions; KEYWORDS: substorm, total pressure, Geotail, CPMN magnetometers, Pi2, positive bay Citation: Yamaguchi, R., H. Kawano, S. Ohtani, S. Kokubun, and K. Yumoto (2004), Total pressure variations in the magnetotail as a function of the position and the substorm magnitude, J. Geophys. Res., 109,, doi: /2003ja Introduction [2] How substorm onsets occur and what controls their occurrence are basic and important questions in the study of substorms. Two popular models are the near-earth neutral line (NENL) model and the current disruption (CD) model, and many studies have been made based on each model [e.g., Baker, 1996; Lui, 1996]. In the NENL model, the substorm onset is triggered by the tail field reconnection at about X GSM 20 R E [e.g., Nagai et al., 1998]. In the current disruption model, the substorm onset is triggered by the disruption of the tail current, caused by some plasma instability, in a thin plasma sheet at about X GSM 8 R E [Ohtani et al., 1998, and references therein]. Validity of the two mechanisms is still under study, but one of the most obvious differences between the two models is the radial distance of occurrence of the onset process. 1 The Institute of Statistical Mathematics, Minato-ku, Tokyo, Japan. 2 Now at Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka, Japan. 3 Department of Earth and Planetary Sciences, Kyushu University, Hakozaki, Fukuoka, Japan. 4 Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland, USA. 5 Solar Terrestrial Environment Laboratory, Nagoya University, Toyokawa, Japan. Copyright 2004 by the American Geophysical Union /04/2003JA [3] The energetics of substorms has drawn considerable attention because substorm is a process in which energy is stored in the magnetotail through the solar wind-magnetosphere interaction and then released explosively, causing the most dramatic phenomena in various regions of the magnetosphere and in the ionosphere. Some studies use the pressure in the magnetotail as a measure of the storage and release of substorm energy. Caan et al. [1978] examined the magnetic pressure variation in the lobe during substorms and found that the magnetic pressure increases before the onset and decreases after the onset. Miyashita et al. [1999] studied the total pressure variation around the substorm onset with data obtained by the Geotail spacecraft [Nishida, 1994]. Their result suggested the total pressure decrease starts first at around (X, Y) GSM ( 18, 7) R E about 1 or 2 min before Pi2 onsets observed at a midlatitude station. [4] The above-mentioned studies addressed the average picture of substorms. However, different substorms have different intensities, and the comprehensive understanding of the substorm magnitude dependence of substorm features (the occurrence area, the pattern of the energy storage and release, etc.) is still lacking. Thus needed is a study on substorms considering both their size and occurrence area. [5] The present study investigates the energy storage and release processes of substorms as a function of both position and substorm intensity. In this study, we focus on isolated substorm onsets. As the measure of the substorm magni- 1of14

2 Figure 1. The map of ground magnetometer stations in the Circum-pan Pacific Magnetometer Network (CPMN); they observe the geomagnetic three components (H, D, and Z) with 1-s or 3-s resolution. tude, we use the amplitude of the positive bay observed at middle and low latitudes. Because the positive bay is a remote effect of the substorm current system, local perturbations of the current density in the current system are smoothed out, and thus the amplitude of the positive bay is regarded as a good indicator of the total intensity of the current [e.g., Kamide and Akasofu, 1974]. As the measure of the energy storage and release in the magnetotail, we use the total pressure obtained by Geotail. [6] We perform a superposed epoch analysis of the total pressure at Geotail for each of substorm groups classified by the observed position and the magnitude. In section 2 we will describe the data sets of this study. In section 3, procedures to make a substorm database will be explained. In section 4, analyses will be performed. In section 5 we will discuss the results. Section 6 presents a summary and conclusion. 2. Data 2.1. Ground Observations [7] In order to select Pi2 onsets and positive bays, we used geomagnetic data obtained by the Circum-pan Pacific Magnetometer Network Group (the CPMN group) [Yumoto et al., 1996, 2001]. The period analyzed is from September 1993 to April Figure 1 shows the locations of the stations of the CPMN, and the station names with emphasized letters are the stations used in this study. Such stations are divided into two groups; one group is along the 210 magnetic meridian (MM), and another group is in South America. Each group includes four stations. The coordinates of the stations are listed in Table 1. The sampling time of the data sets is 3 s. Each data set contains the three geomagnetic components (H, D, and Z) Satellite Observation [8] The Geotail satellite was launched in July Until October 1994, Geotail mostly surveyed the distant-tail region, and the apogee distance ranged from 80 to 220 R E. After November 1994, the apogee was lowered first to 50 R E and then to 30 R E in order to survey the midtail and near-tail region. [9] Magnetic field measurements are carried out with the magnetic field experiment (MGF) on board the satellite [Kokubun et al., 1994]. We use 12-s averages of B x, B y, B z, and B t (the magnetic field intensity) in GSM coordinates. Ion and electron measurements are carried out with the low-energy particle (LEP) experiments [Mukai et al., 1994], which has an upper energy limit of approximately 40 kev for ions and electrons. Ion number density, ion temperature, and plasma ion velocity (V x, V y, and V z in GSM coordinates) are obtained for all observation intervals. The time resolution of the LEP data used in this study is 12 s. 3. Event Selection [10] To carry out a statistical study, we have made a database which contains substorm onset (Pi2 onset) times and substorm intensities (positive-bay amplitude) by using previously mentioned multipoint midlatitude to low-latitude magnetometer data. Then we have selected substorm events 2of14

3 Table 1. Coordinates of Stations Geographic Geomagnetic Station Name Abbrev. Lat. Long. Lat. Long. 210 MM Group Magadan MGA Moshiri MSR Guam GUA Birdsville BSV South American Group Belem BLM Eusebio EUS Teresina TER Santa Maria SMA during which Geotail was located in the magnetotail. The essence of the selection procedures will be described in the following (more details are given in Appendix A) Database Construction From Ground Data [11] We regarded an event as a substorm onset if a Pi2 was observed simultaneously in the 210 MM group or, in the South American group, when they were located near midnight. We have chosen isolated substorm onsets (defined as an onset with no other onsets in the preceding 30-min interval). Figure 2 shows an example of isolated substorm onsets. A Pi2 onset time (t 0 ) was determined by visual inspection (vertical solid line in each panel). We note that the isolated substorm onsets by definition include the first onsets followed by other onsets. [12] To estimate the substorm intensity, we have used the amplitude of the positive bay at 10 min after the Pi2 onset. The positive bay represents an effect of the three-dimensional substorm current system. The H component is expected to be maximum at the longitudinal center of the substorm current system, while the D component should be pmaximum ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi at its azimuthal edges. Thus this study uses DB = DH 2 þ DD 2, instead of DH, as a measure of the substorm intensity, where DH = H t (t min) H t (t 0 ) and DD = D t (t min) D t (t 0 ) (the subscript t means band-pass filtering; see Appendix A for its details.) [13] We note here that as a measure of the substorm intensity, we use DB during the first 10 min rather than the maximum bay amplitude. We do so because there are often multiple onsets from the initial onset time till the maximum bay amplitude time. For such cases, the ionospheric conductivity during the second and following onsets would be enhanced by the particle precipitation during the first onset, which biases the current intensity during the second and following onsets. Thus in this paper, in order to estimate the intensity of substorms with a same standard, we use the first onset; because the peak amplitude of the first onset is usually difficult to identify due to superposition of the following onsets, we use the above-defined DB. Assuming that the first onset has a simple increase-then-decrease waveform, it is natural that DB is proportional to the peak amplitude of the first onset. (We will see later in Figure 11 that DB is fairly proportional to the maximum bay amplitude so that the usage of DB is not different much from using the maximum bay amplitude, anyway.) [14] DB also depends on local time and latitude. We therefore use the normalized amplitude of the positive bay, DB norm, in which the local time and latitude dependence is removed. A total of 997 substorm events was selected. The details are described in Appendix A Event Selection With Geotail [15] We then selected substorm events in which Geotail stayed in the nightside magnetosphere for the 2-hour interval centered at the onset. In order to exclude intervals when Geotail was outside of the magnetosphere, we used similar criteria to what Nakamura et al. [1997] used to select magnetosheath intervals: High density (N > 1/cm 3 ), low temperature (T < 400 ev), antisunward flow (V x < 300 km/s), and large dynamic pressure (mnv 2 > 1 npa). If all the above conditions or (N > 5/cm 3 ) are satisfied even once during the (onset ±1 hour) interval, then the event was discarded. The final database includes 252 events Event Classification by Position and Intensity [16] We have divided the selected substorm events into two groups: A small positive bay group and a large positive bay group. So that the events of each group has sufficient number for the statistical analysis in section 4, we have divided the events in half. [17] As shown in Figure 3, the small (large) positive bay group consists of the first (last) half of the selected 252 events sorted in the ascending order of the positive bay intensity (DB norm ); the median of the 252 DB norm sis nt. Each group contains 126 events. The result of the statistical analysis would justify the above grouping based on the use of DB norm later by showing a feature of the energy storage and release process of substorms which would not appear with undivided events. [18] We have also divided the magnetotail into seven areas according to the X and Y coordinates as listed in Table 2. Figure 4 shows the seven areas and the locations of Geotail at the Pi2 onsets. Table 2 also shows the numbers of the events of each group included in each bin. Table 3 shows the mean intensity of DB norm (the value in the brackets) of each group included in each bin. The value on the left (right) side of each bracket is the small (large) side of the error bar range. [19] Regarding the mean values for the small groups, there are no significant differences because the error bar ranges of all bins are overlapped. The mean values for the large groups in BIN4 and BIN7 are significantly larger than those for BIN2 and BIN3. However, we note that there are 3of14

4 Figure 2. An example of positive bay in H component (top three panels) and Pi2 in dh component. Time derivative of H (bottom three panels), which was simultaneously observed at three stations along the 210 magnetic meridian when they were located in the midnight sector. Vertical solid line in each panel indicates the Pi2 onset defined by visual inspection. no significant differences between those for BIN1 and BIN3 where we mainly focus on the following analysis. 4. Data Analysis 4.1. Superposed Epoch Analysis of the Total Pressure [20] We have performed a superposed epoch analysis of the total pressure referring to the Pi2 onset. By using the magnetic field data and the plasma data of Geotail, we can obtain the magnetic pressure and the thermal pressure in the magnetosphere. Magnetic pressure P mag is defined by P mag ¼ B 2 obs =2m 0; where B obs is the observed magnetic field strength. Thermal pressure P thr is defined here by P thr ¼ nkt ion 1:2; where n and T ion are the number density of ions and the ion temperature, respectively. The factor 1.2 reflects the ð1þ ð2þ contribution of electrons. Then the total pressure P total is defined by P total ¼ P mag þ P thr : ð3þ Before the superposed epoch analysis, we removed from the observed total pressure the average background pressure variation due to the orbital motion of the satellite; Tsyganenko and Stern [1996] (T96) model magnetospheric lobe pressure has been used as the background pressure under the assumption of the pressure balance along the Z GSM total /@z = 0. (We note that Baumjohann et al. [1990] have confirmed by using satellite data that the pressure balance is generally satisfied along the Z GSM direction.) That is, background pressure P BG is defined as where P BG ¼ B 2 T96;lobe =2m 0; B T96;lobe ¼ B T96;lobe x abr ; y abr ; P SW;dyn ; q tilt is the maximum model magnetic field strength along a line parallel to the Z GSM -axis and running through (x abr, y abr ), ð4þ ð5þ 4of14

5 Figure 3. Substorm events selected by comparisons between ground data and Geotail data (252 events in total). They are sorted by the positive bay amplitude (DB norm ). The events are divided into two groups, small positive bay group and large positive bay group, so that each group contains a half of the entire events (i.e., 126 events). where x abr and y abr are the satellite coordinates aberrated by 4 from the GSM coordinates, P SW,dyn and q tilt are the solar wind dynamic pressure and the dipole tilt angle, respectively, and P SW,dyn = 2.0 npa and q tilt =0 are used as the nominal solar wind condition. [21] An underlying assumption here is that the dynamic pressure is the same, on average, for both large and small groups and that the average tilt angle is zero for both groups. However, the former assumption is not actually correct, which we will discuss later. [22] The perturbation of the total pressure is calculated as DP total ¼ P total P BG : We have performed the superposed epoch analysis of thus obtained DP total for each group ( large positive bay group and small positive bay group ) in each bin, during ±1-hour of each Pi2 onset (t 0 ). The resultant total pressure profiles are shown in Figure 5 and Figure 6. [23] The patterns of the total pressure variation for the large positive bay group are generally consistent with Caan et al. s [1978] result; that is, the magnetic pressure in the lobe increases before the onset and decreases after the onset. The range of the satellite s position they used was 20 R E < X GSM < 9 R E. [24] Both figures also show that the increasing rate of the total pressure in BIN1 (Figure 5a) strongly depends on the substorm intensity, while there are weaker dependence in the other BINs, and the total pressure enhancement in BIN1 is the largest of all the bins for both the large positive bay group and small positive bay group. These features will be discussed in section Delay of the Total Pressure Peak From the Onset of Small Substorms Observed Near Earth [25] The result of the superposed epoch analysis of the small substorm group in BIN1 (see Figure 5a) shows that ð6þ the peak of the total pressure is delayed from the Pi2 onset by about 30-min. To understand this delay, all events of the group were visually inspected. Figure 7 shows an example of the large positive bay group, which clearly shows that the total pressure increased till the onset and started decreasing just after the onset and that the positive bay started at the onset. We call this type of events as no-delay type. It is notable that the energy release started just after the first Pi2 onset even though there were some succeeding wave packets. On the other hand, Figure 8 is an example of the small positive bay group, which clearly shows that the peak of the total pressure had a delay from the first Pi2 onset by about 34 min. We also note that there were three or more succeeding wave packets after the first Pi2 wave packet and the pressure started to decrease during the occurrences of the succeeding wave packets. We call this type of event delay type. Eleven out of 13 events in the small positive bay group are classified into the delay type. [26] We note that the the pressure variations in BIN2, especially for the small substorm group, are much smaller than those in BIN1. In addition, BIN2 does not show a coherent response to substorms. Thus even if there exists a delay in BIN2 similar to that in BIN1, it is unidentifiable in the data. The small pressure changes and the incoherence in BIN2 suggest that the effect of the substorm, starting from a midnightside meridian, does not reach the region of BIN Pressure Offset Correction [27] The offsets of DP total s of the large positive bay group and the small positive bay group for BIN 1 are significantly different (Figure 5a). We define here the offset as the value of DP total at the time 1 hour before the Pi2 onset. A possible reason of this offset difference is a difference in the solar wind dynamic pressure. For Figure 5a we assumed the same dynamic pressure, P SW,dyn = 2.0 npa, for each events but it is actually different from case to case, and if the average of P SW,dyn for the small positive bay group is significantly different from that for the large positive bay group, that leads to different values of the background pressure, P BG. [28] To test this idea, we have investigated P SW,dyn by using 10-min averaged interplanetary magnetic field (IMF) data and the plasma ion bulk velocity data obtained by Wind or IMP 8. The procedure to obtain a reference value of P SW,dyn for the background field is as follows. First, a Table 2. Areas of the Bins and the Number of the Events in Each Bin Areas of the Bins X GSM, R E Y GSM, R E Large Positive Bay Number of the Events Small Positive Bay BIN 1 15 < X < 6 jyj < BIN 2 15 < X < 6 jyj >8 7 8 BIN 3 25 < X < 15 jyj < BIN 4 25 < X < 15 jyj > BIN 5 60 < X < 25 jyj < BIN 6 60 < X < 25 jyj > BIN 7 < X < Total of14

6 Figure 4. Geotail positions ( ) at the Pi2 onsets in the X GSM Y GSM plane, along with the geometry of the bins (see Table 2). The top panel shows all of the bins. The bottom panel shows a magnified image of BIN 1, BIN 2, BIN 3, and BIN 4. 4-hour period of the data preceding the onset is selected. Next, the data time, t SW, is corrected for the propagation time lag of the solar wind by tsw 0 ¼ t SW þ XB y YB x = Vx B y þ V y B x ; where X and Y are GSE components of the spacecraft position in the solar wind, B x and B y are GSE components of the IMF, and V x and V y are GSE components of the solar wind ion bulk velocity. The above lag correction equation is the same as the one used by Kawano and Russell [1997]. Here it is assumed that the solar wind is uniform along the IMF field lines. Then a set of three continuous data points in which IMF Bz (in GSM coordinates) was positive is searched backward from the onset time. If these points are detected, the value of P SW,dyn at the time of the center point of the three points is regarded as the reference pressure. If these points are not detected until the head of the data, then the value of P SW,dyn at the time of the point at which IMF Bz (in GSM coordinates) takes the largest value during the period from 90 to 30 min before the onset is selected as the reference pressure. [29] The solar wind data are available for all but one events in BIN 1 (that is, for 10 events in the large positive bay group and 13 events in the small positive bay group). Plotted in Figure 9 against the substorm intensity are the reference solar wind dynamic pressures and their averages for the two group. There is a significant difference between the large positive bay group and the small positive bay group. [30] This result seems to be consistent with the reported empirical relationship in which the magnitude of the AL index is mainly determined by B s V sw 2, where B s is the southward component of the IMF and V sw is the solar wind velocity [Murayama et al., 1980]. This suggests that AL has positive correlation with the solar wind dynamic pressure rv sw 2, where r is the solar wind density. [31] Then we have performed for events in BIN 1 the superposed epoch analysis again along the same procedure as the previous one but by inserting the observed reference solar wind dynamic pressure and the dipole tilt angle into equation (5) for each event. As a result, Figure 10 (right panel) shows a smaller offset difference than before (left panel). 5. Discussion 5.1. Where is the Energy for Substorm Stored and Released? [32] Figures 5 and 6 show that among the BINs which show the increase-then-decrease pattern of the total pressure, the difference between the large-substorm group (thick line) Table 3. Mean of DB norm (nt) and the Error Bar Range in Each Bin Large Positive Bay Small Positive Bay BIN [5.12] [1.33] 1.47 BIN [3.89] [1.49] 1.71 BIN [4.22] [1.42] 1.56 BIN [6.79] [1.38] 1.51 BIN [5.70] [1.48] 1.59 BIN [4.39] [1.42] 1.54 BIN [6.03] [1.47] of14

7 Figure 5. The results of superposed epoch analysis of the total pressure variation around isolated Pi2 onsets (defined as a Pi2 with no other Pi2 wave packets in the preceding 30-min interval) for large positive bay group (thick line) and small positive bay group (thin line) in each of (a) BIN 1, (b) BIN 2, (c) BIN 3, and (d) BIN 4. and the small-substorm group (thin line) is the biggest for BIN 1 ( 15 R E <X GSM < 6R E and 8R E <Y GSM <8R E ). [33] The increasing rate of the total pressure in BIN 1 is strongly correlated with the substorm intensity. That is, there is a significant difference between the large and the small substorm groups: The error bars in BIN1 do not overlap even after the offset in the background pressure is corrected (see Figure 10). On the other hand, the correlation with the substorm intensity is much weaker in the other BINs. This result implies that the supply of the energy used for substorms mainly occurs in BIN 1 and its intensity has a good correlation with the amount of pressure enhancement 7of14

8 Figure 6. The results of superposed epoch analysis of the total pressure variation around isolated Pi2 onsets (defined as a Pi2 with no other Pi2 wave packets in the preceding 30-min interval) for large positive bay group (thick line) and small positive bay group (thin line) in each of (e) BIN 5, (f ) BIN 6, and (g) BIN 7. prior to the onset in there. This is consistent with the reported good correlation between the degree of tail-like magnetic field distortion (which is also the measure of the energy storage) prior to the onset at the geosynchronous orbit and the magnitude of the dipolarization there (which is also the measure of the substorm intensity) [Kokubun and McPherron, 1981; Lopez and Rosenvinge, 1993], and it is also consistent with the reported good correlation between the preonset deviation of the geosynchronous magnetic field from the dipolar configuration and AE [Lopez and Rosenvinge, 1993]. It is in accord with Kaufmann s [1987] model calculation, which suggested the major growth and disruption of the cross-tail current occur in the near-tail region. 8of14

9 Figure 7. An example of the large positive bay group in BIN 1. Top panel: Total pressure variation around an isolated Pi2 onset (defined as a Pi2 with no other Pi2 wave packets in the preceding 30-min interval) at Geotail. Middle panel: An isolated positive bay p (defined as a positive bay with no other positive bay in the preceding 30-min interval) variation of DB = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DH 2 þ DD 2. Bottom panel: An isolated Pi2 onset in bandpassed H data (T = s). The vertical solid lines show the Pi2 onset time. Figure 8. An example of the small positive bay group in BIN 1, in the same format as Figure 7. 9of14

10 Figure 9. A plot of solar wind dynamic pressure before onset for the small positive bay group (S) and the large positive bay group (L) and their averages ( ) against substorm intensity (DB norm ). [34] As is also shown in Figure 5 and Figure 6, the total pressure enhancement in BIN 1 is the largest irrespective of the intensity of substorms. We note that this result does not directly mean that the gain of the energy quantity during growth phase stored in BIN 1 is larger than that in BIN 3 because the total pressure is the energy density and, in order to calculate the energy quantity, the variation of the volume of the magnetosphere for each region needs to be estimated precisely and such estimation is still difficult. However, we stress here that regardless of its cause, both the magnitude and the increasing rate of the total pressure (i.e., energy density) in BIN 1 are highly correlated with the substorm intensity, and this paper reports it for the first time using observed data. [35] It is notable that the pressure profiles in BIN 7 do not show signatures corresponding to passages of plasmoids. It is explained as follows. As a plasmoid moves downtail, its effect on a satellite is maximum when the center of the plasmoid is located at the GSM-X position of the satellite. Since BIN 7 has a wide X coverage, the times (measured from the expansion onset) when plasmoids pass through the satellite position (which has a wide X range) are also widely scattered. Thus when averaged in BIN 7, the plasmoid signals are likely to have been smoothed out. [36] According to previous studies [e.g., Baker, 1996; Lui, 1996], BIN 1 corresponds to the current disruption (CD) region, while BIN 3 corresponds to the NENL region. As stated above, the magnitude of the total pressure variation has a good correlation with the substorm intensity only in BIN 1. [37] A straightforward interpretation of this result is that the process which is said to usually occur in BIN 1, i.e., Figure 10. The offset correction for the result of superposed epoch analysis of DP total in BIN 1. Left panel (the same as Figure 5a) shows DP total before the correction: P SW,dyn = 2.0 npa and q tilt =0. Right panel shows DP total after the correction. For each event, P SW,dyn is its observed value, and q tilt corresponds to its observing time. 10 of 14

11 Figure 11. The result of the superposed epoch analysis of the positive bay corresponding to the events in BIN 1 during ±2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hours around each Pi2 onset. The median of db(t) = dhðtþ 2 þ ddðtþ 2 for the large (small) positive bay group are plotted by a thick (thin) line. CD, controls the substorm intensity. Note this does not deny the occurrence of NENL: It should be occurring, but its efficiency does not appear to significantly control the substorm intensity (see the overlapping error bars in Figure 5c). [38] One may say CD cannot decrease the pressure in BIN 1 because it takes place in the closed-field region; however, actually it can. CD removes the (closed) magnetic flux from BIN 1 via dipolarization (moves the closed flux more earthward). If this removal rate is larger than the flux addition (pile-up) rate from NENL, the total (closed) flux decreases in BIN 1. This means that the total (open plus closed) flux decreases, too. This is consistent with the observation. What reduces the open flux amount in BIN 1 is NENL at BIN 3. To be more precise, NENL first changes some of the lobe flux in BIN1 from open to closed, and then the redistribution of the closed flux in BIN1 causes the decrease in the total magnetic flux. Aggson et al. [1983] observationally suggested an earthward transfer of the magnetic flux just after a large substorm onset in the midnight, lowlatitude, L = 7.5 region of the magnetotail by using the electric field measurement. This may support the above scenario Timing of the Energy Release [39] Pi2s often occur with multiple wave packets. We have found that for the small substorm group, the release of the energy stored in BIN1 is delayed from the first Pi2 onset (see Figure 8), whereas for the large substorm group, the energy is released almost at the same time as the first Pi2 onset (see Figure 7). We also note that for both types, Pi2s often occur with multiple wave packets. [40] From this result we consider that Pi2 is a signal which accompanies some process attempting to trigger the release of the stored energy. If the energy stored in BIN1 is not sufficient, several triggering attempts may be necessary before the energy release is actually triggered (i.e., expansion onset), thus the onset may take place at a later Pi2 onset. [41] Figures 7 and 8 also suggest that the developing time profile of the large positive bays could be different from that of the small positive bays. In order to test this, we have performed the superposed epoch analysis of the ground magnetometer data for each of the large-bay and small-bay groups in BIN 1 during ±2 hours of the Pi2 onset time. As a q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dhðtþ 2 þ ddðtþ 2 result, Figure 11 shows the median of db(t)= for both the large (thick line) and the small (thin line) groups, where dh(t)=h t (t) H t (t 0 ), and dd(t)=d t (t) D t (t 0 ) (see Appendix A). [42] One can see in the figure that each line has a plateau between the onset (t = 0) and t = 0.5 (hour). However, the length of the plateau of the small bay is longer than that of the large bay. The magnitude at the plateau of the small positive bay is about 1/5 of its peak, while that in the large positive bay is almost half of its peak. This result suggests that for the small positive bay group, the main energy release onset is delayed from the first Pi2 onset; this more or less supports our consideration above that if the energy stored in BIN1 is not sufficient, several triggering attempts may be necessary before the energy release is actually triggered. Mishin et al. [2001] statistically suggested that there are two distinct onsets during a course of a substorm development at times. They showed that there are continuous loading of the tail with new open flux merged at the dayside even after the first onset. Our result for the small positive bay group is consistent with this view. 6. Summary and Conclusion [43] In this paper, we have studied the energy storage and release process during the substorm as a function of both the substorm intensity and the position by using the Circum-pan Pacific Magnetometer Network on the ground and Geotail. The results are summarized as follows: [44] 1. Both the magnitude and the increasing rate of the total pressure (i.e., energy density) in BIN 1 ( 15 R E < X GSM < 6 R E and 8 R E <Y GSM <8R E ) are highly correlated with the substorm intensity, while those in BIN 3 ( 25 R E <X GSM < 15 R E and 10 R E <Y GSM <10R E )are not correlated with the substorm intensity. [45] 2. The energy release for the small substorm group in BIN 1 is delayed from the first Pi2 onset. [46] Whether a CD is caused by a NENL or the CD takes place by itself, it is widely agreed that the intensity of the CD which affects the ground substorm intensity because the substorm auroral electrojets are believed to be a part of the current-wedge current system. Then, result 1 suggests that the intensity of CD is correlated well with the energy density in BIN 1, not in BIN 3. [47] The reconnection rate at the NENL should affect the energy release rate in BIN 3. The statistics of BIN 3 then mean that the efficiency of reconnection at the NENL is not correlated with the substorm magnitude. That is, the NENL intensity is not the main factor controlling the substorm intensity; it may act as a background factor making a favorable condition for a substorm. 11 of 14

12 [48] Ohtani et al. [2002] have systematically examined the fast flows in the plasma sheet. Their result suggests that the near-earth reconnection, even if it reaches the lobe field line, does not necessarily trigger the global substorm. It is consistent with the present result. It may be that if an NENL takes place but a CD does not take place, then the reconnected closed fluxes slowly convect earthward and release the stored energy in BIN 1 but cause no global substorm. On the other hand if a CD takes place, it quickly removes the magnetic flux from BIN 1 via dipolarization, which may be the key factor leading to a substorm. [49] Result 2 implies that the amount of the stored energy affects the efficiency of the process triggering CD. If the stored energy is great, one attempt to trigger a CD is enough to cause the major release of the stored energy; on the other hand if the stored energy is less, several attempts to trigger CDs are necessary to cause the major release of the stored energy. Appendix A: Database Construction From Ground Data [50] To select Pi2s and positive bays from the huge data sets, we have used automatic event selection procedures before visual inspection. We have regarded an event as a substorm onset if a Pi2 was observed simultaneously at three stations of the 210 MM group or three stations of the South American group when they were located near midnight. For clear recognition of the energy storage process, we have chosen isolated substorm onsets (defined as an onset with no other onsets in the preceding 30-min interval). A1. Automatic Pi2 Selection [51] We have constructed an automatic procedure to identify the start time and the end time of wave packets which are recognized as Pi2s from data from three ground stations. The procedure consists of two steps. The first step is to pick up wave packets as candidates for Pi2s from each station. The second step is to select the wave packets which can be seen at three stations by comparing the candidates obtained at each station. The details are as follows. [52] Step 1: First, we apply to H-component data (H(t)) of each station a band-pass filter for the Pi2 band (T = sec) and obtain the filtered H component data (H p (t)). (We note that band-pass filters used in this study do not make phase differences from an original data.) Next, H p (t) is squared to obtain a data proportional to the wave power. The H 2 p (t) contains many candidates for Pi2s. To trace the envelope of the wave packets, local maximum points in H 2 p (t) are selected. The selected points constitute a new time series, and we select local maximum points of the new time series to further smooth the wave packets. Then we obtain 2 the envelope data (H penv (t)) in which a wave packet is identifiable as a local maximum point. The local maximum is selected as the peak time (t p ) of the wave packet if it satisfies the following criterion 1 and if the start time (t s ) and the end time (t e ) of the wave packet can be determined 2 as those satisfying the following criterion 2: (1) H penv (t p ) [(nt) 2 ], (2) t s (t e ) is the nearest time to t p before 2 (after) t p satisfying H penv (t s(e) ) H p 2 envðþ t p 4. [53] (The numbers and 4 above have been determined after initial try-and-errors compared with visual inspection.) In this way, from each station, we can obtain a list of the start time and end times of wave packets as candidates for Pi2s. [54] Step 2: To identify a wave packet which is seen at three nightside stations in the 210 MM group or in the South American group, we compare the above-obtained lists. First, we choose a set of three stations from one of the groups. Each set includes a reference station of each group (GUA in the 210MM group and SMA in the South American group) to calculate the substorm intensity, which will be explained in section A5. Then the other two stations in the set are selected in consideration of the data coverage overlapping that of the the reference station and the data quality. We express i-th wave packet at n-th station as a pair of the start time (t n si ) and the end time (t n ei ) as follows: W n i ¼ tsi n ; tn ei n ¼ f1; 2; 3g i ¼ 1; 2; 3... Next, we compare wave packets from the three stations whether they have an overlapped interval. If {W 1 k, W 2 l, W 3 m } have an overlapped interval, then we identify the group as a Pi2 wave packet and add its start time and end time to the final event list. We define the start time of this Pi2 (t P s ) as the latest time in {t 1 sk, t 2 sl, t 3 sm } and the end time (t P e ) as the earliest time in {t 1 ek, t 2 el, t 3 em }. In this way we obtain two lists of Pi2s from the 210 MM group and the South American group. A2. Automatic Positive Bay Selection [55] In order to find perturbations identifiable as positive bays, we have constructed an automatic procedure to apply to the three ground stations data and recorded their start and peak times. This procedure also consists of two steps similar to those for Pi2s. That is, the first step is to find out the perturbations as candidates of positive bays in each station s data. The second step is to select candidates that are simultaneously observed at all stations. The detail is as follows. [56] Step 1: First, we apply to the H component data (H(t)) of each station a band-pass filter (T = min) and obtain the filtered H component data (H b (t)). Next, a local minimum point is searched forward from the beginning of H b (t). When a local minimum point is found at t 0 s, the next coming local maximum is selected, which we denote as t 0 p. If the perturbation pattern from t 0 s to t 0 p satisfies the following criteria, the pattern is identified as a candidate for a positive bay at the station: (1) t 0 0 p t s < 70, (min), (2) H b (t 0 p ) H b (t 0 s ) > 0.5, (nt), (3) H bðþ H tp 0 b ðþ ts 0 t > 0.1, (nt/ p 0 t0 s hour). (The number 70 (min) above comes from the typical length of the growth phase, and the numbers 0.5 (nt) and 0.1 (nt/hour) comes from initial try-and-errors compared with visual inspections.) This procedure is done repeatedly. Then, for each station, we obtain a list of many pairs of a start time and a peak time of perturbation as candidates for positive bays. [57] Step 2: In order to select a perturbation pattern which is seen simultaneously at three nightside stations in the 210 MM group or in the South American group, we first choose a set of three stations from one of the groups. 12 of 14

13 We express the i-th perturbation at the n-th station as a pair of the start time (t 0 si n ) and the peak time (t 0 pi n ) as follows: h i Pi n ¼ tsi 0n ; t0n pi n ¼ f1; 2; 3g i ¼ 1; 2; 3... Next, we compare perturbations from the three stations to see whether they have an overlapped interval. If they have an overlapped interval in {P 1 k, P 2 l, P 3 m }, then we identify the perturbation as a positive bay and add its start time and the peak time to the final list. We define the start time of the positive bay (t Bay s ) as the average of those at the three stations {t 01 sk, t 02 sl, t 03 sm } and the peak time (t Bay p ) as the average of those at the three stations {t 01 pk, t 02 pl, t 03 pm }. In this way, we obtain two lists of positive bays from the 210 MM group and the South American group. A3. Automatic Event Classification [58] The above-selected Pi2s are classified according to timing relationships with the above-selected positive bays as follows. For a clear recognition of the energy storage process, we choose isolated Pi2 (defined as Pi2 events with no other Pi2 in the preceding 30-min interval: t Pi2 si Pi2 t e(i 1) > 30 (min)). In order to use the positive bay as the measure of the substorm intensity, it is expected that an isolated positive bay (defined as a positive bay with no other positive bay in the preceding 30-min interval: t Bay si Bay t p(i 1) > 30 (min)) starts to rise near an isolated Pi2 start time. When an isolated Pi2 onset starts within ±15-min of an isolated positive bay onset, we call this type of isolated Pi2 The first Pi2 with bay. In addition, there is a possibility that an isolated Pi2 is associated with no positive bay or with a very small one which can not be detected, if it is a very small substorm or a pseudosubstorm. When no positive bay is identified within ±15-min of an isolated Pi2, we call this type of isolated Pi2 The first Pi2 without bay. The selection of the two types of substorms is done by comparing the isolated Pi2 list and the positive bay list. A4. Visual Inspection for Pi2 Onset [59] After the automatic selection, the Pi2 onset time (t s Pi2 ) is checked again by visual inspection. In order to define the onset time more precisely, we use time derivative of H(t), dh(t), from the three stations as an analogue to induction magnetometer data. The Pi2 signal is often seen as a higher frequency component superposed on the start of the magnetic increase of a positive bay in H(t). That is, the trend in H(t) is often a bent line, which causes a false negative peak when band-pass filtered. One can minimize this effect by taking time derivative because time derivative of a bent line is a two horizontal lines with a jump at the onset time, and the jump is usually much smaller than the amplitude of Pi2. Thus we define the Pi2 onset time (t 0 ) as a start time of the first impulsive rising of the Pi2 packet in dh(t). Then we identify t 0 via visual inspection of the three time series plots in the same time frame. The solid vertical line in Figure 2 shows an example of thus identified t 0. A5. Substorm Intensity Calculation [60] As we stated above, in the ground stations there are two groups: The 210MM group and the South American Figure A1. The median of DB in each local time bin (1-hour) (solid line) and the fitted curve (dashed line), at GUA (top) and at SMA (bottom). group. We use one station from each group as a reference station in estimating the intensity of substorms: GUA in the 210MM group and SMA in the South American group are the reference stations. We select the substorm events when each reference station was located within 4 hours from local midnight ( 4 < LT < 4 hour). [61] To estimate the substorm intensity, we use the amplitude of the positive bay at 10 min after the Pi2 onset. The positive bay represents the influence of the three-dimensional substorm current system. Therefore the H component is expected to be maximum at the longitudinal center of the current system, while the D component p should be maximum at its azimuthal edges. Thus DB = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DH 2 þ DD 2 instead of DH is used as a measure of the substorm intensity in this study, where DH = H t (t min) H t (t 0 ), DD = D t (t min) D t (t 0 ). H t (t) and D t (t) here mean processed data of H(t) and D(t) by a band-pass filter (T = 200 s 18 hour). [62] Another aspect to consider is the local time effect on the value of DB. Figure A1 shows local time distributions of the median of DBs in each 1-hour bin at each reference station. These profiles are not flat; thus even for the same substorm, DB at a reference station may well vary depending on the local time. 13 of 14

14 [63] In order to correct this local time effect, we first fit a Maxwellian to the local time profile of the median of DBs at each station fðt LT n Þ ¼ a exp hðt LT cþ 2 o þ b; where t LT is the local time, and a, b, c, and h are fitting parameters. In order to obtain the same local time dependence, a common c and a common h is fitted to the two stations data (a and b are different for the two stations). We have obtained these parameters as follows: [a, b] = [0.5762, ] for GUA, [a, b] = [1.9324, ] for SMA, and [c, h] =[ , ] for both stations. We correct the local time effect in each observed DB by using the equation DB 0 = DB f(t) +f(c). That is, DB is corrected to DB 0, which is the value at the peak of the local time distribution of the average DB. [64] We obtain two data sets of DB 0 s, which are from GUA (DB 0 0 GUA s) and from SMA (DB SMA s). Although both data sets contain the values at the same local time (t LT = c), their medians are different because the latitudes of GUA and SMA are different. In order to compare the substorm intensities in the same standard, we normalize 0 DB SMA. That is, because c and h are common in f (t LT )at GUA, f GUA (t LT ) and f (t LT ) at SMA, f SMA (t LT ), there is the following linear relation: f GUA (t LT )=a f SMA (t LT )+b, a = , and b = Thus we normalize DB SMA to DB SMA by using the equation DB SMA = adb SMA + b and 00 0 merge DB SMA s and DB GUA s. In this way we obtained the measure of the substorm intensity in the same standard: DB norm s. With the above procedures, we made a substorm database which includes 997 substorm events, each of which is characterized mainly by the Pi2 onset time t 0 and the amplitude of the positive bay DB norm. [65] Acknowledgments. The authors are grateful to T. Mukai for helpful comments and providing Geotail LEP data. The authors thank T. Nagai for providing Geotail MGF data. We thank R. Lepping for Wind and IMP 8 magnetic field data, K. Ogilvie for Wind solar wind data, A. Szabo for IMP 8 magnetic field data, and A. Lazarus for IMP 8 plasma data. These data were obtained through CDAWeb. The ground magnetometer data used in this paper were provided by the Circum-pan Pacific Magnetometer Network (CPMN) Group. [66] Lou-Chuang Lee thanks Ramon E. Lopez and another reviewer for their assistance in evaluating this paper. References Aggson, T. L., J. P. Heppner, and N. C. Maynard (1983), Observations of large magnetospheric electric fields during the onset phase of a substorm, J. Geophys. Res., 88, Baker, D. N. (1996), Neutral line model of substorms: Past results and present view, J. Geophys. Res., 101, 12,975 13,010. Baumjohann, W., G. Paschmann, and H. Lühr (1990), Pressure balance between lobe and plasma sheet, Geophys. Res. Lett., 17, Caan, M. N., R. L. McPherron, and C. T. 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