JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, A04202, doi: /2010ja016371, 2011

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2010ja016371, 2011 Relation between magnetotail magnetic flux and changes in the solar wind during sawtooth events: Toward resolving the controversy of whether all substorm onsets are externally triggered Chao Song Huang 1 Received 10 December 2010; revised 21 January 2011; accepted 25 January 2011; published 5 April [1] It has been debated for many years whether all substorm onsets are triggered by a sudden change in the solar wind. Because there is not a generally accepted definition of external triggers, a solar wind change may be identified to be an external trigger by some investigators but not a trigger by others. In this paper, we study the substorm onset from the magnetospheric state during sawtooth events. We do not try to determine whether a solar wind change around the onset is a trigger. Instead, we examine whether an external trigger from the solar wind is always necessary for substorm onset and why large changes in the solar wind do not always trigger sawtooth (substorm) onset. We have analyzed 54 sawtooth onsets and corresponding changes in the solar wind. The mean value of the total magnetic flux in the magnetotail at the sawtooth onsets is 0.98 GWb. Sawtooth onset can occur when the changes in the solar wind are very small (0.5 npa in the solar wind dynamic pressure and 1 nt in the IMF B z ). We have also identified a number of large changes in the solar wind without occurrence of sawtooth onset, and the mean value of the magnetotail magnetic flux is GWb. However, the large changes in the solar wind do not cause sawtooth onset when the magnetotail magnetic flux is generally smaller than 0.8 GWb in these cases. The observations suggest that sawtooth onset will occur when the magnetotail magnetic flux is close to a critical value ( 1 GWb, depending on the solar wind and geomagnetic activity), no matter whether the corresponding change in the solar wind is large or small. The observations also suggest that no sawtooth (substorm) onset can be triggered by a solar wind change if the magnetotail magnetic flux is 25% lower than the critical value of the onset, no matter how large the change in the solar wind is. Sawtooth onset appears to be an internal magnetospheric instability process, and a large change in the solar wind is not necessary for the occurrence of sawtooth onset. Citation: Huang, C. S. (2011), Relation between magnetotail magnetic flux and changes in the solar wind during sawtooth events: Toward resolving the controversy of whether all substorm onsets are externally triggered, J. Geophys. Res., 116,, doi: /2010ja Introduction [2] It has been a long standing controversy in the substorm study what causes the expansion onset. Observations show that substorm onsets are often related to discontinuities in the solar wind [Burch, 1972; Caan et al., 1975, 1977; Kokubun et al., 1977; Akasofu and Chao, 1980; Rostoker, 1983; Rostoker et al., 1983; Samson and Yeung, 1986; Nishida et al., 1997; Blanchard et al., 2000; Liou et al., 2003; Liou, 2007; Yue et al., 2010]. It is suggested that a sudden change in the solar wind, such as a 1 Institute for Scientific Research, Boston College, Chestnut Hill, Massachusetts, USA. Copyright 2011 by the American Geophysical Union /11/2010JA northward turning of the interplanetary magnetic field (IMF) and/or an enhancement of the solar wind dynamic pressure, can trigger the onset. McPherron et al. [1986] conducted a statistical survey of solar wind triggering of substorm onsets. They found that 60% of their events appear to be externally triggered and that 40% occurred when IMF B z was steadily southward. Horwitz [1985] and Henderson et al. [1996] also showed that substorm onsets could occur in the absence of noticeable changes in the IMF and solar wind pressure. Hsu and McPherron [2002, 2003, 2009] performed detailed analysis of more than 200 substorms and found that the ratio of triggered and nontriggered substorms is about 60/40. They suggested that substorm onset is a consequence of an internal magnetospheric instability that is highly sensitive to changes in magnetospheric convection induced by a sudden change in the IMF. Internal magne- 1of11

2 tospheric instability processes that can cause substorm onsets have been discussed by Lui [1996], Pu et al. [1999], Freeman and Morley [2004], and Kan [2007]. [3] On the other hand, Lyons [1995, 1996] proposed that the expansion phase of substorms results from a reduction in the large scale electric field imparted to the magnetosphere from the solar wind. He suggested that most, and perhaps all, expansion onsets are triggered by IMF changes including both northward turnings and reductions in the magnitude of the y component. Lyons et al. [2003, 2005] showed that substorm onsets are associated with a reduction in the strength of large scale convection. They suggested that solar wind changes cause substorm onset only if the changes lead to a reduction in the strength of convection within the inner plasma sheet. [4] Substorms can be divided into two categories according to geomagnetic activity: quiet time isolated substorms and storm time substorms. Recurrent substorms often occur during magnetic storms, and the resultant magnetosphericionospheric disturbances are generally much stronger than those of isolated substorms. Sawtooth events in the Earth s magnetosphere are global, large amplitude oscillations of energetic plasma particle fluxes at geosynchronous orbit. The plasma particle fluxes show a well defined sawtooth shape, with gradual decreases followed by rapid increases [Borovsky et al., 1993; Belian et al., 1995]. The recurrent injections of the plasma particle fluxes at geosynchronous orbit have a most probable period of 2.7 h. Sawtooth events have been studied extensively in recent years [Huang, 2002; Huang et al., 2003a, 2003b, 2004, 2005, 2009; Reeves et al., 2003; Lui et al., 2004; Henderson, 2004; Clauer et al., 2006; Henderson et al., 2006a, 2006b; Cai et al., 2006; Pulkkinen et al., 2006, 2007; DeJong et al., 2007, 2009; Huang and Cai, 2009; Cai and Clauer, 2009]. The observations and simulations show that each cycle of sawtooth oscillations is related to the following processes: magnetic reconnection onset in the midtail, injection of energetic plasma particles from the tail to the inner magnetosphere, plasmoid formation in the tail, magnetic dipolarization of the magnetotail, auroral intensifications, and all other signatures of substorms. A sawtooth event is a series of individual tooth events, and each individual tooth represents one substorm. It is becoming widely accepted that sawtooth events are quasiperiodic substorms. Sawtooth events often occur during continuous southward IMF. Pulkkinen et al. [2007] found that only 20% of the sawtooth oscillations have associated solar wind or IMF triggers. [5] Huang et al. [2003a, 2004] suggested the following scenario to explain the generation of periodic substorms (sawtooth oscillations). Magnetospheric substorm processes have an intrinsic cycle time of 3 h. The magnetosphere takes 3 h after one substorm onset to reach the state for the next onset to occur. Each cycle of the periodic substorms can occur under stable IMF and solar wind conditions, and the onset does not have to be triggered by either a northward IMF turning or a solar wind pressure impulse. A sudden change in the solar wind can trigger a substorm onset if and only if the magnetosphere has reached the critical state conducive to the generation of substorms. In the case of no external triggering from the solar wind, substorms will still occur when the magnetosphere has reached the unstable state, and an internal plasma instability can trigger substorm onsets. Henderson et al. [2006b] also proposed that the periodicity of sawtooth events results because the magnetosphere only becomes susceptible to (external or internal) triggering once it is driven beyond some stability threshold. [6] The solar wind is varying with time, and we can always find a change, small or large, in the solar wind around a substorm onset. There is not a generally accepted definition of external triggers. In particular, there is not a criterion of how large a change in the solar wind must be for being a trigger. A case identified by some investigators to be not externally triggered may be identified to be externally triggered by others. The controversy of how many substorms are externally triggered becomes the issue of how large a change in the solar wind pressure or IMF can be defined as a trigger. [7] In this paper, we study the occurrence of sawtooth onset from the magnetospheric state. We will find the magnetotail magnetic flux at each onset and the maximum changes in the solar wind pressure and IMF B z around each onset. We will also find large solar wind changes that do not cause sawtooth onset. We do not try to identify whether a solar wind change around the onset is an external trigger. Instead, we determine whether the magnetotail magnetic flux must reach a critical value for an onset to occur, whether an external trigger from the solar wind is always necessary, and why large changes in the solar wind do not always trigger sawtooth onset. 2. Observations [8] We first present two examples of sawtooth events. Figures 1a 1c show the IMF B y, IMF B z, and solar wind pressure on 18 April 2001, respectively. The solar wind data are measured by the Advanced Composition Explorer (ACE) satellite located at 220 R E upstream and have been shifted to the Earth s bow shock nose with the minimum variance analysis technique developed by Weimer et al. [2003]; the IMF components are plotted in the GSM coordinate. In all cases analyzed in this paper, the solar wind and IMF data have been shifted to the bow shock nose with the above technique. Figures 1d 1f show the proton flux measured by three geosynchronous satellites. The energy channels of the proton flux are 50 75, , , , and kev. The gradual decrease of the proton flux occurs when the magnetotail becomes more stretched during the growth phase of substorms, and the sudden increase corresponds to proton flux injections from the magnetotail to the inner magnetosphere at the expansion onset. [9] We use the following criteria to identify the substorm onset during sawtooth events [Cai et al., 2006]: At least one geosynchronous satellite is located around local noon (3 MLT hours from local noon) and one around local midnight (3 MLT hours from local midnight), and the plasma particle flux injection is observed globally. Because a sudden enhancement in the solar wind dynamic pressure can also cause geosynchronous energetic plasma particle fluxes to increase [Lee et al., 2005], we checked other measurements to make sure that the sudden increases of the proton flux in our cases are indeed flux injections at substorm onset but not the compression effect of solar wind pressure enhancements without substorm. The measurements include auroral 2of11

3 Figure 1. Examples of sawtooth events. (a f) Interplanetary magnetic field (IMF) B y, IMF B z, solar wind dynamic pressure, and proton fluxes measured by the LANL 01A, , and geosynchronous satellites, respectively, on 18 April (g m) The case of 22 October The vertical dotted lines denote the sawtooth onsets. The vertical gray lines denote the solar wind changes that do not cause sawtooth onsets. brightening, magnetotail magnetic dipolarization, time delays of proton flux increases between dayside and nightside, etc. [Huang et al., 2003b, 2005; Henderson et al., 2006a, 2006b]. In this paper, the onset of an individual tooth (substorm) during sawtooth events is termed the sawtooth onset. A sawtooth event is a series of individual tooth events, and the onset of an individual tooth is different from the beginning of a sawtooth event. [10] In the case of 18 April 2001 (Figure 1, left), three sawtooth onsets occur at 00:47, 03:10, and 06:08 UT, as denoted by the vertical dotted lines. The first onset is obviously related to a sudden enhancement of the solar wind pressure and can be easily identified as an externally triggered case. In contrast, the IMF components and solar wind pressure only show some small perturbations around the onsets at 03:10 and 06:08 UT. The small solar wind perturbations may be, or may not be, external triggers, depending on the criterion used by the investigator. Here we want to indicate that large changes occur in the solar wind, as denoted by the gray vertical lines. At 04:09 UT, the IMF B z suddenly increases by 35 nt, from 24 to 11 nt, and the IMF B y decreases by 18 nt. At 05:01 UT, the solar wind pressure suddenly increases by 15 npa, accompanied by an increase of the IMF B y and a decrease of the IMF B z. The prominent phenomenon is that such large changes in the solar wind do not trigger sawtooth onsets. The decrease of the proton flux around 04:09 UT (the first gray line) represents a local variation around the LANL satellite and is not a global injection event. [11] Figure 1 (right) presents another case on 22 October Four sawtooth onsets occur at 11:02, 13:45, 15:52, and 17:50 UT, as denoted by the vertical dotted lines. The 3of11

4 first onset at 11:02 UT is related to an increase in both the IMF B y and B z, the second onset at 13:45 UT is related to a decrease in both the IMF B y and B z, and no obvious changes in the solar wind occur around the third and fourth onsets. Two large increases of the solar wind pressure occur at 17:02 and 18:26 UT, as denoted by the gray vertical lines, but do not trigger sawtooth onsets. The solar wind pressure enhancement at 17:02 UT is accompanied by an increase in the IMF B y and a decrease in the IMF B z, and the second pressure enhancement at 18:26 UT is accompanied by an increase in the IMF B y and B z. [12] The observations of the two sawtooth events in Figure 1 suggest that the sawtooth onsets can be related to, or triggered by, sudden changes in the solar wind but can also occur without obvious changes in the solar wind. On the other hand, very large changes in the solar wind, as those denoted by the gray lines, do not trigger sawtooth onsets. It is difficult to explain these phenomena from the solar wind data alone. In the following, we examine the magnetotail magnetic flux at the onset of each individual tooth. [13] Huang et al. [2009] reported the measurements of the total magnetic flux in the magnetotail and in the polar cap during sawtooth events. The total magnetic flux in the magnetotail is calculated as follows. The magnetospheric parameters used in this paper were measured by the Geotail satellite in the tail distance between 19 and 31 R E. The equivalent lobe magnetic field is defined as B L 2 /2m 0 = B T 2 /2m 0 + N i k(t i + T e ) and includes the contribution of the plasma pressure, where B T =(B x 2 + B y 2 + B z 2 ) 1/2 is the strength of the magnetospheric magnetic field. The tail radius, as well as the cross section of the magnetotail, at the Geotail position is calculated with the empirical model of Shue et al. [1998] by using the shifted solar wind data. The total magnetic flux in the magnetotail is obtained from the product of the equivalent lobe magnetic field and the tail cross section. Huang et al. [2009] compared the magnetotail magnetic flux with the total open magnetic flux in the polar cap. The polar cap magnetic flux is derived from the measurements of the Far Ultraviolet (FUV) imager on board the Imager for Magnetopause to Aurora Global Exploration (IMAGE) satellite and the Ultraviolet Imager on board the Polar satellite [DeJong et al., 2007]. The magnetotail magnetic flux is in very good agreement with the polar cap magnetic flux during sawtooth events. The detailed calculation and comparison of the magnetotail and polar cap magnetic fluxes were given by Huang et al. [2009]. Most cases used in this paper are the same as those used by Huang et al. [2009]. [14] We now present the magnetotail magnetic flux during the sawtooth event on 18 April This is a well known example of sawtooth events and has been analyzed in detail [Huang, 2002; Huang et al., 2003b, 2005, 2009; Lui et al., 2004; Clauer et al., 2006; Henderson et al., 2006a]. Figure 2a shows the IMF B y and B z components. The IMF B z is continuously southward and stable throughout the entire day, and the IMF B y is also stable, except for a few sudden changes. Figures 2b and 2c depict the solar wind pressure in linear scale and in logarithm scale, respectively. The solar wind pressure shows a large enhancement at 00:30 UT and another enhancement at 02:38 UT and then becomes small. Small variations in the solar wind pressure are displayed in the logarithm plot (Figure 2c). Figures 2d and 2e show the proton flux measured by the LANL 02A and geosynchronous satellites, and the vertical dotted lines denote the sawtooth onsets. Figure 2f shows the total magnetic flux in the magnetotail, derived from the Geotail satellite measurements. [15] The magnetotail magnetic flux in Figure 2f shows very regular, periodic variations. Sawtooth onset occurs when the magnetic flux approaches 1 GWb. The large spike in the magnetic flux immediately after an onset, such as the one after 08:00 UT, is caused by the compression effect of a tailward moving plasmoid and does not represent an increase of the magnetic flux [Huang, 2002]. Small perturbations in the solar wind pressure exist, as depicted in the log scale plot, throughout the entire day. We can indeed pick up a perturbation of the solar wind pressure around each sawtooth onset if we do not care how small the perturbation is. However, most sawtooth onsets, except for the one at 02:38 UT, do not show any obvious correlation with the small perturbations in the solar wind pressure. [16] The vertical gray lines in Figure 2 are used to denote the solar wind changes without sawtooth onset. The gray line at 09:25 UT indicates a sudden increase in the IMF B y. The perturbations of the solar wind pressure at 12:45, 15:10, and 17:22 UT are larger than, or comparable to, those around most sawtooth onsets. However, the changes in the IMF B y and solar wind pressure denoted by the gray lines do not cause sawtooth onsets. No obvious differences exist between the solar wind pressure changes around the onsets (dotted lines) and those without onset (gray lines). In contrast, we can easily see the difference in the magnetotail magnetic flux: The sawtooth onset occurs when the magnetotail magnetic flux is 1 GWb, and solar wind changes do not trigger sawtooth onset when the magnetotail magnetic flux is GWb. [17] We present two more examples in Figure 3. In the case depicted in Figure 3 (left), three sawtooth onsets occur at 01:59, 06:11, and 09:53 UT, as denoted by the vertical dotted lines. The first onset at 01:59 UT may be related to a perturbation in the IMF B y, and other two onsets may be related to an increase in the IMF B z. We may say that these onsets are triggered by the solar wind changes. However, we want to indicate that larger changes in the solar wind exist, as denoted by the vertical gray lines. A decrease in the IMF B y and an increase in the IMF B z occur at 02:47 UT, simultaneous increases in the IMF B y, IMF B z, and solar wind pressure occur at 03:07 UT, and a negative spike in the IMF B y and an increase in the IMF B z occur at 03:27 UT. These solar wind changes do not trigger sawtooth onset. Figure 3 (right) shows the case on 20 March Four sawtooth onsets are denoted by the vertical dotted lines and not related to any noticeable changes in the solar wind. The vertical gray lines indicate much larger enhancements in the solar wind pressure that do not trigger sawtooth onset. [18] A common feature in the two cases of Figure 3 is that sawtooth onset occurs when the magnetotail magnetic flux is close to 1 GWb, no matter whether there is a sudden change in the solar wind. In contrast, much larger changes in the solar wind pressure and IMF components occur and do not trigger sawtooth onset when the magnetic flux is about GWb. This feature is similar to that observed in the case of Figure 2. [19] We have searched the Geotail data and the geosynchronous satellite proton flux data over and 4of11

5 Figure 2. The sawtooth event on 18 April From top to bottom: (a) IMF B y and B z, (b and c) solar wind dynamic pressure, (d and e) proton fluxes at geosynchronous orbit, and (f) total magnetic flux in the magnetotail. The vertical dotted lines denote the sawtooth onsets. The vertical gray lines denote the solar wind changes that do not cause sawtooth onsets. found that Geotail was in the magnetotail between 19 and 31 R E in 17 sawtooth events. Examples of the sawtooth events are given in Figures 2 and 3. There are 54 individual sawtooth onsets in the 17 events. The magnetotail magnetic flux immediately prior to the substorm onset may represent the magnetospheric condition for the onset to occur and correspond to the maximum energy stored in the magnetotail. We calculated the magnetic flux and merging electric field for each onset. The merging electric field is defined by Kan and Lee [1979] as E m = V sw (B y 2 + B z 2 ) 1/2 sin 2 (/2), where V SW is the solar wind velocity, B y and B z are the IMF components, and is the IMF clock angle. Considering that the magnetic flux varies with time, we have averaged the magnetic flux over 5 min prior to each onset and used the averaged value to represent the flux at the onset. The merging electric field is averaged over 60 min prior to each onset; this 60 min interval presumably corresponds to the accumulation time of the flux in the tail for substorms [Huang et al., 2009]. [20] Figure 4 shows the magnetotail magnetic flux as a function of the merging electric field. The red dots represent the 54 sawtooth onsets in 17 sawtooth events. The solid line is derived from the data regression with least squares fitting of the 54 onsets and is given by F T,Saw = E m, where F T,Saw is the magnetotail magnetic flux in GWb at the sawtooth onset, and E m is the merging electric field in mv m 1. The detailed derivation of the empirical formula and its explanation can be found in work by Huang et al. [2009]. The result suggests that the magnetotail magnetic flux must reach the critical value for the onset to occur. Here we emphasize that the magnetic flux at sawtooth onset increases with the merging electric field. [21] The blue circles in Figure 4 represent the cases in which sudden changes in the solar wind occur but do not 5of11

6 Figure 3. Examples of sawtooth events. (a f) IMF B y and B z, solar wind dynamic pressure, proton fluxes at geosynchronous orbit, and total magnetic flux in the magnetotail, respectively, on 24 March (g m) The case on 20 March The vertical dotted lines denote the sawtooth onsets. The vertical gray lines denote the solar wind changes that do not cause sawtooth onsets. cause sawtooth onset. Examples of solar wind changes without sawtooth onset are denoted by gray vertical lines in Figure 3, and detailed discussion will be given later. There is some overlap between the cases at sawtooth onset (red dots) and the cases without sawtooth onset (blue circles) in Figure 4. This overlap may be caused by the uncertainties in the magnetotail magnetic flux derived from the single point measurements of the Geotail satellite. An important feature of Figure 4 is that the magnetotail magnetic flux without sawtooth onset is generally lower than that with sawtooth onset, implying that no onset will occur if the magnetotail magnetic flux is smaller than the critical value. [22] We now find the maximum changes in the solar wind around each sawtooth onset. In some cases, the solar wind changes can be clearly identified by the eye, such as the increase of the solar wind pressure at 02:38 UT in Figure 2 and the increases of the IMF B z at 06:11 and 09:53 UT in Figure 3 (left). However, the IMF components and/or solar wind pressure do not show noticeable changes at most sawtooth onsets. We use a computer program to calculate the maximum changes in the solar wind pressure and the IMF B z. As mentioned earlier, the solar wind data have been shifted to the bow shock nose. Considering that some uncertainties may exist in the time shift of the solar wind data and in the time of sawtooth onset identified from the proton flux injections, we select the maximum solar wind change in the range of ±15 min around each onset. We first pick up a minimum value in the solar wind pressure (or the IMF B z ) and then calculate the increase of the solar wind parameter in 10 min. If there are multiple minimum values in the solar wind data around an onset, we calculate all increases of the solar wind parameter after each minimum and take the largest one for this onset. We also examine by the eye whether the change of the solar wind pressure/imf B z 6of11

7 Figure 4. The magnetotail magnetic flux as a function of the merging electric field. The red dots represent the cases at sawtooth onset. The blue circles represent the cases in which sudden changes in the solar wind occur but do not cause sawtooth onset. picked up by the computer program is the largest one around the onset. [23] The next step is to identify, solely by the eye, large changes in the solar wind without sawtooth onset in the 17 sawtooth events. In general, a sudden change in the solar wind is considered as a trigger of a substorm onset if the change approximately coincides with the onset but not a trigger if the change is far away from the onset. We use 30 min as the minimum separation between solar wind changes and sawtooth onsets. In other words, the solar wind changes must be at least 30 min away from the closest sawtooth onset, so they cannot be considered as a trigger for the onset. Because small variations always exist in the solar wind, we can find as many changes as we want if we do not use a threshold for the solar wind changes. In our analysis, we set the following criteria: The increase of the solar wind pressure must be larger than 1 npa, and the increase of the IMF B z must be larger than 2 nt. The change in the solar wind pressure and IMF B z must be abrupt and occur within 10 min; we do not include gradual variations of the solar wind in the statistics. Examples of sudden changes in the solar wind without sawtooth onset are denoted by the vertical gray lines in Figure 3. In total, there are 45 cases of IMF B z increase and 32 cases of solar wind pressure increase. There is no physical reason of why the minimum changes of the solar wind should be these values. We will have more cases if the minimum values are smaller and less cases if the minimum values are higher. The solar wind changes denoted by the gray lines in Figure 2 are not included in the following analysis because they are too small. [24] The statistical results are presented in Figure 5. The red dots represent the magnetotail magnetic flux at the 54 sawtooth onsets. The blue circles represent the magnetotail magnetic flux at the changes of the solar wind pressure and IMF without sawtooth onset. Figure 5a shows the magnetotail magnetic flux as a function of the net increase of the solar wind pressure. At sawtooth onsets (red dots), the mean value of the magnetic fluxes is 0.98 GWb, and the mean value of the corresponding increases of the solar wind pressure is 1.20 npa. In the 32 cases (blue circles) without sawtooth onset in Figure 5a, the mean value of the magnetotail magnetic fluxes is 0.79 GWb, and the mean value of the corresponding increases of the solar wind pressure is 2.69 npa. The mean magnetic flux without sawtooth onset is 24% lower than that at the sawtooth onsets. [25] Figure 5c shows the magnetotail magnetic flux as a function of the net increase of the IMF B z. At sawtooth onsets (red dots), the mean value of the magnetic fluxes is 0.98 GWb, and the mean value of the corresponding increases of the IMF B z is 3.86 nt. In the 45 cases (blue circles) without sawtooth onset, the mean value of the magnetic fluxes is 0.74 GWb, and the mean value of the corresponding increases of the IMF B z is 7.14 nt. The mean magnetic flux without sawtooth onset is 32% lower than that at the sawtooth onsets. [26] Figures 5b and 5d show the magnetotail magnetic flux as a function of the relative increase of the solar wind parameters. The relative increase of the solar wind pressure is the ratio of the net increase of the pressure to the pressure value immediately prior to the increase. In the cases of IMF northward turning, the IMF B z can change from negative to positive or from negative to less negative. The net increase of B z is the change of B z and always positive. The relative increase of the IMF B z is the ratio of the net increase of B z to the absolute value of B z immediately prior to the increase. [27] Figure 5 reveals important characteristics of the magnetotail magnetic flux at sawtooth onset and without onset. The magnetic flux at sawtooth onset (red dots) is generally higher than 0.8 GWb and does not have a clear trend of increase or decrease with the change of the solar wind pressure or the IMF B z (or with the relative change in Figures 5b and 5d). The two red data points with magnetic flux of 0.7 GWb represent the two sawtooth onsets that occur when the merging electric field is relatively small (see Figure 4). The change of the solar wind pressure and IMF B z can be very small at the sawtooth onsets. Thirty three sawtooth onsets occur when the increase of the solar wind pressure is smaller than 1.0 npa, and 19 onsets occur when the increase of the solar wind pressure is smaller than 0.5 npa. Twenty four sawtooth onsets occur when the increase of the IMF B z is smaller than 2 nt, and 14 onsets occur when the increase of the IMF B z is smaller than 1 nt. When larger changes in the solar wind occur but do not cause sawtooth onset, the magnetotail magnetic flux (blue circles) is generally lower than 0.8 GWb. The mean value of the solar wind pressure increase without sawtooth onset in the 32 cases is 2.2 times that at sawtooth onset, and the mean value of the IMF B z increase without sawtooth onset in the 45 cases is 1.8 times that at sawtooth onset. 3. Discussion [28] It has been debated for many years whether all substorms are triggered by sudden changes in the solar wind [McPherron et al., 1986; Hsu and McPherron, 2002, 2003, 2009; Lyons, 1995, 1996]. The primary difficulty in resolving this controversy is that no definition of an external trigger is generally accepted by all investigators in the space 7of11

8 Figure 5. Statistical results of the magnetotail magnetic flux and corresponding changes in the solar wind. The red dots represent the magnetotail magnetic flux at sawtooth onsets. The blue circles represent the magnetotail magnetic flux when sudden changes in the solar wind occur but do not cause sawtooth onsets. The magnetotail magnetic flux is plotted as a function of (a) the net increase of the solar wind pressure, (b) the relative increase of the solar wind pressure, (c) the net increase of the IMF B z,and (d) the relative increase of the IMF B z. physics community. Any solar wind parameter (solar wind dynamic pressure, IMF B y, IMF B z, etc) is always varying with time. If the change of the solar wind is rather large and abrupt, such as the solar wind pressure increase at 00:47 UT in Figure 1c and the one at 02:38 UT in Figure 2b, and is related to a substorm onset, most (perhaps all) investigators will agree that the solar wind change is a trigger of the onset. However, many sawtooth onsets occur when the variations in the solar wind are very small, as shown in Figure 2 and in Figure 3 (right). In this study, 19 out of 54 sawtooth onsets occur when the change of the solar wind pressure is smaller than 0.5 npa. If we think that a large change (say, 5 npa) of the solar wind pressure can trigger a substorm onset, can a smaller change (say, 1 npa, or even 0.1 npa) trigger an onset? If a solar wind pressure change as small as npa is used as a trigger, we can certainly find such a trigger around every sawtooth onset, and then we may say that all substorm onsets are triggered externally by the changes in the solar wind. The questions are whether the sawtooth onset is indeed triggered by the small changes in the solar wind and whether the changes are necessary for the occurrence of the sawtooth onset. We cannot answer these questions if we only examine the solar wind data. [29] On the other hand, we have presented examples in which large changes in the solar wind do not trigger sawtooth onset. These examples are denoted by the gray vertical lines in Figures 1 and 3. Lyons et al. [2005] suggested that an IMF northward turning does not cause a substorm onset when it occurs simultaneously with a significant decrease in the solar wind pressure. Also, an increase in the solar wind pressure under strongly southward IMF conditions does not cause a substorm response when it occurs simultaneously with a further southward turning of the IMF. They termed such events as null events. In our cases, that large solar wind changes do not cause sawtooth onset does not appear to be the nullifying effect. For example, in Figure 3 (left), an IMF northward turning occurs at 02:47 UT (the first gray line), and the solar wind pressure does not show a noticeable 8of11

9 change. An IMF northward turning and a solar wind pressure increase occur simultaneously at 03:07 UT (the second gray line). The variation of the IMF B y at 02:47 UT is opposite to that at 03:07 UT. In the cases of Figure 3 (right), the increases of the solar wind pressure occur while both the B y and B z components of the IMF only show small, irregular perturbations. [30] The average value of the magnetotail magnetic flux is 0.98 GWb at the sawtooth onsets and GWb without sawtooth onset. There is an overlap of the magnetic flux in the range of GWb between the sawtooth onsets and the cases without onset, as denoted by the yellow shading in Figure 5. This overlap may be caused by several reasons. First, the magnetotail magnetic flux at sawtooth onset is not a constant but depends on the merging electric field and storm activity [Huang et al., 2009]. If the solar wind driver is weak, a sawtooth onset can occur when the magnetic flux is relatively small (e.g., 0.7 GWb). Under strong solar wind driving conditions, the magnetotail magnetic flux must reach a larger value (e.g., 1 GWb) for an onset to occur, and no onset will occur even if the magnetic flux is greater than 0.7 GWb. As can be seen in Figure 4, the cases without sawtooth onsets (blue circles) are distributed generally below those with sawtooth onsets (red dots). In particular, the magnetotail magnetic flux at the four blue circles with merging electric field of mv/m reaches GWb. This amount of magnetic flux is close to or higher than the critical flux value with merging electric field of < 3 mv/m but still below the critical flux value with merging electric field of > 6 mv/m. Therefore the overlap of the magnetic flux in Figure 5 is an expected phenomenon. Second, the magnetotail magnetic flux is calculated from the single point measurement of the Geotail satellite and the empirical formula of the tail radius. Some uncertainties exist in the magnetic flux derived from this method and also contribute to the overlap. [31] On the basis of the study of Huang et al. [2009] and the results of this paper, we propose the following mechanism for the expansion onset of sawtooth events. The total magnetic flux in the magnetotail must reach a critical value for a sawtooth onset to occur. The critical value of the magnetic flux depends on the solar wind and storm activity. The sawtooth onset will occur when the magnetotail magnetic flux is close to the critical value, no matter whether the change in the solar wind is large or small at the moment. On the other hand, if the magnetotail magnetic flux is much smaller than the critical value, no sawtooth onset will occur even if large changes in the solar wind impact the magnetosphere. [32] In this mechanism, the sawtooth onset is an internal instability process and determined primarily by the state (the total magnetic flux) of the magnetosphere. The observations suggest that large changes in the solar wind are not necessary for the occurrence of sawtooth onset and that the sawtooth onset can occur when the solar wind changes are very small. However, it is uncertain whether internal or external perturbations are responsible for triggering these sawtooth onsets because small perturbations always exist inside the magnetosphere and in the solar wind. [33] In fact, the above mechanism is the same as that proposed by Huang et al. [2003a, 2004]. Huang et al. [2003a] suggested that the magnetosphere takes 3 h after one substorm onset to reach the state for the next onset to occur and that the onset does not have to be triggered by either a northward IMF turning or a solar wind pressure impulse. Huang et al. [2004] suggested that a sudden change in the solar wind can trigger a substorm onset if and only if the magnetosphere has reached the critical state conducive to the generation of substorms. The observations in the present paper indeed show that large changes in the solar wind do not trigger sawtooth onset when the magnetotail magnetic flux is smaller than 0.8 GWb (the blue circles in Figure 5). Henderson et al. [2006b] suggested that the periodicity of sawtooth oscillations results because the magnetosphere only becomes susceptible to (external or internal) triggering once it is driven beyond some stability threshold (or enters a metastable configuration). [34] It should be mentioned that we do not exclude the possibility of solar wind triggering of sawtooth/substorm onset. We indeed found that a number of sawtooth onsets are related to a change in the solar wind. The solar wind change may cause an internal magnetospheric instability [Lui, 1996; Pu et al., 1999; Freeman and Morley, 2004; Kan, 2007] and result in the onset. Hsu and McPherron [2002, 2003, 2009] suggested that substorm onset is a consequence of an internal magnetospheric instability that is highly sensitive to changes in magnetospheric convection induced by a sudden change in the IMF. Our observations and interpretation are consistent with their suggestion. [35] The results of this paper reveal that the occurrence of sawtooth onset depends on the state of the magnetosphere but not on the amplitude of the solar wind change. Whether a solar wind change can trigger a sawtooth onset depends on the level of the total magnetic flux stored in the magnetotail. It appears unnecessary to continuously debate whether a small change in the solar wind is an external trigger. Instead, we suggest focusing on the total magnetotail magnetic flux that determines whether an onset will occur. Another issue is why large changes in the solar wind do not always trigger substorm onset. This study shows that no onset can be triggered if the magnetotail magnetic flux does not reach the critical value. Magnetospheric substorms are often described as an energy (magnetic flux) loading unloading process [Russell and McPherron, 1973; Hones, 1984; Baker et al., 1996; Nagai et al., 1998]. In this scenario, magnetic flux is transferred from the solar wind to the magnetotail during the growth phase of substorms, and the expansion onset occurs when the magnetic flux in the magnetotail reaches a maximum value. The results of our paper are consistent with the loading unloading scenario. [36] However, it is difficult to determine how close the magnetotail magnetic flux must be to the critical value for an onset to be triggered and how much the magnetic flux must be lower than the critical value so that an onset cannot be triggered by a solar wind change. McPherron and Hsu [2002] found that there is a reduction of 25 30% in the lobe magnetic field after substorm onsets. Huang et al. [2009] found that the average value of the magnetic flux at the sawtooth onset is 1 GWb in the magnetotail and that the relative decrease of the magnetic flux from the maximum value at the sawtooth onset to the minimum value after the onset is 25%. In other words, the minimum value of the magnetotail magnetic flux after sawtooth/substorm onset is 25% lower than the maximum value at the onset. In this 9of11

10 study, we only picked up the large solar wind changes at which the magnetotail magnetic flux is close to the minimum value. The average value of the magnetotail magnetic flux without sawtooth onset is GWb and is 24 32% lower than the average value of the magnetotail magnetic flux at the sawtooth onsets. The observations suggest that no sawtooth/substorm onset can be triggered by a solar wind change if the magnetotail magnetic flux is 25% lower than the maximum flux at the onset, no matter how large the change in the solar wind is. [37] In this paper, we only analyzed sawtooth events, and all numbers (such as the average values of the magnetotail magnetic flux, solar wind pressure changes, and IMF B z changes) are derived from sawtooth events. As reported by DeJong et al. [2007] and Huang et al. [2009], the total magnetic flux in the magnetotail or in the polar cap during sawtooth events is 1.5 times that during isolated substorms. However, we suggest that the mechanism proposed here should be applicable to isolated substorm processes. More investigations are needed to determine under what solar wind and magnetospheric conditions an isolated substorm can be, or cannot be, triggered by a change in the solar wind. 4. Conclusions [38] We have analyzed 54 sawtooth onsets and corresponding changes in the solar wind. The total magnetic flux in the magnetotail at the sawtooth onsets is generally higher than 0.8 GWb, with a mean value of 0.98 GWb. The mean value of the corresponding increases of the solar wind pressure around the sawtooth onsets is 1.20 npa, and the mean value of the increases of the IMF B z is 3.86 nt. The changes in the solar wind at sawtooth onset can be very small. Nineteen sawtooth onsets occur when the increase of the solar wind pressure is smaller than 0.5 npa, and 14 onsets occur when the increase of the IMF B z is smaller than 1 nt. The magnetotail magnetic flux at sawtooth onset does not show a clear trend of increase or decrease with the change (or relative change) of the solar wind pressure or IMF B z. [39] We have also identified a number of large changes in the solar wind without occurrence of sawtooth onset. The net increase of the solar wind pressure in 32 cases varies from 1.0 to 15.7 npa, with a mean value of 2.69 npa, and the mean value of the magnetotail magnetic flux is 0.79 GWb. The net increase of the IMF B z in 45 cases varies from 2.0 to 42.0 nt, with a mean value of 7.14 nt, and the mean value of the magnetotail magnetic flux is 0.74 GWb. However, the large changes in the solar wind do not cause sawtooth onset when the magnetotail magnetic flux is generally smaller than 0.8 GWb in these cases. [40] The observations suggest that sawtooth onset will occur when the magnetotail magnetic flux is close to a critical value ( 1 GWb, depending on the solar wind and geomagnetic activity), no matter whether the corresponding change in the solar wind is large or small. The observations also suggest that no sawtooth/substorm onset can be triggered by a solar wind change if the magnetotail magnetic flux is 25% lower than the critical value at the onset, no matter how large the change in the solar wind is. The occurrence of sawtooth onset depends on the state of the magnetosphere but not on the amplitude of the solar wind change. Sawtooth onset can occur when the changes in the solar wind are very small, and a large change in the solar wind is not necessary for the occurrence of sawtooth onsets. [41] Acknowledgments. This work was supported by National Science Foundation award AGS We thank Xia Cai of Virginia Polytechnic Institute and State University for providing a list of sawtooth events. We thank the Geotail team for providing the Geotail magnetic field data (PI: T. Nagai) and plasma data (PI: Y. Saito) through DARTS at Institute of Space and Astronautical Science, JAXA in Japan. We also thank Los Alamos National Laboratory for providing the energetic plasma flux data measured by geosynchronous satellites and the NASA CDAWeb for providing access to the solar wind data. [42] Masaki Fujimoto thanks George Siscoe and another reviewer for their assistance in evaluating this paper. References Akasofu, S. I., and J. K. Chao (1980), Interplanetary shock waves and magnetospheric substorms, Planet. Space Sci., 28, , doi: / (80) Baker, D. N., T. I. Pulkkinen, V. Angelopoulos, W. Baumjohann, and R. L. McPherron (1996), Neutral line model of substorms: Past results and present view, J. Geophys. 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Huang, Institute for Scientific Research, Boston College, 402 St. Clement s Hall, 140 Commonwealth Ave., Chestnut Hill, MA 02467, USA. (chaosong.huang.ctr@hanscom.af.mil) 11 of 11