ULF waves excited by negative/positive solar wind dynamic pressure impulses at geosynchronous orbit

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009ja015016, 2010 ULF waves excited by negative/positive solar wind dynamic pressure impulses at geosynchronous orbit X. Y. Zhang, 1,2 Q. G. Zong, 1,3 Y. F. Wang, 1 H. Zhang, 4,5 L. Xie, 1 S. Y. Fu, 1 C. J. Yuan, 1 C. Yue, 1 B. Yang, 1 and Z. Y. Pu 1 Received 25 October 2009; revised 17 March 2010; accepted 2 April 2010; published 9 October [1] When a solar wind dynamic pressure impulse impinges on the magnetophere, ultralow frequency (ULF) waves can be excited in the magnetosphere and the solar wind energy can be transported from interplanetary space into the inner magnetosphere. In this paper, we have systematically studied ULF waves excited at geosynchronous orbit by both positive and negative solar wind dynamic pressure pulses. We have identified 270 ULF events excited by positive solar wind dynamic pressure pulses and 254 ULF events excited by negative pulses from 1 January 2001 to 31 March We have found that the poloidal and toroidal waves excited by positive and negative pressure pulses oscillate in a similar manner of phase near 06:00 local time (LT) and 18:00 LT, but in antiphase near 12:00 LT and 0:00 LT. Furthermore, it is shown that excited ULF oscillations are in general stronger around local noon than those in the dawn and dusk flanks. It is demonstrated that disturbances induced by negative impulses are weaker than those by positive ones, and the poloidal wave amplitudes are stronger than the toroidal wave amplitudes both in positive and negative events. The potential impact of these excited waves on energetic electrons at geosynchronous orbit has also been discussed. Citation: Zhang, X. Y., Q. G. Zong, Y. F. Wang, H. Zhang, L. Xie, S. Y. Fu, C. J. Yuan, C. Yue, B. Yang, and Z. Y. Pu (2010), ULF waves excited by negative/positive solar wind dynamic pressure impulses at geosynchronous orbit, J. Geophys. Res., 115,, doi: /2009ja Introduction [2] The magnetospheric activities of the Earth are generally controlled by the solar wind and interplanetary magnetic field (IMF) conditions. It is well known that the solar wind dynamic pressure pulses have effects on global magnetospheric systems, for example, the Chapman Ferraro current, region 1 current, cross tail current, auroral electrojets [Sibeck, 1990; Zesta et al., 2000], and the ring current [McPherron and O Brien, 2001; Wang et al., 2003]. Shi et al. [2008a, 2008b] presented a methodology of using the modular Tsyganenko storm magnetic field model (TS04) as a tool to investigate the response of magnetospheric currents to the solar wind dynamic pressure enhancements during magnetic storms. The energy coupling between the solar wind and the magnetosphere manifests in a variety of ways, such as magnetic reconnection, auroral activities, and wave perturbations. The sudden increase/decrease of the solar 1 Institute of Space Physics and Applied Technology, Peking University, Beijing, China. 2 State Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing, China. 3 Center for Atmospheric Research, University of Massachusetts, Lowell, Massachusetts, USA. 4 NASA Goddard Space Flight Center, Greenbelt, Maryland, USA. 5 Physics Department and Geophysical Institute, University of Alaska Fairbanks, Fairbanks, Alaska, USA. Copyright 2010 by the American Geophysical Union /10/2009JA wind dynamic pressure will cause the compression/inflation of the magnetosphere. The magnetic field on the ground will consequently exhibit a positive or negative pulselike signature [Araki, 1994]. A sudden increase/decrease of the solar wind dynamic pressure is denoted as a positive or negative impulse. Positive impulses are often excited by interplanetary shocks, mostly accompanied by coronal mass ejections (CMEs) or corotating interaction regions (CIRs). These positive impulses are the primary cause of sudden storm commencement (SSC). The magnetopause current will intensify when a positive impulse impinges on the Earth smagnetosphere. At the same time, auroral activities in the dayside polar region may be suddenly strengthened and migrate eventually to the night side [Zhou and Tsurutani, 1999; Laundal and Ostgaard, 2008]. In addition, ULF waves will be excited in the inner magnetosphere as a result of the interaction between the Earth s magnetic field and positive solar wind pressure impulses [Lessard et al., 1999; Tan et al., 2004; Zong et al., 2009]. Further, the energetic particles may be accelerated by these waves [Southwood and Kivelson, 1981; Elkington et al., 2003; Perry et al., 2005; Tan et al., 2004; O Brien et al., 2001, 2003; Zong et al., 2007; Kress et al., 2007; Zong et al., 2009]. Although most of the positive impulses are associated with shocks, other types of positive impulses exist, for example, the front edge of the heliospheric plasma sheet (HPS) [Winterhalter et al., 1994]. The feature of this type of positive pulses is that the plasma number density increases while the solar wind velocity re- 1of14

2 Figure 1. Illustration the poloidal and toroidal waves excited by a solar wind positive/negative impulse at 0:00 LT, 6:00 LT, and 12:00 LT at geosynchronous orbit [Zhang et al., 2009]. The arrows schematically show the drift motion direction of ions (solid) and electrons (dashed) from midnight. mains unchanged. The dynamic pressure variations of this type of positive pulse are usually less than those associated with shocks. In addition, if the trailing edge of the HPS structure embedded in the background solar wind is clear enough, a positive/negative impulse pair on the leading and trailing edges of the HPS can be observed [Takeuchi et al., 2002]. [3] Recently, Takeuchi et al. [2002] investigated the interplanetary sources of the negative impulses statistically. They found that negative impulses are usually associated with tangential discontinuities embedded inside CIR, at the leading edge of the interplanetary magnetic clouds and the trailing edge of the HPS. They also found small scale plasma bubbles located in the CIR for the first time. There was a negative and a positive impulse at the leading and the trailing edge of the plasma bubbles, respectively. [4] The origins of ULF waves in the magnetosphere are caused by either the external solar wind perturbations or internal plasma instabilities. At present, Kelvin Helmholtz (K H) instability [e.g., Anderson et al., 1990; Zhu and Kivelson, 1991; Lessard et al., 1999; Hudson et al., 2004; Rae et al., 2005; Takahashi and Ukhorskiy, 2007] and solar wind dynamic pressure pulses or interplanetary shocks [Zong et al., 2009] are generally believed to be the two most important external sources of ULF wave excitation inside the magnetosphere. The K H instability can produce largescale vortices that can transport the solar wind material into the magnetosphere [Fairfield et al., 2000; Hasegawa et al., 2004]. Also, surface waves triggered by the K H instability can propagate inward via viscous effects and excite a field line resonance (FLR) in the magnetosphere [Hudson et al., 2004; Rae et al., 2005; Claudepierre et al., 2008]. On the other hand, when a solar wind dynamic pressure pulse or interplanetary shock impinges on the magnetopause, ULF waves can be excited inside the inner magnetosphere [Zong et al., 2009], thus transporting the solar wind energy into the Earth s magnetosphere. The above two mechanisms can be distinguished by their preferable occurring regions (local time). The K H instability mechanism requires a shear flow in order to satisfy the threshold condition of the instability, with the main occurrence region lying at the dawn and dusk flanks of the magnetopause [Kivelson and Pu, 1984; Hudson et al., 2004; Claudepierre et al., 2008]. In contrast, the solar wind dynamic pressure pulses compress the magnetopause first and then launch fast magnetosonic waves into the magnetosphere [Kepko and Spence, 2003; Hudson et al., 2004; Claudepierre et al., 2009]. These waves could further stimulate FLR at the dayside magnetosphere around magnetic local noon. [5] It is interesting to point out that responses of the Earth s magnetosphere to negative solar wind impulses are rarely studied even though the geomagnetic effect of the negative impulse impact is not ignorable. Sato et al. [2001] found that some auroral activity enhanced dramatically during impact of negative impulses. They proposed that FLRs were excited by the negative impulse impact and auroral electrons were thus accelerated by the field aligned current associated with the FLRs in the polar region. This process would lead to intensification of the auroral activity. In contrast, by using the Ultraviolet Imager (UVI) data on the Polar satellite, Liou et al. [2006] and Liou [2007] reported that the intensity of the aurora decreased apparently, while the size of the aurora extended from the dayside to the nightside in response to negative impulses. Liou [2007] suggested that during negative impulses, the inflation of the magnetosphere would result in an increment of the magnetic mirror ratio and a reduction of the particle loss cone. This effect would further lead to auroral activity weakening. It was also suggested that the onset of magnetospheric substorm expansion phase may be triggered by negative dynamic pressure pulses. [6] Previous numerical studies of ULF waves excited by solar wind impulses have confirmed the coupling of the global cavity mode and the FLRs [Allan et al., 1986; Zhu and Kivelson, 1988; Lee and Lysak, 1989]. However, they focused only on the single positive impulse. In a previous study, by using the numerical model developed by Lee and Lysak [1991a, 1991b], we have studied ULF waves and the compression/expansion of the magnetosphere (denoted by the increase/decrease of the parallel component of the magnetic field) in response to positive/negative pressure pulses with multiple satellite observations [Zhang et al., 2009]. A part of the work is summarized in Figure 1. 2of14

3 Table 1. MHD Simulation Results 0 (LT) 06 (LT) 12 (LT) Positive Pulses Poloidal + + Toroidal + Negative Pulses Poloidal + Toroidal + + [7] Figure 1 illustrates poloidal and toroidal waves excited by a positive/negative impulse at three different locations ( 0:00 local time (LT), 6:00 LT, 12:00 LT) at geosynchronous orbit. The amplitude, duration, and period of the positive and negative impulses are all the same, while the phase is opposite. The blue solid lines stand for the magnetospheric response to the positive impulse, and the red dashed lines represent perturbations due to the negative impulse. Characteristics of the waves at 06:00 LT and 18:00 LT are exactly the same due to the azimuthal symmetry assumption in the simulation, thus, we show only the temporal profile of the magnetic field at 18:00 LT. Our simulation boundaries are at 12:00 LT and 0:00 LT and the solar wind dynamic pressure impulses are imposed at 12:00 LT with the form of electric field pulses. Considering the boundary condition effect, we use the simulation results at 11:00 LT and 23:00 LT instead of evaluating the ULF wave responses at 12:00 LT and 0:00 LT. It is worth noting (Figure 1) that the radially/azimuthally oscillating magnetic field (poloidal/toroidal waves) at 11:00 LT and 23:00 LT are in antiphase [Zhang et al., 2009]. The periods are similar and the amplitudes are larger at 11:00 LT than that at 23:00 LT. The polarization distributions of poloidal and toroidal waves at geosynchronous orbit above are shown in Table 1. [8] The problems concerning ULF waves at geosynchronous orbit, such as their global distributions and possible interactions with energetic particles in the magnetosphere, will be addressed in this paper by combining multisatellite observations and numerical simulations. Solving these problems will contribute greatly to the understanding of the basic physics of mass, momentum, and energy transport. 2. Observations 2.1. Event Selecting and Data Processing Methodology [9] We have searched for solar wind dynamic pressure impulse events based on the OMNI ( nasa.gov/cdaweb/istp_public/) data from 1 January 2001 to 31 March The 1 min data from the OMNI Web site are used to determine the solar wind conditions at 1 AU, including the magnetic field, the velocity, the proton density, and the dynamic pressure. The solar wind dynamic pressure impulse events are selected manually from the daily plots with the following criteria: (1) the variation of dynamic pressure exceeds 1 npa or 50% and (2) the duration of the dynamic pressure change lasts no longer than 45 min. Five hundred twenty four dynamic pressure pulse events with 270 positive and 254 negative pulse events have been identified and the details are shown in Table 2. [10] The 1 min geosynchronous magnetic field data from Geostationary Operational Environmental Satellite 8 (GOES 8), GOES 10, GOES 11, and GOES 12 [Singer et al., 1996] during 2001 to 31 March 2009 are used to study the magnetic field response to the solar wind dynamic pressure impulses. Using 1 min solar wind data at 1 AU from the OMNI Web site we have manually estimated the travel time from the Earth s bow shock nose to geosynchronous orbit according to the solar wind speed. It is noted that the solar wind and IMF data provided by the OMNI Web site have been shifted to 1 AU at the Earth s bow shock nose. Since the data sets have been shifted to geosynchronous orbit according to the solar wind speed, the arrival time can also be used as the zero point of epoch time series. The magnetic field data from 1.5/3 h prior to the zero epoch time (the arrival time of the pressure impulse) to 1.5/3 h following the zero epoch time are then extracted for case/statistical study, respectively. For the case study, the solar wind and IMF data from ACE within a 3 h interval, centered at the time of the dynamic pressure change, are also extracted. The arrival time of solar wind dynamic pulses at geosynchronous orbit are determined by the solar wind speed and are further confirmed by sharp compression signatures. The OMNI data in the same time period as GOES satellite data are used in our statistical study. To study the local time dependance of magnetic field response, our data sets have been binned into six 4 h sectors (02:00 06:00, 06:00 10:00, 10:00 14:00, 14:00 18:00, 18:00 22:00, and 22:00 02:00). [11] It has been shown that the L shell difference due to being at different geomagnetic latitudes is always smaller than 1 R E [Onsager et al., 2004], which is much shorter than the Pc5 ULF wavelength of km. The influence on the phase and amplitude of the resonant/propagating waves/ pulses is negligible. Thus, in our statistical study, we neglect the influence of the latitude (L shell) difference. [12] In order to analyze the properties of ULF waves excited by dynamic pressure pulses, the magnetic fields are projected to the mean field aligned (MFA) coordinate system [Takahashi et al., 1990; Zong et al., 2007], in which the parallel direction p is determined by a 20 min sliding averaged magnetic field, the azimuthal direction a is parallel to the cross product of p and the spacecraft position vector, and the radial direction r completes the triad. For the case study, the magnetic field data are then filtered with the 150 s to 600 s band pass filter Case Study: ULF Waves Excited by Positive Impulses at Dawn ( 06:00 LT) and Dusk ( 18:00 LT) Sectors [13] Figure 2 (left) shows that a positive solar wind dynamic pressure impulse hit the Earth s magnetosphere on Table 2. Dynamic Pressure Impulse Database Year Total Positive Negative Through March to March of14

4 Figure 2. Measurements from ACE, GOES 8, and GOES 11 satellites on (left) 19 August 2002 and (right) 31 July The magnetic field measured by GOES satellites is projected to the mean field aligned (MFA) coordinate system. (a h) The interplanetary magnetic field (IMF) Bx and Bz, the solar wind speed, the number density of solar wind protons and the solar wind dynamic pressure (Psw) at 1 AU. (i n) The parallel, radial and azimuthal magnetic field components that are filtered by the 150 s to 600 s band pass filter. The arrival of the solar wind dynamic pressure impulses are marked with red dashed lines. The parallel direction p is determined through the 20 min sliding average of the magnetic field, the azimuthal direction a is parallel to the cross product of p and the spacecraft position vector. Finally, the radial direction r completes the triad. 19 August At around 11:40 UT, marked by a dashed line, the GOES 8 satellite was located at the dawn (around 06:30 LT) side. [14] Figure 2a shows the x and z components of the magnetic field (Bx and Bz) during 10:10 13:10 universal time (UT). Bz was consistently positive during this time period. Meanwhile, there was a solar wind density jump from about 6 cm 3 to more than 15 cm 3, and a dynamic pressure enhancement from 3.5 to 8 npa, although the solar wind speed decreased slightly from 530 to 510 km/s. The IMF Bx experienced a change from 3 to 3 nt at around 12:40 UT, which can be considered as the sign of a heliospheric current sheet (HCS) [Winterhalter et al., 1994]. However, the dynamic pressure pulse (Figure 2d) at around 11:40 UT is found at the front edge of the HCS. [15] At geosynchronous orbit, disturbances in the magnetic field (Figures 2e 2g (left)) have been observed by GOES 8. The measured magnetic field has already been projected to the MFA coordinate system and filtered with a 150 s to 600 s band pass filter to reveal the Pc5 ULF wave response. At the bottom of the figure, UT is converted into LT by using LT = UT + Long/15, where Long denotes the longitude of the GOES satellites. [16] Two types of perturbations are identified in the response of the magnetic field component of three ULF wave modes to the dynamic pressure impulses: for the first type perturbation, the magnetic field first decreases and then increases during its first cycle, thus this type of variation is denoted by /+; for the second type of perturbation, the magnetic field first increases and then decreases during its first cycle and is denoted by +/. [17] As shown in Figures 2e 2g (left), Br (poloidal) and Ba (toroidal) components are in phase (+/ ), while the compressional component Bp is 180 out of phase ( /+) with Br and Ba components. Due to the previous magnetic field variation, the initial oscillation excited by the solar wind dynamic pressure impulse is somehow ambiguous. 4of14

5 Figure 3. The format is the same as Figure 2 but for two negative solar wind dynamic pressure impulses on (left) 7 October 2006 and (right) 11 November The periods of both B r and B a variations were found to be about 8 min during the first two cycles. [18] Figure 2 (right) shows another event occurred on 31 July At 03:50 UT, the GOES 11 satellite was located at the dusk side (around 18:55 LT). The solar wind density jumped from 9 to 20 cm 3, along with a dynamic pressure enhancement from 2.5 to 6.4 npa, while the velocity remained almost unchanged. Both the IMF Bx and By changed their signs at around 03:50 UT, which can be considered as the sign of a HCS. Again, the dynamic pressure pulse (Figure 2d) at around 03:50 UT was found at the front edge of the HCS. The corresponding magnetospheric response observed by GOES 11 at geosynchronous orbit is marked by a dashed line (see Figure 2 (right)). The compressional mode (parallel magnetic field B p ) was the /+ type perturbation with an amplitude of nearly 1 nt. Meanwhile, the poloidal and toroidal modes started to oscillate in the +/ type. It is interesting to point out that the both events observed at dawn and dusk side show the same polarization behaviors Case Study: ULF Waves Excited by Negative Impulses at Dawn ( 06:00 LT) and Dusk ( 18:00 LT) Sectors [19] As a comparison, an example of ULF waves excited by a negative impulse at the dawn ( 06:00 LT) and dusk ( 18:00 LT) sector is shown in Figure 3. It can be seen that on 7 October 2006, a negative solar wind dynamic pressure impulse was observed by ACE. At around 16:05 UT, the density dropped from more than 40 cm 3 to less than 10 cm 3, and the solar wind dynamic pressure decreased from 11.2 to 2.4 npa, while the velocity changed slightly. Meanwhile, a definite change of the IMF Bx and Bz polarity was observed. It is shown in Figure 3a that Bx changed from 3 to 4 nt and Bz from 5 to 15 nt. [20] During this time period, GOES 11 satellite was located at around 07:00 LT. From 07:05 LT (marked by a dashed line), all three modes (compressional, poloidal, and toroidal waves) started to oscillate in the +/ type, although the amplitudes were smaller for the poloidal and toroidal waves than that for the compressional mode. [21] Figure 3 (right) illustrates another negative impulse observed at 03:25 UT on 11 November As shown in Figure 3 (right) both solar wind density and dynamic pressure experienced a sudden decrease, dropping from 21 to 7cm 3 and from 5.4 to 1.8 npa respectively. The solar wind speed remained nearly constant at around 360 km/s during this time period. [22] During this event, GOES 10 was located at around 18:25 LT. All three modes, the compressional, poloidal, and toroidal magnetic field recorded by GOES 10, started to oscillate in the +/ type. Comparing Figures 2 and 3 carefully, 5of14

6 Figure 4. The different responses of noon and midnight for positive impulses on 9 November 2006 and 3 August The format is the same as in Figure 2. we can see that the filtered B p was oscillating in the /+ type after a positive solar wind dynamic pressure impulse, whereas B p excited by a negative pulse varied in the +/ type at both the dawn and dusk sectors at geosynchronous orbit Case Study: ULF Waves Excited by Positive Impulses at Noon ( 12:00 LT) and Midnight ( 0:00 LT) Sectors [23] ULF waves excited by positive solar wind impulses at noon ( 12:00 LT) and midnight ( 0:00 LT) sectors have also been investigated. Two of those typical cases are given in Figure 4 and Figure 5. Figures 4a 4e (left) present the solar wind conditions during 17:30 20:30 UT on 9 November At around 18:50 UT, a positive solar wind dynamic pressure impulse was observed. The solar wind density jumped from around 12 to 24 cm 3 and the solar wind speed increased from 350 to 390 km/s. The solar wind dynamic pressure enhanced from 3.5 to 8 npa. The disturbed magnetic field at geosynchronous orbit observed by the GOES 8 satellite located at around 13:45 LT is depicted in Figures 4e 4g (left). Beginning at 13:45 LT (marked by a dashed line), signatures of the excited waves (Figures 4e 4g) were similar to those observed on 19 August Similarly to cases shown in Figure 2 and 3, both poloidal and toroidal waves (Figures 2f, 2g, 3f, and 3g) were excited simultaneously. Poloidal B r was oscillating in the /+ type with an amplitude of 4 nt, while B a was the +/ type with a much smaller initial amplitude (0.5 nt). All of these waves oscillated with a period of 8 9 min. [24] As shown in Figure 4 (right), at around 07:12 UT on 3 August 2001, the solar wind experienced increases in density (from 6 to 27 cm 3 ), velocity (from 380 to 450 km/s), and dynamic pressure (from 1.6 to 10.4 npa). At this time, GOES 10 was located near midnight (around 22:30 LT). It can be seen from the figure that the parallel component B p varied in phase for both cases in Figure 4 (left) and Figure 4 (right). Meanwhile, the radial component B r and azimuthal component B a oscillated in antiphase, but the latter one (Figure 4 (right)) was with an obviously larger amplitude. Comparing ULF waves excited by positive impulses at noon ( 12:00 LT, Figure 4 (left)) and midnight ( 0:00 LT, Figure 4 (right)) carefully, we find that the magnetospheric response at noon and midnight are in antiphase (180 ), which agrees with our simulation results shown in Figure 1. Further, the poloidal mode wave excited by a positive impulse with a similar amplitude is stronger near noon than that at the dawn or dusk side, which is also consistent with our simulation results. The possible propagation mechanism for this case may be similar to propagation away from 6of14

7 Figure 5. The different responses of noon and midnight for negative impulses on 7 October 2006 and 26 March The format is the same as in Figure 2. midnight that has been seen by Weatherwax et al. [1997] in riometer data. Weatherwax et al. [1997] suggested this can be explained by a substorm model proposed by Liu et al. [1995] in which compressional waves are thought to be resonantly converted to shear Alfvén waves on field lines threading the plasma sheet boundary layer. However, Lessard et al. [1999] concluded that substorms were not directly responsible for exciting the resonances. Recently, it has been shown that ULF waves can be directly excited by interplanetary shock or solar wind dynamic pressure pulse impact [Zong et al., 2009] Case Study: ULF Waves Excited by Negative Impulses at Noon ( 12:00 LT) and Midnight ( 0:00 LT) Sectors [25] In order to study ULF waves excited by a negative impulse at noon ( 12:00 LT) sector, a negative dynamic pressure case is given in Figure 5 (left). The solar wind conditions during 16:05 16:10 UT on 7 October 2006 are shown in Figure 5 (left). The proton density dropped from 42 to 8 cm 3. The dynamic pressure also underwent a decrease from 11.2 to 2.4 npa, while the solar wind speed varied smoothly. At this time GOES 12 was located at around 11:00 LT. From 11:05 LT, the solar wind dynamic pressure dropped quickly and the whole magnetosphere experienced an expansion. Stimulated B p is found to be oscillating in the +/ type. There was also an obvious enhancement of the amplitude of both poloidal (B r ) and toroidal (B a ) waves, although with different inital phase: positive (B r ) or negative (B a ). But B r was stronger than B a. [26] In Figure 5 (right), we have shown a different case to examine ULF waves excited by negative impulse at the midnight ( 0:00 LT) sector. During this event, as we can see, the solar wind experienced drops in density (from 10 to 3.5 cm 3 ), velocity (from 440 to 430 km/s), and dynamic pressure (from 3.6 to 1.2 npa) at around 04:05 UT on 26 March When this impulse impacted the Earth s magnetosphere, the GOES 8 satellite was at the midnight sector (23:05 LT). The observed ULF waves at geosynchronous orbit are shown in Figures 5e 5g (right). A strong +/ wavelike perturbation of B p with an amplitude of about 4 nt was observed immediately after the pulse impact. Both the excited poloidal and toroidal waves vary in antiphase although there was some ambiguity here. This feature is in agreement with the MHD simulation results shown in Figure 1. The amplitude of excited poloidal and toroidal waves was about 1.6 and 4 nt, respectively. This demonstrates again that ULF waves in the magnetosphere excited by positive and negative solar wind dynamic pressure impulses are antiphase (see Figures 4 and 5). 7of14

8 Figure 6. (left) Superposed epoch analysis for all the positive dynamic pressure impulse events with northward IMF at the epoch zero and (right) events with southward IMF at the epoch zero. On each plot are the temporal profiles (gray) and medians (purple) of solar wind conditions, IMF z component and the magnetic field in geosynchronous orbit. The red lines above/below the purple line represent the upper/ lower quartiles of sorted parameters. Zero on the epoch time axis, denoted by the blue vertical dashed line, corresponds to the arriving UT of dynamic pressure impulse at geosynchronous orbit for all the events. Meanwhile, 9 min before and after the epoch zero are marked by the blue dotted line Statistical Study: ULF Wave Response to Solar Wind Positive and Negative Pressure Impulses [27] The responses of three ULF wave modes at geosynchronous orbit to the positive/negative solar wind dynamic pressure impulses differ in term of the wave amplitude and phase as shown in the case study sections. The superposed epoch analysis method has been used extensively in space physics as an effective tool to uncover the underlying physics in a large database. In this section we use superposed epoch analysis to study the different responses of ULF waves at geosynchronous orbit to the positive/negative solar wind dynamic pressure impulses for all 524 identified cases. [28] Figure 6 shows superposed epoch analysis results for all 270 positive dynamic pressure impulse events. Cases with northward IMF Bz (IMF Bz is positive at the epoch zero time) are shown in Figures 6 (left), while those with southward IMF Bz are shown in Figures 6 (right). The gray lines in Figures 6a 6c represent the temporal profiles of solar wind dynamic pressure, number density, and velocity, respectively, for all the cases. Figure 6d show the IMF Bz. The purple line is the median value line for each solar wind and IMF parameter shown in Figures 6a 6d. The red lines above/below the purple line in Figures 6a 6d represent the upper/lower quartiles of the sorted solar wind and IMF parameters. With the same format as Figures 6a 6d, Figures 6e and 6g represent the three ULF wave modes: magnetic field components Bp, Br, and Ba. Zero on the epoch time axis, denoted by a cyan vertical dashed line, corresponds to the arrival UT of dynamic pressure impulses at geosynchronous orbit for all events. Meanwhile, 9 min before and after the epoch zero are marked by two cyan dotted lines. [29] As shown in Figures 6a 6g, the temporal profiles of each parameter for different cases are diverse with the gray lines filling the entire area of each figure. However, the characteristics of positive solar wind dynamic pressure 8 of 14

9 impulse are well revealed by the purple median value lines in Figures 6a 6c. [30] As shown in Figure 6 (left), the dynamic pressure increases from 3 to nearly 6 npa, the number density increases from 7 to nearly 12 cm 3, while the solar velocity changes little. The upper quartiles of the three solar wind parameters in Figures 6a 6c exhibit substantial enhancements from 5.5 to more than 10 npa for the dynamic pressure, from 14 to 22 cm 3 for the solar wind density, but no obvious change for the solar wind speed. Correspondingly, the lower quartile has an increment of the solar wind dynamic pressure from 2 to 3 npa and density from 4 to 8cm 3. The IMF Bz at 1 AU shown in Figure 6d shows a decrease of the median value (from 3 nt to around 0), the upper quartile (from 8 to 5 nt), and the lower quartile (from a little more than 0 to 3 nt) at around the arrival time of these dynamic pressure impulses. As a consequence, the parallel component of the geosynchronous magnetic field B p increases from 106 to 113 nt for the median value and from 128 to 136 nt for the upper quartile, i.e., the magnetosphere is compressed by 6.6%. Meanwhile, the radial component of the magnetic field B r increases from 0.4 to 0.7 nt for the median value and from 1 to 2.2 nt for the upper quartile, while the azimuthal component B a increases from 0.8 to 1.3 nt for the upper quartile though the median value shows little change. [31] In Figure 6 (right), the dynamic pressure increases from 3 to nearly 4.5 npa, and the number density increases from 8 to nearly 13 cm 3, while the velocity changes little. The upper quartiles in Figures 6a 6c reveal that the solar wind pressure increases from 5 to 8.5 npa, the density gets denser from 14 to 22 cm 3 while solar wind speed varies little. Also, the lower quartiles of the three solar wind parameters in Figures 6a 6c show a jump from 2 to 3 npa in dynamic pressure, from 5 to 7 cm 3 in proton density, whereas there is no obvious change in velocity. From Figure 6d, the IMF Bz at 1 AU shows an increase from 3.5 to 1 nt for the median value, nearly 0 to 3 nt for the upper quartile, and 8 to 5 nt for the lower quartile between the two blue dashed lines. At the same time, B p increases from 106 to 112 nt for the median value, from 124 to 134 nt for the upper quartile, indicating that the magnetosphere is compressed by 5.7%. Also B r jumps from 0.4 to nearly 1.0 nt for the median value and from 1.7 to more than 3.0 nt for the upper quartile, and B a increases from 1.5 to 2.7 nt for the upper quartile while the median value shows little change. [32] Thus, the wave disturbance amplitude of the radial component B r is apparently larger than that of the azimuthal component B a, implying that the poloidal mode is more intense than the toroidal mode at geosynchronous orbit under the impact of a positive solar wind dynamic pressure impulse. The upper and lower quartiles show a similar result. The B p, B r, and B a data plotted here have not been filtered as shown in the case study sections, and we do not distinguish different local time sectors here, thus the different /+ and +/ types of perturbation in B p, B r, and B a cannot be seen from Figures 6e 6g. [33] All 254 ULF wave cases excited by negative solar wind pressure impulses are superposed according to the arrival time (epoch 0) of the solar wind impulses to give an ensemble distribution. These negative cases are also divided into two categories according to the IMF Bz polarity (northward or southward at the epoch 0, shown in Figures 7 (left) and Figures 7 (right)). As shown by the median value lines in Figures 7a 7c, the dynamic pressure and proton density of the solar wind decrease significantly in a short time after the arrival of the solar wind dynamic pressure impulses. Meanwhile, the solar wind speed remains unchanged. And Figure 7d shows similar characteristics as those in Figure 6. Figures 7d 7f show variations of B p, B r, and B a components at geosynchronous orbit. By comparing Figure 6 with Figure 7, it can be easily found that ULF waves excited by a positive impulse are stronger than those by a negative one at geosynchronous orbit. Meanwhile, Figures 6d and 7d and show that the dynamic pressure impulse cases with southward IMF at around the zero epoch time induce much stronger disturbances in the magnetic field at geosynchronous orbit than those with northward IMF. On the other hand, at least for some occasions, it may well be that solar wind dynamic pressure pulses modulate the existing Pc5 waves, as shown by Olson [1987] that Pc 5 ULF waves are observed on most days. [34] In order to examine the responses of three magnetic field components to both positive and negative solar wind dynamic pressure impulses at different local time sectors in detail, the above data sets are binned according to the epoch time (5 min resolution) and the local time (4 h resolution) from 3 h prior to the impulse onset to 3 h following the impulse onset. The absolute values of parallel, radial, and azimuthal components are used to describe the strength of the magnetic field. These cases are accumulated in grids according to LT observed by GOES satellites and the amplitude plotted is the median of all the observations in each grid. The results of 270 positive solar wind dynamic pressure pulse events and 254 negative pulse events are given in Figure 8 (positive impulse) and Figure 9 (negative impulse). [35] Figures 8 and 9 show that the amplitude of parallel magnetic field component (B p ) increases/decreases after positive/negative impulse arrival. Another interesting result from Figures 8 and 9 is that the amplitude of the poloidal wave is larger than that of toroidal wave. Also, both B r and B a show an enhancement in the first 20 min after the zero epoch time at any local time for positive impulses, and last at least 3 h over the noon afternoon sector, while the disturbances excited by negative impulse are not so distinct. 3. Discussion [36] In this paper, after examining more than 8 years of data systematically we find that ULF waves can be excited by both positive and negative solar wind dynamic pressure impulses. However, only positive pressure pulses have been discussed in previous studies [e.g., Sibeck et al., 1989; Mathie and Mann, 2000]. [37] It can be seen from Figure 6 that the amplitude of the parallel component (B p ) of the magnetic field increases significantly for positive solar wind dynamic pressure impulses, indicating that the magnetic field at geosynchronous orbit is strongly compressed. The compression is observed at almost all local times, although these sudden variations appear to be weaker at the dawn and dusk sides than those at noon and midnight. In contrast, the statistical studies show that the B p strength decreases (Figure 7) when a negative 9of14

10 Figure 7. Superposed epoch analysis for all the negative dynamic pressure impulse events with the same format as in Figure 6. solar wind dynamic pressure impulse impinges on the magnetosphere. This indicates that the magnetosphere would expand after a negative pressure impact. The results shown in Figures 6 and 7 suggest that both an increase and a decrease of the solar wind dynamic pressure at 1 AU cause a significant change of the magnetic field at geosynchronous orbit. The observations shown in this paper suggest that the change of solar wind pressure will induce the compression or expansion of the whole magnetosphere. This may further cause global geomagnetic activity. It is interesting to point out that the magnetospheric response to a positive impulse is much stronger than that to a negative impulse (Figures 6 and 7). A similar conclusion has also been drawn in Andrioli et al. [2007] in which they found that SI amplitude is generally larger for (SI+) than that for (SI ). [38] We have found that the strength of both Br and Ba (shown in Figures 1 7) increase suddenly and immediately after a solar wind dynamic pressure pulse impinges on the magnetosphere, indicating that the ULF waves observed at geosynchronous orbit can be excited by a solar wind dynamic pressure pulse. The observed strengthened ULF oscillations of poloidal and toroidal waves in Figures 2 5 suggest that the solar wind energy can be transported into the magnetosphere by exciting ULF waves. Further, as shown in Figures 6 and 7, oscillations excited by positive impulses lasted longer ( 85 min) than those excited by negative impulses ( 25 min). [39] The excitation of ULF Pc5 waves was historically attributed to the Kelvin Helmholtz instability. Pc5 waves generated by KHI show minimum activity around noon near the subsolar stagnation region compared with the dawn and dusk sector [e.g., Anderson et al., 1990; Zhu and Kivelson, 1991; Lessard et al., 1999; Hudson et al., 2004; Rae et al., 2005; Takahashi and Ukhorskiy, 2007]. However, our study shows that ULF waves associated with solar wind dynamic pressure pulses exhibit a maximum at local noon, consistent with the scenario; ULF waves can be excited when a solar wind dynamic pressure pulse or interplanetary shock impinges on the magnetopause as observed by multispacecraft [Zong et al., 2009] and full MHD simulation [Kress et al., 2007], thus transporting the solar wind energy into the Earth s magnetosphere. [40] For the 7 October 2006 case, the GOES 11 and 12 satellites happened to be at two different positions on the equatorial plane, and the variations of the magnetic field are plotted in Figure 3 (left) and Figure 5 (left). By using the 10 of 14

11 Figure 8. Superposed epoch analysis of the magnetic field at geosynchronous orbit for all the 270 events of positive solar wind dynamic pressure impulses. (a) the change of median amplitude of parallel magnetic field (B p ) versus local time and epoch time. Twenty four hours of local time are divided into six 4 h sectors. (b and c) The radial magnetic field B r and the azimuthal magnetic field B a, respectively, with the same format as in Figure 8a. correlation analysis of the observations from the azimuthally separated GOES satellites [Takahashi et al., 1985], m ¼ ; ð1þ where d denotes the phase difference of ULF waves observed at two GOES satellite positions at geosynchronous orbit separated by a longitudinal angle of d. Given Onsager s work [Onsager et al., 2004] as mentioned in the introduction of this paper, the L shell difference (less than 1 Re) due to being at different geomagnetic latitudes is much shorter than the ULF wavelength ( km). Thus, the differences of geomagnetic latitudes and L values accounted by distinct longitude and local times between the two GOES satellites have minor effect on the calculation of m values in our paper. The toroidal wave number m was found to be around 1. [41] The ULF particle resonance condition is w = mw d, where w d denotes the drift frequency of particles with specific energy at geosynchronous orbit. ULF wave interaction with energetic particles is considered as an important mechanism for MeV electron acceleration at geosynchronous orbit [Southwood and Kivelson, 1981; O Brien et al., 2001, 2003], thus, it is worth discussing the potential impact of observed waves excited by both positive and negative pulses on the energetic particle acceleration and/or deceleration [Zong et al., 2009]. [42] The rate of energy change of a particle by interacting with a ULF wave [Southwood and Kivelson, 1982] in the absence of parallel electric field is dw =dt þ qe V d where dw/dt, E, V d, and m are the rate of the particle energy gain, wave carried electric field, longitudinal drift velocity, and the magnetic moment of the particle, respectively. There are two factors contributing to the electron acceleration or deceleration: the compression or expansion rate of magnetic field intensity, and the perturbed electric field. ð2þ 11 of 14

12 Figure 9. Superposed epoch analysis of the magnetic field at geosynchronous orbit for all the 254 events of negative impulses. The format is the same as in Figure 8. [43] As shown in the cases of Figures 2, 3, 4, and 5 and the statistical results in Figures 6 and 7, the magnetic field compression or expansion is significant only in the first few minutes as reflected by the profile of B p. Given that the maximum magnetic field enhancement (see Table 3 for positive dynamic pressure) and decrement (see Table 4 for negative dynamic pressure) were about 20% and 11%, respectively, the compression or expansion effect alone can be considered to accelerate or decelerate the energetic particles by 20% or 11%. [44] As discussed in Zong et al. [2009], the ULF waves excited by positive and negative dynamic pressure pulses Table 3. Characteristics of the Magnetic Field Parallel Component at Different Local Time for Positive Dynamic Pressure Impulses Locations (LT) DB p (nt) DB p (%) DB r (nt) DB r (%) DB a (nt) DB a (%) can accelerate or decelerate energetic particles. Since there is no electric field data available for geosynchronous orbit satellites, we are not able to give a quantitative calculation for the particle acceleration or deceleration. Nevertheless, based on numerical simulations [Zhang et al., 2009; Lee and Lysak, 1989], we can obtain a best guess of the electric field associated with both poloidal and toroidal wave modes at geosynchronous orbit using a dipole magnetic field prior to perturbation. [45] The estimated electric field by a full MHD approach is about 0.28 mv/m by taking DB 10 nt, the wave period as 6 min and the wavelength as 10 4 km. This is much Table 4. Characteristics of the Magnetic Field Parallel Component at Different Local Time for Negative Dynamic Pressure Impulses Locations (LT) DB p (nt) DB p (%) DB r (nt) DB r (%) DB a (nt) DB a (%) of 14

13 smaller than the observed amplitude of the ULF wave electric field ( a few mv/m and up to tens of mv/m) excited by the solar wind dynamic pressure pulses [Zong et al., 2009; Brautigam et al., 2005; Wygant et al., 1994]. It should be noted that since ULF waves are MHD waves, it is better to calculate the electric field through a full MHD approach, not simple Faraday s law [Vasyliunas, 2005]. [46] By using MHD simulation results [Lee and Lysak, 1989; Zhang et al., 2009], we are able to estimate the amplitude of ULF electric field near 12:00 LT at geosynchronous orbit during solar wind dynamic pressure pulses impact. From the onset of the pulse, the first 300 s of data in the different components of the magnetic field and electric field induced by 10 input pulses of different amplitude have been read. And we pick out the maximum values of the simulation results to do the linear regression analysis of corresponding E and B components to get the coefficients shown in this paper. For the toroidal mode, E r = * B a, and for the poloidal mode, E a = * B r, where the unit for E and B is mv/m and nt, respectively. Thus, the amplitude of the ULF electric field component excited by both positive and negative solar wind dynamic pressure pulses could reach a few mv/m and up to tens of mv/m [Zong et al., 2009; Brautigam et al., 2005] which would affect the energetic particles significantly [Zong et al., 2009; Kress et al., 2007]. The drift motion of energetic particles at geosynchronous orbit is mainly in the azimuthal direction, that is, the direction of the poloidal wave electric field. A resonant ion will be accelerated if the ULF wave electric field has the same sign as the drift velocity (the opposite sign for an electron) and will be decelerated if the ULF electric field has the opposite sign (the same sign for an electron) along its drift path. It should be mentioned here, particles in drift resonance will see an approximately constant electric field in their frame of reference (resonance frame) since the observed wave is propagating azimuthally at a speed comparable to that of the particles and thus resonant particles will be accelerated/decelerated most significantly [Elkington et al., 2003; Perry et al., 2005; Zong et al., 2009]. However, the discussion above is just a qualitative analysis of possible effects of ULF waves on the energetic particles moving at geosynchronous orbit. 4. Summary and Conclusion [47] In this paper, we have studied systematically ULF waves excited by positive and negative solar wind dynamic pressure pulses at geosynchronous orbit. We have identified 270 ULF events excited by positive solar wind dynamic pressure pulses and 254 ULF events excited by negative pulses from 1 January 2001 to 31 March Main results are summarized as follows: [48] 1. Both observational and numerical simulation results show that poloidal and toroidal modes of ULF waves oscillate in similar phase around dawn and dusk at geosynchronous orbit. But the phases of these waves are opposite near local noon and midnight. [49] 2. Statistical and simulation outcomes illustrate that the magnitude of ULF waves resulting from solar wind dynamic pressure impulses is larger around 12:00 LT than at dawn and dusk. [50] 3. Analysis of the database shows that the magnetospheric response to positive pulses is much stronger than that to negative ones. [51] 4. Observations show that the amplitude of poloidal waves is stronger than toroidal waves both in positive and negative pulse events. The potential impact of these waves on energetic particles at geosynchronous orbit is outlined. [52] Acknowledgments. This work is partly supported by the National Natural Science Foundation of China grants and by the Specialized Research Fund for State Key Laboratories. 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