Multipoint study of magnetosheath magnetic field fluctuations and their relation to the foreshock

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2011ja017240, 2012 Multipoint study of magnetosheath magnetic field fluctuations and their relation to the foreshock O. Gutynska, 1 J. Šimůnek, 2 J. Šafránková, 1 Z. Němeček, 1 and L. Přech 1 Received 6 October 2011; revised 1 March 2012; accepted 2 March 2012; published 14 April [1] The magnetosheath is occupied with a variety of low-frequency fluctuations from different sources. Among them, the bow shock and dominantly foreshock processes are often considered as their major contributors. We use distant (Wind) and close (Geotail) interplanetary magnetic field monitors and compare their measurements with simultaneous magnetic field observations within the dawn (Time History of Events and Macroscale Interactions During Substorms (THEMIS)) and dusk (Cluster) magnetosheath. We have found that coherent low-frequency ( Hz) variations can be registered in all locations; thus, their source is in the solar wind. On the other hand, no correlation was found for fluctuations of higher frequencies (up to 10 1 Hz); therefore, these fluctuations should be generated by local sources. We suggest that one of these sources is connected with magnetopause processes because the fluctuation amplitude grows toward the magnetopause. Citation: Gutynska, O., J. Šimůnek, J. Šafránková, Z. Němeček, and L. Přech (2012), Multipoint study of magnetosheath magnetic field fluctuations and their relation to the foreshock, J. Geophys. Res., 117,, doi: /2011ja Introduction [2] Interaction of the solar wind with the Earth magnetic field results in the formation of a bow shock in front of the magnetopause. The region between these two surfaces, the magnetosheath, contains many types of low-frequency waves that play an important role in the redistribution of energy and momentum from the bow shock toward the magnetopause. The internal solar wind fluctuations, foreshock waves, waves generated by the bow shock or magnetopause, and waves that are created in the magnetosheath itself are listed among possible sources of the magnetosheath variations. It is believed that the waves in the magnetosheath are strongly controlled by the upstream bow shock structure, by the q BN angle between the upstream magnetic field and the bow shock normal, and the local plasma b. [3] In the magnetosheath downstream a quasi-perpendicular shock, regular compressional waves with the periods about 20 s have been identified as mirror waves, which are nonpropagating in the plasma rest frame [Song et al., 1992a; Fazakerley and Southwood, 1994]. On the other hand, a predominant occurrence of ion cyclotron modes was referred [Anderson et al., 1994] near the magnetopause because the magnetic flux tubes pile up and plasma deplete when approaching the magnetopause, thus their growth rate is greater than that of the mirror instability. Upstream the quasi-parallel shock, the foreshock region is formed by 1 Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic. 2 Institute of Atmospheric Physics, Czech Academy of Science, Prague, Czech Republic. Copyright 2012 by the American Geophysical Union /12/2011JA particles reflected from the bow shock [Fairfield, 1976]. Interaction of reflected particles with the ambient solar wind excites many kinds of fluctuations and these fluctuations are convected through the foreshock by the solar wind flowing into the magnetosheath and can be amplified at the bow shock. Thus the field fluctuations are often of the same order of magnitude as the background field downstream the quasiparallel shock [Engebretson et al., 1991]. [4] Numerous studies have been dedicated to the origin and nature of plasma waves in the magnetosheath and adjacent regions. Song et al. [1990, 1992a, 1992b] identified a standing slow mode wave in front of the magnetopause when the density increases while the IMF strength decreases, and higher-frequency mirror modes can be convected with the magnetosheath flow. Later, Hubert and Samsonov [2004] and Samsonov and Hubert [2004] reanalyzed these observations and showed that the origin of this apparently standing region is connected with temporal variations of the IMF and solar wind density. On the other hand, Hubert et al. [1998] suggest that the distance from the bow shock is a key parameter determining the nature of plasma waves. [5] Blanco-Cano et al. [2006] studied a foreshock morphology and its influence on the magnetosheath using global hybrid simulations. The authors confirmed expectations that the magnetosheath is permeated by a variety of waves resulting from the convection of upstream waves as well as from a local wave generation. The authors presented different wave characteristics in the quasi-parallel and quasi-perpendicular parts of the magnetosheath, similarly like several further authors, including the following: (1) Němeček et al. [2002] found a significantly higher level of variations in the dawn magnetosheath and identified the foreshock as the most important source of magnetosheath fluctuations; (2) Sibeck and Gosling [1996] proposed that a portion of the observed 1of12

2 Figure 1. Trajectories and mutual configuration of all spacecraft in the X Y plane (in the GSE system) during a whole investigated time interval, UT. Schematically, the model magnetopause [Shue et al., 1997] and bow shock [Jeřáb et al., 2005] are shown. Geotail moves from the solar wind toward the bow shock, both Cluster 2 (C2) and Cluster 3 (C3) move toward the magnetopause, THB moves from the magnetopause into the middle magnetosheath, and THC scanned the magnetosheath along the magnetopause. fluctuations results from scanning of the radial magnetosheath profile as it oscillates back and forth but that the most of these variations originate in the foreshock; (3) Shevyrev et al. [2003], Shevyrev and Zastenker [2005], and Shevyrev et al. [2007] defined properties of plasma and magnetic field fluctuations in the different regions of undisturbed solar wind, foreshock, quasi-parallel, and quasi-perpendicular magnetosheath and found a higher level of plasma and magnetic field fluctuations in the foreshock than that in the undisturbed solar wind and in the quasi-parallel magnetosheath when the level of plasma and magnetic field variations is larger than that in the quasi-perpendicular case; and (4) Constantinescu et al. [2007] found a high concentration of low-frequency wave sources in the electron foreshock and in the cusp region. [6] Narita et al. [2006] revealed an organization in the wave propagation pattern; the upstream waves propagate upstream in the plasma frame, while the magnetosheath waves propagate toward the flank region and toward the magnetopause, thus wave properties are different in the upstream and the downstream regions. Nevertheless, they are similar at the quasi-parallel and quasi-perpendicular shocks suggesting that the upstream waves are not transmitted to the downstream across the shock and that the downstream waves do not depend on the q BN angle. [7] Gutynska et al. [2008] have studied low-frequency magnetic field fluctuations and found the typical correlation lengths of these fluctuations to be about 1 R E in a statistical sense. Gutynska et al. [2009] confirmed that the correlation length is generally of the order of 1 R E being longer for fluctuations of large amplitudes in the frequency interval from to Hz. Moreover, the authors estimated the influence of the foreshock dividing the analyzed set between dawn and dusk events, however, they did not find any substantial difference, similarly to the findings of Narita et al. [2006]. Based on these facts, the authors concluded that the upstream fluctuations penetrating the magnetosheath are correlated over longer distances than intrinsic magnetosheath variations. However, their statistical study was based on Cluster observations, and thus there was half a year gap between their dawn and dusk events. Moreover, the study was limited to spacecraft separations of 5 R E. [8] In this case study, we enjoy the advantage of both Cluster and Time History of Events and Macroscale Interactions During Substorms (THEMIS) missions when the Cluster spacecraft were orbiting in the dusk and the two THEMIS spacecraft in the dawn magnetosheath and, simultaneously, solar wind conditions were monitored in two locations: Wind near the L1 point and Geotail in front of the bow shock. Overview of the spacecraft locations is seen in Figure 1 and their coordinates are summarized in Table 1. From four Cluster spacecraft we used only two: Cluster 2 and 3 because of their location in the magnetosheath. Such configuration ensures that if one of the magnetosheath spacecraft pair is behind the foreshock, the second pair does not. Simultaneous observations of the dawn/dusk magnetosheath provide a good possibility to investigate propagation of the solar wind features through the magnetosheath at different places (near the magnetopause vs the middle of the magnetosheath; on different magnetosheath flanks, etc.) and to discuss the possible foreshock influence. The paper focuses on the spatial correlation of the solar wind and magnetosheath variations with a motivation to determine an optimum location of upstream (and/or magnetosheath) monitor for investigation of magnetopause processes. 2. Data Set and Data Processing [9] The event was registered on 6 December 2008 by two THEMIS and Cluster probes. THEMIS B (THB) was orbiting outbound through the dawn magnetosheath and THEMIS C (THC) near its apogee skimmed the vicinity of the magnetopause. On the other hand, the two Cluster spacecraft (Cluster 2 and 3) located in the dusk magnetosheath moved toward the magnetopause being led by Cluster 2 (the separation between Cluster 2 (C2) and Cluster 3 (C3) along the magnetopause normal was 1.5 R E ). The parts of spacecraft orbits are shown in Figure 1, and their coordinates at the beginning and at the end of the investigated interval are listed Table 1. Locations of the Spacecraft at Two Times and Distances of a Particular Spacecraft to the Model Magnetopause Spacecraft Time (UT) GSE Location of Spacecraft X, R E Y, R E Z, R E R MP, R E THB THC C C Geotail of12

3 that this distance is a good parameter for characterization of the spacecraft location within the magnetosheath. [10] To analyze the sources of magnetosheath fluctuations in the frequency range from 10 4 to 10 1 Hz, we used spinaveraged magnetic field from Cluster (Fluxgate Magnetometer [Balogh et al., 2001]) with a temporal resolution approximately 4 s without any further processing. To their comparison with THEMIS observations, we used magnetosheath magnetic field from THB and THC with the resolution of 3 s [Auster et al., 2008]. As monitors of upstream conditions, we used data from the solar wind spacecraft lagged on the corresponding propagation time to the bow shock nose: Wind [Lepping et al., 1995] and Geotail [Kokubun et al., 1994] magnetic fields with time resolutions of 3 s. [11] The present paper deals with a case study of one interval of a 12 h duration. We apply the same techniques as those of Gutynska et al. [2009], i.e., the whole time interval was broken into half-hour subintervals and the cross-correlation functions between the solar wind and magnetosheath spacecraft were computed for each time interval. The amplitude of fluctuations is described by the standard deviation computed on the same subinterval. Since the whole interval is rather long, the relative position of the spacecraft with respect to the magnetopause changes as it can be seen from Figure 1 and Table 1. Figure 2. Magnetic field measurements of the spacecraft. Shown are the magnetic field strength of (a) Wind, (b) Geotail, (c) Cluster 2, (d) Cluster 3, (e) THEMIS B, (f) THEMIS C, and (g) computed q BN from the Wind magnetic field at two locations (THB and C2) in the magnetosheath. The vertical lines divide a whole time interval into the three parts discussed throughout the paper (see sections 3 and 4.3 for explanation). in Table 1 together with estimated distances of a particular spacecraft from the model magnetopause [Shue et al., 1997]. These distances were measured along the radius vector pointing to the particular spacecraft. The negative value of this distance (C2 at 1600 UT) means that the model predicts the spacecraft located in the magnetosphere. However, it indicates an inaccuracy of the model because no magnetopause crossing of C2 was observed prior to 1630 UT. Cluster was located in middle latitudes (Z 8 R E ) and the Shue et al. [1997] model does not include the magnetopause indentation in the cusp region. Consequently, the negative distance from the model magnetopause is not surprising. Thus, we believe 3. Overview of the Event [12] An overview of the measurements of the magnetic field in the magnetosheath and input solar wind magnetic field is shown in Figure 2. Figures 2a and 2b present the interplanetary magnetic field (IMF) observations that exhibit moderate fluctuations. The features at L1 (Wind, Figure 2a) are more or less well reproduced in the Geotail data (Figure 2b) until 1000 UT. After 1000 UT, Geotail enters gradually a region of enhanced fluctuations and the features corresponding to those observed in the Wind data can be hardly identified. Figures 2c and 2d show the magnetic field strengths as measured by two Cluster spacecraft in the dusk magnetosheath. We have chosen C2 and C3 as representatives because they were separated by largest distance but their separation does not exceed 3.5 R E during the event. The IMF is compressed by a factor of 4 in the magnetosheath and one can note a similarity between Geotail and Cluster observations. However, although being separated by 3.5 R E only, levels of fluctuations observed by C2 and C3 differ several times at the end of the interval. [13] Magnetic field profiles measured by THB and THC (Figures 2e and 2f) do not resemble the upstream measurements and, although THB is located just downstream of THC with an average separation of about 12 R E, it is difficult to identify corresponding features in their data. Moreover, there is a significant difference in levels of fluctuations measured at these two locations, THC always observed larger fluctuations than THB. [14] Since the observations are simultaneous, the differences should be connected with the spacecraft locations and/ or with the IMF orientation with respect to the bow shock normal. It is generally expected that the changes of fluctuation characteristics are connected with the variations of the q BN angle. We compute this angle as the angle between the 3of12

4 Figure 3. (a) Relative standard deviations (RSD) and (b) standard deviations (SD) of the magnetosheath magnetic field fluctuations observed by C2 (crosses) and C3 (triangles) as a function of the q BN angle. The color scale shows the estimated distance of the spacecraft from the magnetopause. IMF vector (Wind data) and the normal to the Jeřáb et al. [2005] model bow shock surface at the point where the magnetosheath streamline coming through a particular spacecraft crosses the bow shock. We use this method because the study of Hayosh et al. [2005] has shown that q BN computed this way is the best description of the IMF direction for characterization of the magnetosheath fluctuations. These angles are shown in Figure 2g for THB and C2. [15] The interval under study can be broken into three parts (see Figure 2). The IMF was oriented roughly along the Parker spiral until 0830 UT, thus THEMIS was behind the quasiparallel bow shock, whereas the bow shock upstream of Cluster was nearly perpendicular. The second subinterval (between 0830 and 1230 UT) was characterized by large changes of the q BN angle at both flanks but the IMF direction was stable and corresponded to THEMIS being behind the quasi-perpendicular and Cluster behind quasi-parallel shocks during the last subinterval. This can probably explain why THEMIS observations differ from upstream data in the first subinterval. [16] On the other hand, enhanced fluctuations are seen only by C2, whereas their level is constant at C3 and THC, and even decreases at the THB location during the last subinterval. It suggests that not only q BN but other parameters would control magnetosheath fluctuations. 4. Analysis of Fluctuations [17] We analyze magnetic field fluctuations in detail using different techniques in this section Analysis of Fluctuation Amplitudes [18] The magnetic field generally increases from the bow shock to magnetopause due to magnetic field pileup and the structures embedded in the background flow (e.g., mirror mode waves) and blown down with the magnetosheath flow would do the same even if they do not grow. We suggest to use the relative standard deviation (RSD) for a quantification of such effects. On the other hand, the standard deviation, SD would be better for a description of growth/decay of waves propagating with respect to the ambient plasma. For these reasons, we use both quantities in Figure 3. The plots show RSDs (Figure 3a) and SDs (Figure 3b) as a function of the q BN angle for both the C2 and C3 spacecraft. The color scale represents the radial distance from the model magnetopause [Shue et al., 1997]. The spacecraft moved from the bow shock toward the magnetopause and larger distances correspond to earlier times. One can note that the level of magnetosheath fluctuations decreases with increasing q BN. This trend is clearly seen for RSDs but it is visible in the plot of SDs as well. However, the color of the points shows that the high level of fluctuations was observed near the magnetopause and that this level decreases toward the bow shock. Consequently, we are not able to resolve what of these two factors, q BN or the distance from the magnetopause is more important. The relative standard deviations are about equal for Geotail (not shown) and C3 that could suggest that these two spacecraft observe similar fluctuations but the fluctuations at the C2 location are significantly amplified. [19] At this time, THB was located in the opposite magnetosheath flank and moved from the magnetopause toward the bow shock. Consequently, it was near the magnetopause when upstream q BN was low and in the middle of the magnetosheath during the interval of large q BN. For this reason, the triangles in Figure 4a that belong to THB show even quantitatively similar profiles to those in Figure 3a. However, a comparison of THB and THC data reveals that the spacecraft closer to the magnetopause always observes larger fluctuations than that near to the bow shock. It is true for RSDs (Figure 4a) as well as for SDs (Figure 4b). It suggests that a portion of fluctuations is generated locally at the magnetopause or an amplification of the magnetosheath fluctuations toward the magnetopause. Our correlation analysis in section 4.4. would distinguish between these two possibilities Wavelet Analysis [20] The most important characteristic of magnetic field fluctuations is their frequency spectrum. Since the driving (upstream parameters) is unsteady and the spacecraft change 4of12

5 Figure 4. (a) Relative standard deviations (RSD) and (b) standard deviations (SD) of the magnetosheath magnetic field fluctuations observed by THB (triangles) and THC (crosses) as a function of the q BN angle. The color scale shows the estimated distance of the spacecraft from the magnetopause. their locations with respect to the magnetosheath boundaries in course of the analyzed interval, the wavelet spectrum is more appropriate. This technique enables one to identify the dominant frequencies and to locate them in time and space. [21] Figure 5 displays the Morlet transform with the wave number equal to 6 [Torrence and Compo, 1998] applied on the data shown in Figure 2. For clarity, we use the period instead of the frequency on the vertical axis. The analyzed interval of periods ranges from 10 to 8000 s. [22] The upstream monitor, Wind (Figure 5, first panel), exhibits a significant power at periods above s until 1400 UT. The second solar wind spacecraft, Geotail (Figure 5, second panel), repeats even details of the Wind observations until 1200 UT but it records fluctuations in a broader frequency range later. The fluctuation power is significantly enhanced in the magnetosheath but no clear difference between dawn and dusk sides can be seen in the wave power throughout the interval. The magnetosheath spectra exhibit a larger portion of short-period fluctuations but the spectral lines observed in the solar wind can be identified in both magnetosheath flanks until 1200 UT. From this it follows that the solar wind fluctuations of these periods penetrate the magnetosheath regardless of the IMF orientation with respect to the bow shock normal. Moreover, the IMF orientation seems to exhibit only a small (if any) effect on the locally generated fluctuations of shorter periods because the overall difference between dawn and dusk pairs of the spacecraft (Cluster vs THEMIS) is smaller than the difference between two spacecraft at the same flank (C2 vs C3 or THB vs THC). It confirms our previous analysis and contradicts to the general expectation that the amplitude of the magnetosheath fluctuations would be always larger behind the quasi-parallel bow shock and implies that other sources of magnetosheath fluctuations should be considered Fourier Analysis [23] Since the magnetosheath is a high-beta region, the magnetic field fluctuations can be connected with turbulence of the plasma flow around the magnetopause. Due to limitations of the data set used in this study, we can investigate the frequency range from 10 4 to 10 2 Hz that would be characterized by a power law spectrum with a slope of 5/3 for a fully developed turbulence [e.g., Goldstein et al., 1995]. Figure 6 presents the frequency spectra measured at three different regions (in the pristine solar wind by Wind, in front of the bow shock by Geotail, and in the magnetosheath represented by C2) and in three time intervals marked in Figure 2. The spectral index of 5/3 is colored in each plot by the green line for the sake of reference. [24] In spite of different wave powers in the analyzed intervals (compare blue lines in Figures 6a 6c), the spectral index in the solar wind is close to 5/3. The same is true for Geotail observations near the bow shock in the first two intervals (black lines in Figures 6a and 6b). It means that there was enough time for the full dissipation because these regions are far away from possible fluctuation sources. [25] The spectral slope underwent a dramatic change when Geotail entered the foreshock (Figure 6c). The content of the lowest frequencies is the same as that at the Wind location but the spectrum is significantly enhanced at higher frequencies that are generated by foreshock processes. Since the spectrum is measured within or in the close vicinity of the source region, there is not enough time for effective damping of high-frequency components. [26] All frequency spectra measured within the magnetosheath (C2, red lines in Figures 6a 6c) show an enhanced portion high-frequency fluctuations but when the spacecraft is in the magnetosheath proper and behind the quasi-perpendicular shock (Figure 6a), the overall enhancement of the magnetosheath fluctuation power with respect to upstream is about one order of magnitude. On the other hand, this difference rises to two orders of magnitude for low frequencies in the last interval (Figure 6c). C2 is behind the quasi-parallel shock and close to the magnetopause during this time. The foreshock processes do not generate the lowfrequency fluctuations (compare blue and black lines in Figure 6c), thus the most probable source of these fluctuations is the magnetopause or magnetosheath itself. However, 5of12

6 Figure 5. Wavelet frequency spectra of magnetic field fluctuations observed in the solar wind (Wind), in the solar wind or in the foreshock (Geotail), and in different magnetosheath locations (C2, C3, THB, and THC). Note that the Wind observations are propagated to the bow shock nose (time shift of 48 min). 6 of 12

7 Figure 6. Fourier spectra of magnetic field fluctuations observed by Wind, Geotail, and C2 in three investigated time intervals from Figure 2. Corresponding straight lines show average spectral slopes, and the spectral index of 5/3 is given by the green line as reference. taking into account the dimensions of the dayside magnetosheath, the waves with frequencies of 10 4 Hz can be hardly excited there because the corresponding wavelength would be significantly larger Correlation Analysis [27] The wavelet analysis suggests that (1) the fluctuations with periods of 2000 s and longer are of solar wind origin, and (2) the fluctuations with a shorter period observed in different magnetosheath places exhibit similar spectra and they could have a common source (bow shock, magnetopause or magnetosheath itself). However, similar frequencies do not necessarily mean the same source. For this reason, we have performed a correlation analysis for two frequency bands that were defined by the band pass filters. The low-frequency band contains frequencies observed in the solar wind ( Hz, i.e., corresponding periods of s). The length of the time interval for correlation was 2 h and the investigated range of the lag, DT was 30 min. Note that the Wind data were time shifted using the actual upstream velocity prior to the correlation. [28] We have computed cross correlations between all pairs of the spacecraft but we are showing only three examples in Figures 7a 7c, each of which consists of two plots: the top plot presents the measured magnetic field after an application of the band pass filter, and the bottom plot shows the cross-correlation coefficient multiplied by 100. [29] Figure 7a compares the observations of two upstream monitors. One can note almost perfect correlation coefficients (0.85 1) until 0830 UT, a little worse correlation ( ) until 1400 UT and almost no correlations later. There are two reasons: the amplitude of IMF fluctuations in the pristine solar wind and the IMF orientation. The fluctuations of the IMF magnitude are large and IMF is oriented nearly along the Parker spiral until 0830 UT. Between 0830 and 1400 UT, the amplitude of fluctuations is still large but the IMF orientation fluctuates. The largest correlation coefficients in this interval are observed around 1030 UT when IMF returned to the Parker spiral orientation that characterizes the first interval. On the other hand, after 1400 UT, the amplitude of fluctuations at the Wind location becomes small and IMF turns its orientation. The enhanced level of fluctuations at the Geotail location can be thus attributed to the foreshock effects. Since these fluctuations are generated locally, the correlation coefficient drops down. [30] Figure 7b displays correlations of Geotail and C3, and it tests if the foreshock fluctuations can be identified in the magnetosheath. Figure 7b shows a very nice correlation until 0830 UT. This correlation can be attributed to the IMF fluctuations recorded by Wind and Geotail that were blown across the bow shock without any substantial modification. The correlation analysis reveals a portion of correlated fluctuations until 1100 UT and then the fluctuations in upstream and downstream regions become uncorrelated. The time interval after 1100 UT corresponds to the radial or ortho-parker IMF orientations that are favorable for a foreshock formation at locations of the C2 and Geotail spacecraft. We can conclude that foreshock effects modify the upstream fluctuations to a degree that does not allow them to be identified in the magnetosheath and that the foreshock fluctuations are not directly blown down through the bow shock. [31] Figure 7c presents a search for fluctuations that can be observed in the whole dayside magnetosheath. We show the cross correlations between C3 and THB magnetic fields because these spacecraft are in the magnetosheath proper nearly through the whole interval, with a possible exception of the first hour (until 0500 UT) when THB was rather close to the magnetopause. Looking at Figure 7c, we can conclude that the only correlated features are those coming from upstream ( UT). The foreshock effect or a close proximity of the magnetopause prevents these upstream features to be observed in the magnetosheath and locally generated fluctuations are not correlated over the THB C3 separation. The enhanced correlation coefficients after 1400 UT would be probably attributed to a random coincidence of some features because the time delays are negative at 15 UT. It means that the structure would be observed first by THB that is located more downstream than THC. The positive time lag at 1530 UT is consistent with observations of a structure from the solar wind but such 7of12

8 Figure 7. Filtered profiles of the magnetic field magnitude (top plots) and cross-correlation coefficients (bottom plots). The spacecraft pairs are listed in the headings; the magnetic field profile belonging to the first of them is in red. The computed cross-correlation coefficients are multiplied by 100 and shown by the color scale. 8 of 12

9 Figure 8. Cross-correlation coefficients of magnetic field fluctuations as a function of the q BN angle. (a) Cross correlations between C2 and C3. (b) Cross correlations between THB and THC. The color scale presents the time of measurements. structure would be registered by other spacecraft, and it is not the case. [32] Figure 7 has shown that the long-period fluctuations of solar wind origin are well correlated through the whole dayside magnetosheath, probably with an exception of a layer adjacent to the magnetopause. However, shorter periods typical for the magnetosheath should be investigated on shorter scales. For this reason, we have shortened the time interval for the correlation to 20 min and did not apply any filter to the original signal. Since the frequency spectrum of magnetosheath fluctuations is very similar to that recorded in the foreshock (Figure 5), we plot the peak of the correlation as a function of the q BN angle. [33] Due to the spatial separation of the magnetosheath spacecraft, we have two angles for each correlation function and thus each correlation coefficient appears twice in Figure 8 which shows the value of the cross-correlation coefficients as a function of the q BN angle for the C2 and C3 and THB and THC spacecraft pairs. Figure 8a (Cluster) seems to suggest that the correlation coefficient is determined by q BN because large values of this coefficient were observed only if q BN was larger than 50. However, the color of the points corresponds to the time of measurements and one can note that the low values of q BN were observed at the end of the interval when the spacecraft approached the magnetopause. Consequently, we have two candidates for the lack of correlation: the quasi-parallel bow shock and the magnetopause vicinity. To resolve their importance, we plotted the correlations between the THEMIS spacecraft in Figure 8b using the same format. This plot shows that there is no organization of correlation coefficients with q BN and that the only clear trend is a gradual decrease of the correlation coefficients with time. The large values observed at the beginning of the time interval correspond to an enhanced level of the upstream fluctuations. [34] The analysis of Figure 8 confirms the conclusion made earlier, but the cross correlation that Figure 8 shows was computed over the whole frequency range. Since the wave power is concentrated in low frequencies, the possible correlation of a high-frequency part can be missed in these calculations. For this reason, we present correlation properties of fluctuations in the frequency range of Hz (i.e., periods from 10 to 1000 s) that are typical for the foreshock and magnetosheath (Figure 5). In order to estimate their source and the way of the propagation, we have calculated the cross correlation on a 20 min interval with the time lag ranging from 10 to +10 min. Since the number of experimental points in this interval is 400 only, correlations on a level 0.3 or lower are not reliable (see discussion by Gutynska et al. [2009]), thus we are showing correlations exceeding this level in Figure 9. All three parts of Figure 9 demonstrate essentially the same: a lack of correlations even between the shortly separated spacecraft across the bow shock (Geotail and C3, Figure 9a), in the dusk (C2 and C3, Figure 9b) or in the dawn magnetosheath (THB and THC, Figure 9c) for fluctuations in the analyzed frequency range. The points where the correlation coefficient exceeds 0.5 can be found only in left parts of the plots and all of them are connected with abrupt IMF changes. We can conclude that the magnetosheath fluctuations in this frequency range are generated locally and that they do not propagate from the foreshock or over distances comparable with the separation of the magnetosheath spacecraft. Since THB and THC are located on similar streamlines, we can conclude that the lifetime of these fluctuations seems to be shorter than 2 min (the time of a propagation of the magnetosheath plasma from THC to THB). This is consistent with the finding of Gutynska et al. [2008] that the correlation length of magnetosheath fluctuations does not exceed 1 R E in the frequency 9of12

10 Figure 9. Filtered profiles of the magnetic field magnitude (top plots) and cross-correlation coefficients (bottom plots). The spacecraft pairs are listed in the headings; the magnetic field profile belonging to the first of them is in blue. The computed cross-correlation coefficients are multiplied by 100 and shown by the color scale. 10 of 12

11 range of Hz and does not depend significantly on the magnetic field orientation with respect to the streamline or plasma flow direction. 5. Summary and Conclusion [35] The presented case study complements a comprehensive analysis of magnetosheath fluctuations by Gutynska et al. [2009] and points out several basic problems connected with statistical results. Statistical studies using distant solar wind monitors cannot properly describe the solar wind input to the magnetosheath because they do not take into account the evolution of the IMF features [e.g., Šafránková et al., 2009] and they cannot include the foreshock effects. We have shown that: [36] 1. Low-frequency (in the range of Hz) upstream fluctuations can be identified at all locations in the magnetosheath, probably with an exception of the magnetopause vicinity, but they can be significantly modified by foreshock processes. [37] 2. Coherent IMF fluctuations of higher frequencies were identified neither in observations of a monitor just upstream of the bow shock nor at the magnetosheath. The lack of correlations between upstream and downstream regions is consistent with the study of wave propagation patterns by Narita et al. [2006]. [38] 3. The amplitude of magnetosheath fluctuations increases toward the magnetopause. This is true for both the standard and relative standard deviations and it suggests that the magnetopause processes are an important source of magnetosheath magnetic field variations. [39] 4. We did not found foreshock fluctuations propagating to the magnetosheath directly or via a mode conversion at the bow shock [Blanco-Cano et al., 2006]. The lack of the correlation between a foreshock monitor and nearby magnetosheath spacecraft suggests that the foreshock fluctuations are destroyed at the bow shock and new fluctuations are generated there. On the other hand, our study does not exclude an indirect excitation of magnetosheath magnetic field fluctuations by the pressure fluctuations generated in the foreshock [Sibeck and Gosling, 1996]. However, this mechanism can be applied only on a low-frequency part of the fluctuation spectrum. [40] The similarity of frequency spectra of fluctuations in the magnetosheath and in the foreshock is connected with a similar way of their excitation in a similar background plasma rather than with their propagation across the bow shock. There were several attempts to identify a direct response of the magnetospheric magnetic field to quasiperiodic fluctuations in the foreshock [e.g., Fairfield et al., 1990], but our study shows that fluctuations in the analyzed frequency range do not reach the magnetopause, thus they cannot directly affect the magnetosphere. On the other hand, the high level of fluctuations in a magnetosheath layer adjacent to the magnetopause that was observed at both flanks regardless of the IMF orientation suggests that the solar wind magnetosphere interaction is unstable in nature and that it cannot be described by quasi-static models. [41] We would like to point out that we did not find the mirror mode structures in the analyzed case. These waves are often reported as a typical wave mode in the magnetosheath [e.g., Tatrallyay and Erdos, 2002; Tatrallyay et al., 2008] and we cannot exclude that these waves can be correlated over larger distances under some circumstances, although the case study of Horbury and Lucek [2009] found their correlation lengths of the order of 1 R E. The excitation of mirror mode waves requires high plasma beta and large temperature anisotropy [Treumann et al., 2004] and the relation of these conditions to the upstream state should be further investigated. [42] Acknowledgments. The authors acknowledge the Geotail, Wind, and Cluster teams for the magnetic field data and NASA contract NAS and V. Angelopoulos for use of data from the THEMIS mission. Specifically, we thank K. H. Glassmeier, U. Auster, and W. Baumjohann for the use of FGM data provided under the lead of the Technical University of Braunschweig and with financial support through the German Ministry for Economy and Technology and the German Center for Aviation and Space (DLR) under contract 50 OC The present work was supported partly by the Czech Grant Agency under contracts 205/09/0170 and 205/09/0112 and partly by the Research Plan MSM and Project ME 09106, which are financed by the Ministry of Education of the Czech Republic. O. Gutynska thanks the Charles University Grant Agency (GAUK ) for the support. [43] Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper. References Anderson, B. J., S. A. Fuselier, S. P. Gary, and R. E. 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