Cluster observations of hot flow anomalies

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2003ja010016, 2004 Cluster observations of hot flow anomalies E. A. Lucek, T. S. Horbury, and A. Balogh Blackett Laboratory, Imperial College, London, UK I. Dandouras and H. Rème Centre d Etude Spatiale des Rayonnements, Toulouse, France Received 2 May 2003; revised 16 March 2004; accepted 9 April 2004; published 12 June [1] On 2 April 2002, Cluster entered the solar wind at high northern latitudes and observed a series of disturbances upstream of the bow shock. We suggest that these were signatures of a sequence of hot flow anomalies (HFAs), observed at different stages of development. We estimate the orientation and motion of the HFAs and structures within them using multispacecraft data and examine the variation of plasma flow in the context of the orientation of the underlying discontinuities. We demonstrate that the motional electric field at each disturbance was in a direction such that it would act to focus ions reflected from the bow shock toward the discontinuity, consistent with current understanding of HFA formation. The first disturbance consisted of hot plasma flowing along the estimated discontinuity plane during the core of the event, together with a weakened solar wind beam. Toward the edge of the event, compressed solar wind plasma flowed approximately perpendicular to the discontinuity plane, consistent with expansion of the hot plasma. We suggest that the presence of multiple ion distributions signifies that the HFA was at an early stage of its evolution. A second HFA, which had a more complex signature, contained a single ion distribution within the event core, which is the more typical signature of an HFA. It also contained a large velocity deflection, consistent with expansion of the plasma perpendicular to the discontinuity plane. The final HFA event we present is associated with a shock encounter, demonstrating the level of complexity that can be associated with the bow shock response to changing upstream conditions. INDEX TERMS: 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions; 2154 Interplanetary Physics: Planetary bow shocks; 7811 Space Plasma Physics: Discontinuities; 7839 Space Plasma Physics: Nonlinear phenomena Citation: Lucek, E. A., T. S. Horbury, A. Balogh, I. Dandouras, and H. Rème (2004), Cluster observations of hot flow anomalies, J. Geophys. Res., 109,, doi: /2003ja Introduction [2] Hot flow anomalies (HFAs) are transient perturbations of the terrestrial bow shock first identified using data from the AMPTE and ISEE missions [Schwartz et al., 1985; Thomsen et al., 1986]. They occur upstream of the bow shock, and were first characterized observationally by a region of depressed magnetic field filled with hot plasma flowing in a direction significantly deflected from the solar wind velocity vector. HFAs can cause large perturbations to the background solar wind, drive shocks and inject energized particles into the upstream plasma. They were discovered to have a signature in the magnetosheath [Paschmann et al., 1988; Schwartz et al., 1988; Safránková et al., 2000] and later it was found that they can even affect the magnetopause sufficiently for a ground response to occur [Sibeck et al., 1999]. A comprehensive survey of their observational characteristics can be found in the work of Schwartz et al. [2000]. Copyright 2004 by the American Geophysical Union /04/2003JA [3] HFAs are thought to be generated by the interaction of thin tangential discontinuities (TDs) with the bow shock. If the plane of an interplanetary discontinuity lies at a small angle to the Sun-Earth line, so the normal to the discontinuity has a large component perpendicular to the sunward direction, then the line of intersection between the TD and the bow shock tracks slowly across the shock surface as the TD is convected antisunward by the solar wind flow. At the line of intersection, ions which have been reflected from the bow shock can be directed upstream as a result of the change in magnetic field direction at the discontinuity. If the motional electric field on either or both sides of the discontinuity is directed toward the discontinuity, then these particles are focused toward the centre of the discontinuity plane [Burgess, 1989; Thomas et al., 1991; Thomsen et al., 1993; Schwartz et al., 2000]. [4] The action of the motional electric field generates a population of energized ions, streaming away from the bow shock along the TD. Simulations and observations show that if the motional electric field is directed toward the discontinuity on both sides, a more symmetric HFA signature is typically generated than if the electric field only 1of10

2 points toward the discontinuity on one side [e.g., Thomsen et al., 1993]. Observations of HFAs containing two ion populations, a solar wind beam and a reflected ion distribution, have been made [Thomsen et al., 1988], and have been interpreted as the signature of an HFA at an early stage of evolution. Later, instabilities driven by the two ion populations convert the relative streaming energy of the two populations to thermal energy of a single, hot, thermalized ion population [Thomsen et al., 1988]. [5] The core of the HFA expands under the internal pressure of the energetic ion population, generating a cavity bounded by a compression, or a shock if the expansion rate is great enough, propagating into the surrounding plasma. Previous observations have shown that a shock is more likely to be observed by a spacecraft on exiting the structure [Schwartz et al., 1988], which is typically the edge of the cavity which is propagating against the solar wind. Simulations of the interaction process have been successful in reproducing the major physical characteristics of these events [Thomas et al., 1991; Lin, 2002]. [6] The orientation of the TD determines the velocity at which the TD tracks across the bow shock. In order for an HFA to develop, the tracking velocity needs to be slow relative to the velocity of a reflected ion. The ratio between these two velocities is a useful measure of the interaction time within which an HFA can develop [Schwartz et al., 2000]. [7] A further common feature of HFAs documented in previous studies has been called an internal recovery [e.g., Thomsen et al., 1986, 1988; Fuselier et al., 1987]. An internal recovery is a short time within the hot, low-density HFA cavity when the plasma parameters return to values nearer to those of the solar wind. Sometimes the recovery is complete or the plasma is compressed over the solar wind state. Thomsen et al. [1988] suggested that these internal recoveries are regions of compressed solar wind plasma within the larger HFA structure. [8] A further class of disturbances observed upstream of the bow shock are foreshock cavities [e.g., Sibeck et al., 2002]. These consist of a bundle of magnetic field flux tubes with enhanced suprathermal particle flux which expand under the excess particle pressure, generating small compression regions in the plasma on both edges. These disturbances are generated upstream when changes in the interplanetary magnetic field direction act to connect part of the upstream region to the bow shock. If the bow shock configuration is such that reflected ions escape upstream and undergo Fermi-acceleration, then these flux tubes can be populated by ion distributions characteristic of the foreshock. Expansion then occurs, causing enhancements in magnetic field magnitude and plasma density, similar to, but less extreme than the compression regions bounding HFAs. Foreshock cavities differ from HFAs in that they are typically bounded by small changes in magnetic field direction, rather than having an interplanetary discontinuity embedded within them, as in the case of an HFA. Also, the plasma inside a foreshock cavity is neither heated nor deflected significantly. Foreshock cavities are the signature of an isolated region of foreshock which has affected the surrounding plasma, rather than the consequence of a sharp interplanetary discontinuity interacting with the bow shock. [9] Most studies of HFAs to date have been in the terrestrial environment, but recently HFAs have also been identified upstream of the Martian bow shock [Øieroset et al., 2001], and in principle the same mechanism could operate wherever a discontinuity of appropriate thickness interacts in this way with a collisionless shock. Such a mechanism might be an important process by which particles are energized in regions such as at interplanetary shocks in the heliosphere, or at shocks propagating through the corona, driven, for example, by coronal mass ejections. Although the suprathermal particles generated by HFAs are not particularly energetic, they might act as a seed population for other shock acceleration processes. We aim, therefore, to understand the mechanism by which the particles are energized, and the bulk structure and evolution of these events. [10] The observations made by single and dual spacecraft of HFAs are sufficient to characterize the local properties of the energized plasma within the HFA cavity. In addition the orientations of the discontinuities bounding the cavity have been estimated in various studies using minimum variance techniques [Sonnerup and Cahill, 1967] and the characteristics of shocks generated at the edges have been examined [e.g., Fuselier et al., 1987]. However, these data are not sufficient to probe the three-dimensional structure of the HFA, nor are they well suited to examining HFA time evolution. [11] In 2000 the four Cluster spacecraft were launched into a polar orbit, with an apogee of 19.6 R E. The satellites fly in a tetrahedron formation, allowing for the first time for some distinction to be made between spatial structures and temporal variations, and for the three dimensional form of plasma signatures to be measured. In this paper we present data from one Cluster orbit when the spacecraft observed a sequence of disturbances upstream of the bow shock. We argue in this paper that these disturbances are signatures of HFAs rather than foreshock cavities. We use four point magnetic field data from the FGM instruments [Balogh et al., 2001] to obtain unambiguous estimates of the orientation of a variety of boundaries associated with the HFAs, and the velocity of those boundaries along the normal to their surface. This allows us to get a good idea of the three dimensional structure of these events. We are then able to place observations of both the bulk plasma behavior and ion distribution functions available from the CIS instruments [Rème et al., 2001] in the context of what we can learn about the three dimensional structure of the HFAs. We have not examined in detail electron data from the PEACE instrument [Johnstone et al., 1997], but we have been able to use electron moments in order to calculate the Mach numbers of some of the shocks associated with these events. Future studies will draw on a wider range of instruments to make a more detailed examination of the kinetic processes occurring within these events. 2. Overview [12] On 2 April 2002 (day 92) at 0328 UT Cluster crossed the bow shock into the solar wind at high northern latitudes, at (+9.9, 2.2, +8.1l) R E in GSE coordinates, corresponding to 1110 LT. We note for reference that GSE coordinates are used throughout this paper. The tetrahedron separation scale was of the order of 100 km, and the four spacecraft typically observed 2of10

3 interval 2), and a complex sequence of HFA-like signatures and shocks (interval 3). Figure 1. Overview of the three HFA events. Panels show magnetic field elevation angle, q B, and longitude angle, f B, in GSE coordinates; magnetic field magnitude, jbj; proton density, N p ; proton temperature, T p ; velocity vector elevation and longitude angles, q V and f V ; and velocity magnitude, jvj. The three intervals containing HFAs are numbered 1, 2, and 3. Data are from Cluster 3. The vertical dashed line labeled a indicates the bow shock crossing. well correlated magnetic field and plasma signatures in the magnetosheath and solar wind. The characteristics of the bow shock crossing were consistent with a super critical, quasi-perpendicular shock, and there was no discernible ultralow-frequency (ULF) wave activity characteristic of the ion foreshock in the upstream region. Cluster then encountered a number of disturbances. Figure 1 shows an overview of the data recorded by spacecraft 3 between 0320 and 0410 UT. The dotted vertical line (labeled a) shows the outbound bow shock crossing at 0328 UT. Three time intervals are indicated by bold horizontal bars in all panels, labeled 1, 2 and 3. The same labeling convention is used in all figures showing a time series of plasma and magnetic field data: time intervals are indicated by heavy horizontal bars on each panel and are labeled by numbers, and transitions are indicated by vertical dotted lines across all subpanels, and are labeled using lowercase letters. For boundary normals and velocities quoted in this paper, we use the convention that the normal direction has a positive X GSE component, and the direction of motion of the boundary is indicated by the sign of the velocity of the discontinuity along its normal. A positive velocity thus indicates sunward motion. [13] Sections 3.1, 3.2 and 3.3 discuss intervals 1, 2 and 3 respectively. We show that these intervals contain a young HFA (within interval 1), a well developed HFA (in 3. Observations 3.1. Interval 1 [14] Figure 2 shows a close-up of the plasma and magnetic field measured by Cluster 3 during interval 1 shown in Figure 1. The first interplanetary discontinuity which passed over the Cluster spacecraft (indicated on Figure 2 by the interval labeled 1) had a duration of about 20 seconds, and occurred at 0335:10 UT. Cluster was located close to the bow shock at this time, within 1500 km of the location of the last bow shock encounter, and so if an HFA signature had been generated, we would expect Cluster to have observed it. We are confident therefore that this discontinuity did not generate an HFA. The discontinuity passed over each of the four satellites, with a time delay between the crossings related to the discontinuity orientation. These time delays can be used to infer the normal to the discontinuity and its velocity along the normal direction, under the assumption that the discontinuity was a plane traveling with constant velocity [e.g., Schwartz, 1998]. [15] Application of the timing method showed that the discontinuity in interval 1 on Figure 2 had a normal inclined to the Earth-Sun line, as required for generation of an HFA, and that it would first intersect the bow shock north of the Cluster tetrahedron, and then move southward over the tetrahedron as a result of convection in the solar wind flow. However, although the orientation of the discontinuity in interval 1 was appropriate for HFA generation, it did not Figure 2. Close-up view of the data during the first HFA event, in the same format as Figure 1. Data are from Cluster 1. Vertical dashed lines indicate transitions, and heavy horizontal bars indicate time intervals referred to in the text. 3of10

4 appear to be a TD, since it had a nonzero magnetic field component along the normal. It was also not a sharp discontinuity, being composed of several changes in magnetic field direction. In addition calculation of the motional electric field on either side of the discontinuity showed that it acted to move reflected ions away from the discontinuity plane. Therefore we would not expect this discontinuity to have generated an HFA [Thomas et al., 1991], and we do not consider it further. [16] The interval between transitions a and b on Figure 2 contains a disturbance which we interpret as the signature of an HFA. It consists of a central hot core (interval 2) within which the flow vector is strongly deflected, and is flanked by compressions (transitions a and b). The signature of the discontinuity which underlies this HFA can be seen most clearly in the second panel of Figure 2 which shows a change in the longitude angle of the magnetic field within interval 2, at around 0336:20 UT. The horizontal dashed line shows the direction of the magnetic field before the discontinuity, for comparison with the magnetic field direction after the spacecraft exited the disturbance. The change in angle was approximately 70. The discontinuity, therefore, was embedded in the event, consistent with the signature of an HFA. If the event were a foreshock cavity, we would expect it to be bounded by interplanetary discontinuities. We suggest therefore that this was the signature of an HFA rather than a foreshock cavity. [17] In passing through the HFA, the spacecraft first encountered a weak compression region (transition a), which bounded one side of the event. The extent of the core of the event (interval 2), can be seen from the low magnetic field magnitude jbj and ion density N p, increased ion temperature T p, and a flow deflection, here clearly visible in the angles of the velocity vector. The interior of the event was also characterized by large amplitude, rapid variations in the magnetic field direction, shown in the top two panels. These fluctuations showed significant differences at the different spacecraft, indicating that variations were occurring on spatial scales smaller than the spacecraft separation, which was 100 km at this time in the mission. Thomsen et al. [1986] also reported that large differences in the magnetic field signatures at ISEE-1 and ISEE-2 were observed when the spacecraft separation exceeded several hundred kilometers. Simulations by Onsager et al. [1991] suggest that instabilities should generate waves with wavelengths of 10 or more ion inertial lengths: the fluctuations seen here, with scales of 100 km when the ion inertial length is >100 km, are therefore significantly smaller than those seen in the simulations. The differences between each spacecraft pair contain information on the scale lengths of magnetic field variations in different directions, and in principle these scale lengths can be estimated by statistical analysis of the differences between spacecraft, although we do not perform such an analysis here. [18] The spacecraft exited the event through a compressed region bounded by transition b at 0336:48 UT. Associated with the magnetic field decrease at transition b there was a small increase in the bulk plasma velocity (panel 8 on Figure 2), consistent with transition b being a reverse shock. The spacecraft then crossed another structure (between transitions c and d), which we suggest was a further encounter with the expanding event. The details of these four transitions are discussed in more detail later in this section. [19] We first estimated the orientation of the discontinuity which was embedded in the HFA during interval 2. We were unable to apply spacecraft timing analysis to calculate the normal direction in this case, since the discontinuity was interrupted by the HFA. In the case of a tangential discontinuity, however, an estimate of the normal to a discontinuity can be made using data from a single spacecraft by calculating the cross product of the upstream and downstream magnetic fields. Under the assumption that the discontinuity was a TD, we estimated the discontinuity normal to be n dis = [0.17, 0.07, 0.98], predominantly in the Z GSE direction. [20] It is often useful to compare features seen close to the Earth, which have been modified by interaction with the terrestrial environment, with data recorded upstream. We used the orientations of the discontinuity and the local solar wind velocity vector to predict the time at which we would expect it to have passed the ACE spacecraft. In this case, however, although there were a number of features in the ACE data which might correspond to these two discontinuities observed by Cluster, the similarity is not great enough for us to be confident in their association. The predicted time of observation at ACE is very sensitive to the estimation of the discontinuity normal vector, especially when the normal is predominantly in Z GSE as in this case. Also, ACE was situated approximately 18 R E below the ecliptic plane, at (+220.4, 1.9, 18.2) R E in GSE coordinates, and if the discontinuity was closely aligned with the ecliptic plane it is possible that it did not cross the ACE orbit. We therefore do not pursue the association between the Cluster observations and the ACE data. [21] The normal vector to the discontinuity underlying the HFA within Figure 2, interval 2, was almost entirely contained within the X-Z GSE plane. Cluster was located near noon, and so this HFA can conveniently be represented in the X-Z GSE plane. This discontinuity normal was also mainly in the Z GSE direction, indicating that the plane of the discontinuity was nearly parallel to the GSE equatorial plane. Thus as the discontinuity was convected antisunward by the solar wind, the line at which the discontinuity intersected the bow shock tracked southward relatively slowly. The velocity at which the TD tracked across the bow shock was estimated [e.g., Schwartz et al., 2000]. The expected bow shock orientation, calculated using a model bow shock and the Cluster location, was found to be n bs = [0.93, 0.14, 0.34]. Using the observed upstream solar wind velocity and the estimated discontinuity orientation, n dis, we estimated the speed at which this TD tracked southward across the tetrahedron to be 110 km/s. The corresponding velocity projected onto the bow shock surface was about v dis = [50, 0, 130] km/s. It is difficult to calculate the uncertainty in the velocity since tilting the discontinuity normal closer to the Z GSE direction causes a large reduction in the tracking velocity. A slow traversal of the bow shock, such as was estimated here, might be expected for discontinuities which generate clear HFA-like disturbances, since discontinuities which track quickly across the bow shock have little opportunity to develop. One measure of the interaction time is the ratio between the tracking velocity and the velocity of a reflected solar wind 4of10

5 Figure 3. Schematic of the first HFA event projected onto the X-Z GSE plane. We interpret the HFA as bubble expanding under internal pressure. The form of the bubble is constrained by the following information: the spacecraft location (filled circle) relative to a model bow shock surface, the estimated discontinuity plane (heavy dashed line), the velocity perturbation vectors (faint lines), plotted assuming that the discontinuity tracks southward at 110 km/s, and the orientations of the compression and shock at the edges of the event. See color version of this figure at back of this issue. ion. For HFA generation this ratio should be significantly less than 1 [Schwartz et al., 2000]. In this case the ratio was 0.16, implying that there was sufficient time for an HFA to develop from this TD. [22] The orientation of the discontinuity normal underlying the HFA in interval 2 of Figure 2 implied that the TD first intersected the bow shock northward of the spacecraft, and that as it convected over the tetrahedron the spacecraft passed from the region southward of the discontinuity to that northward of the discontinuity. Calculation of the motional electric field around this discontinuity showed that E was first directed northward (i.e., toward the discontinuity) with a value of jej 1.9 mv/m, and then after the passage of the HFA across the spacecraft, E was directed southward (i.e., still toward the discontinuity), with a larger amplitude of jej 3.6 mv/m. Therefore E was directed toward the discontinuity on both sides, with the size of the electric field greater after the discontinuity. Consequently, ions reflected at the bow shock would be expected to be focused along the discontinuity plane. [23] We applied timing discontinuity analysis [Schwartz, 1998] to four point magnetic field data from the two transitions a and b. It was found that the normal vector defining the orientation of the leading edge of the initial magnetic field compression (transition a) was n a = [0.46, 0.40, 0.79]. The velocity of this compression along the normal vector was estimated to be only 15 km/s in the solar wind frame (i.e., antisunward), a value which is of the order of the uncertainty in the measurement, consistent with the observation of a small compression. In contrast the normal vector to transition b, which the spacecraft crossed at the end of the event, was n b = [0.60, 0.26, 0.76], with a velocity in the solar wind frame of 340 km/s. Calculation of the Alfvén and fast magnetosonic Mach numbers using upstream magnetic field data and electron moments gives values of approximately 5 in each case, consistent with transition b being a shock propagating sunward, into the solar wind plasma. [24] If the HFA generated by a particular discontinuity was steady in time, then as the line of interaction between the interplanetary TD and the bow shock tracked southward across the Cluster formation, the spacecraft would take data along a cut through the structure. Although the HFA in interval 2 of Figure 2 was very unlikely to be exactly time stationary, as long as the timescale on which it developed was somewhat shorter than the time in which it crossed the spacecraft, then the variations seen by the spacecraft will have been dominated by the spatial variations rather than temporal evolution. [25] Figure 3 is a schematic diagram, generated by mapping data recorded as a function of time, onto the cut Cluster made through the structure, based on the estimated velocity of the TD as it tracked southward. This picture is dependent on the assumption that the HFA did not develop significantly during its passage. It shows the discontinuity, compression and shock orientations, together with the model bow shock orientation and location extrapolated from the position at which Cluster crossed the bow shock at 0328 UT. It is clear from Figure 3 that the discontinuity originally intersected the bow shock northward of the spacecraft location. The structure sketched in Figure 3 was then convected antisunward over the spacecraft. Cluster, therefore, first encountered the antisunward propagating edge of the expanding bubble (transition a in Figure 2), which had a component of its motion in the same direction of the solar wind, and hence generated only a weak compression. The HFA was convected over the Cluster spacecraft, and finally the satellites passed through the sunward propagating edge of the bubble, which was directed against the solar wind flow and moving rapidly enough to generate a shock (transition b in Figure 2). The orientations of the magnetic field compression and the shock were nearly parallel (within 12 ) consistent with being generated by the expansion of the HFA perpendicular to the discontinuity plane. Therefore although the HFA has a scale size of 3000 km in the Z GSE direction, we expect it to be more extended in the Y GSE direction, along the plane at which the discontinuity intersects the bow shock. We cannot estimate the size of the HFA in the X GSE direction but the entry and exit normals being nearly parallel suggests that the structure is longer in this direction than in Z GSE. The picture we have for this structure therefore is of a sheet around 3000 km thick, which intersects the bow shock in a line and extends into the solar wind along the TD plane: Figure 3 shows a cross section of this structure. [26] The dynamics of an HFA are influenced by two effects [e.g., Lin, 2002]: the flow of energized particles away from the place where the discontinuity intersects the bow shock, and the expansion of the plasma in the core of the HFA under excess internal pressure. We examined the internal dynamics of the HFA by analyzing the perturbation to the bulk plasma velocity, which corresponded approximately to the effect of the additional energized particle 5of10

6 Figure 4. Two cuts through Cluster 3 CIS ion distributions, in the X-Z GSE plane (Y GSE = 0), showing (a) the ion population before the spacecraft entered the HFA at 0335:51 UT and (b) the heated ion population flowing sunward and southward within the HFA at 0336:27 UT. The log of the particle flux is indicated by the color scale, with red and orange regions indicating higher flux levels. See color version of this figure at back of this issue. population in this case. Figure 3 shows velocity perturbation vectors (bold vectors) projected onto the estimated path of Cluster through the HFA as the structure tracked southward across the tetrahedron. These are the instantaneous differences between the local velocity vector and the solar wind velocity outside of the HFA. It can be seen from this figure that close to the centre of the HFA, where the discontinuity plane lay, the plasma motion was dominated by flow along the discontinuity. At the southern edge (entry), the perturbed velocity vectors were small and parallel to the edge of the structure, as deduced from four spacecraft timings, consistent with the weak compression signature in the magnetic field magnitude and density, seen in transition a in Figure 2. In contrast, at the exit, which was accompanied by a shock labeled transition b in Figure 2, the perturbed velocity vectors were parallel to the normal to the edge, consistent with expansion of the structure. It appears, therefore, that the plasma within the HFA was influenced in this case both by particles streaming along the discontinuity, and by expansion of the cavity. [27] The HFA during interval 2 indicated on Figure 2 was associated with a deflection of the velocity moment of the plasma. It is important, however, to also examine the proton distribution function, since the velocity moment is most relevant when the plasma contains a single particle population with a Maxwellian form, which might not be the case inside the HFA. Figure 4 shows two examples of proton distributions measured by the CIS HIA sensor on Cluster 3. The color scale shows particle flux, with red indicating higher fluxes, plotted as a function of the velocity components in GSE coordinates. The first distribution (Figure 4a) was measured in the undisturbed solar wind at 0335:51 UT, just upstream of the bow shock, before Cluster entered the HFA and shows the narrow solar wind beam, flowing in the negative X GSE direction with a X GSE velocity component of approximately 700 kms 1. The second distribution (Figure 4b) was recorded in the centre of the HFA at 0336:27 UT. The solar wind beam was significantly reduced in density and was slowed slightly, and there was an additional population of heated protons flowing in the negative Z GSE and positive X GSE directions with speed components of 300 kms 1, consistent with flow along the discontinuity plane, away from the bow shock. The density of the solar wind beam shown in Figure 4a was measured to be 1.25 cm 3. The total density inside the HFA cavity was reduced, consistent with expansion of the HFA core under excess internal pressure. Calculation of the densities of the reduced density solar wind beam and the reflected ions shown in Figure 4b showed that the populations had approximately equal densities. This implies that about half of the incident solar wind beam was reflected, consistent with previous observations which reported that several HFAs were associated with strong ion reflection [e.g., Thomsen et al., 1988]. [28] The presence of two populations is unstable to wave generation, which is consistent with the observed presence of wave activity within the HFA, and the waves would act to generate a single thermalized population [e.g., Gary, 1991]. Future work will seek to compare the wave amplitude and wave characteristics with the properties of the particle distribution and with the predicted growth rates of associated instabilities. However, as in previous observations of such ion distributions [Thomsen et al., 1993] we interpret the presence of two populations as an indication that the HFA was at an early stage of its evolution, and that observations made later would show a single population within the HFA core. [29] Figure 2 shows that the spacecraft exited the HFA at transition b, and then just a little later encountered another structure between 0337:05 and 0337:30 UT, labeled by transitions c and d. Unlike the interval between transitions a and b, this structure does not have the plasma characteristics of a HFA cavity. There is no elevation in temperature, or reduction in density. Rather the plasma appears compressed, similar to the compressed plasma between the end of the core of the HFA indicated by the extent of interval 2 and transition b shown on Figure 2. The plasma compression in the region between transitions c and d is reminiscent of internal recoveries sometimes seen within the HFA cavity [e.g., Thomsen et al., 1986, 1988] which were suggested to be compressed solar wind plasma within the HFA, comoving with it. However, this example differs from these events in that it does not lie within the HFA core. Instead it is encountered by the spacecraft after Cluster exited the HFA structure (interval 2) through a shock (b), which was carried over the spacecraft by the solar wind flow, despite the shock having a sunward directed velocity in the plasma frame. [30] Application of timing discontinuity analysis to the entry (c) and exit (d) of the four spacecraft as they crossed the interval of compressed plasma gives normal orientations and velocities in the GSE frame of n c = [0.04, 0.18, 0.98], (V.n c ) gse = 162 km/s and n d = [0.62, 0.21, 0.75], (V.n d ) gse = 170 km/s. Thus in the GSE frame transition c moved northward, and transition d moved southward and antisunward. The corresponding velocities in the plasma frame were (V.n c ) pl = 196 km/s and (V.n d ) pl = 260 km/s. Calculation of the Alfvén and fast magnetosonic Mach numbers gives values of 3 and 2.7 for transition c, and just below 4 for transition d which also exhibits high-frequency wave activity consistent with whistler waves. We conclude therefore that Cluster encountered shocks on both entry to and exit from the region of compressed plasma. 6of10

7 [31] Timing analysis showed that the first boundary (c) was traveling northward, away from the centre of the HFA, while the second, exit boundary (d) was traveling southward with the corresponding reversal in spacecraft ordering across the boundaries. This is consistent with the motion of a boundary over the spacecraft formation, then the reversal of this motion, and its passage back in the opposite direction. This is inconsistent with an internal recovery which would be expected to be approximately comoving with the HFA. In addition, the orientations and velocities of transitions c and d suggest that they were not encounters with the bow shock: the spacecraft entered through a compression which had an orientation mostly in the positive Z GSE direction, perpendicular to the solar wind flow direction. However, the high density, low temperature and high magnetic field magnitude within this second structure are consistent with it being the compressed solar wind between the edge of the HFA core, and the shock propagating into undisturbed solar wind plasma. Thus we suggest that the northward edge of the expanding HFA moved first northward (c), and then back southward (d) over the Cluster tetrahedron without Cluster actually entering the hot HFA core. We suggest that this scenario could occur for one of the following reasons: 1. the line of interaction between the bow shock and the interplanetary TD underlying the HFA could have moved northward for a short time, before continuing southward, and hence the HFA structure moved in the same way. This could arise from nonplanarity of the TD, but since Cluster did not recross the HFA core, we are not able to make a new estimate of any change in the interplanetary TD orientation. 2. The rate at which the HFA expanded perpendicular to the underlying TD plane could have increased so that for a time the northward expansion velocity of the HFA exceeded the speed at which the TD tracked southward, causing the northward edge to recross the tetrahedron. Such a change in expansion rate might arise from an increase in the reflected ion fraction at the bow shock, perhaps because the intersection line of the TD was closer to the bow shock nose where the shock is stronger. Alternatively the expansion rate could increase because of the evolution of the ion distribution function in the HFA cavity from two populations to a single hot (and hence higher pressure) population. Again, since the spacecraft did not reenter the HFA cavity, we cannot check this hypothesis by reexamining the ion distribution function there. [32] The spacecraft observations of this HFA form a relatively complete and coherent picture of the structure. The HFA differed from most previously reported examples since it contained two distinct ion populations in its core, rather than a single population. Since Cluster was located within about 1500 km of the previous bow shock location, we suggest that this can be explained by the HFA not being well developed at the time it was observed [Thomsen et al., 1993]. In the next two sections we describe two additional encounters with HFAs, each of which was associated with a more energetic particle population, and more complex plasma signatures, both of which indicate that these HFAs were more evolved Interval 2 [33] Figure 5 shows the data recorded during Figure 1, interval 2. In this case a discontinuity at 0340:50 UT Figure 5. Close-up view of data from Cluster 3 recorded during interval 1 on Figure 1. The format is the same for Figure 1. (labeled by interval 1 on Figure 5) caused a very complex HFA which lasted for over two minutes, followed by a second encounter (interval 3 on Figure 5) lasting for several more minutes. These two encounters were separated by a time (interval 2, Figure 5) when Cluster appeared to be located in the ion foreshock, which at the time was populated by ultralow-frequency (ULF) waves. The CIS instrument recorded a solar wind beam within this region, together with a more diffuse ion population, which is often associated with ULF foreshock waves [e.g., Hoppe et al., 1981]. The magnetic field and plasma signatures were quite complex, especially for the HFA in interval 3, and there are aspects which we do not yet fully understand. The HFA in interval 1 was also associated with a larger perturbation of the bulk velocity than the example described in section 3.1. [34] The spacecraft encountered a relatively sharp boundary at the edge of the structure in interval 1, accompanied by two compressions at 0340:31 UT (transition a in Figure 5) and 0340:38 UT (transition b) visible in the magnetic field and plasma density, but not associated with a significant change in bulk velocity. We once again estimated the orientation of the discontinuity which lay within the HFA in interval 1 from the cross product of the magnetic field before and after the HFA. In this case we used an upstream interval between 0340:10 and 0340:20 UT (not marked on Figure 5), together with a downstream interval during the ULF wave activity (0342: :15 UT: interval 2). The choice of downstream interval was not ideal, and is likely to affect the accuracy of the normal calculation. However, this remains the best downstream interval to use: the magnetic field direction earlier was likely to have been affected by the HFA, and the earliest interval of undisturbed solar wind was 7of10

8 Figure 6. Cut in the X-Z GSE plane through the ion distribution recorded at 0341:40 UT within the core of the second HFA. There is a single, hot ion distribution with a northward component. The log of the particle flux is indicated by the color scale, with red and orange regions indicating higher flux levels. See color version of this figure at back of this issue. several minutes later, by which time the magnetic field direction was likely to have changed. We found a normal of n dis =[ 0.02, 0.02, 1.00], which was almost entirely in the Z GSE direction. The plane of the discontinuity calculated for the event in interval 1 was therefore much closer to the solar wind flow direction than for the event described in the previous section, and so we would expect this TD to have taken longer to track across the bow shock. This would give a longer interaction time and therefore, perhaps, a larger flow deflection signature than in the previous example. [35] Using the relative timings of the spacecraft as they crossed the two part compression on entry to the HFA gave normal directions and speeds in the GSE frame of n a = [0.01, 0.01, 1.00] (v.n a ) gse = 145 km/s; n b = [0.04, 0.11, 0.99] (v.n b ) gse = 305 km/s. These normal directions are almost perpendicular to the solar wind velocity vector, and so the speeds along the normals are the same in the GSE and plasma frames. The second of these transitions has magnetosonic and Alfvén Mach numbers of 5. The orientations of these two compressions at the edge of the HFA were nearly parallel to the estimated TD normal, consistent with expansion of the cavity perpendicular to the TD plane. The positive Z GSE component indicated that the TD intersected the bow shock south of the spacecraft, and then tracked northward across the satellites. This scenario is consistent with the velocity deflection observed within the HFA, which was deflected first northward, and then briefly southward, consistent with an expanding bubble tracking from south to north over the spacecraft. [36] The velocity deflection associated with this event was very dramatic, especially between 0340:53 and 0341:43 UT (Figure 5, interval 1). Knowledge of the velocity moment is not a complete description of the plasma, especially if there were multiple populations present, but the CIS ion distribution function at this time (Figure 6) showed that the solar wind beam was entirely absent, and that the plasma was dominated by a hot, isotropic population of particles flowing northward and sunward, characteristic of the typical ion population observed within an HFA [e.g., Schwartz et al., 2000]. As for the HFA described in section 3.1, within the core region of this event the magnetic field measured at the four spacecraft showed some significant differences. Cluster then apparently exited the HFA at 0342:50 UT (Figure 5, transition c) although the transition was much less clear than that of the entry, and the spacecraft entered a region containing ULF transverse wave activity (Figure 5, interval 2), characteristic of the foreshock. Cluster remained in the foreshock until 0343:20 UT and then reencountered an HFA-like structure (interval 3), crossing a compression at 0343:20 UT (transition d) which was similar to the one observed a few minutes earlier. The final exit was less clear but occurred at about 0345:30 UT. The HFA-like structure in interval 3 is more complex, although not associated with such a dramatic velocity deflection, and we do not comment on it further. [37] To summarize, the HFA within interval 2 was more complex than that described in section 3.1. It was also more developed, containing a single hot particle distribution, more typical of previously reported HFAs. Again we can trace the orientation and motion of the boundaries at the edge of the HFA, and relate these to the properties of the underlying TD and ion distribution within the cavity Interval 3 [38] We discuss the final interval (interval 3, Figure 1) briefly in order to demonstrate the complexity which can arise from the interaction of multiple HFA-like perturbations. This interval is also noteworthy because it contained an energetic particle signature between 0354 and 0356 UT (P. Daly, personal communication, 2003). [39] We can deduce far less about the disturbances within interval 3 than for either of the other two intervals. Cluster was in the foreshock during this time, the presence of foreshock waves making it difficult to estimate the orientations of discontinuities from the upstream and downstream magnetic field directions. Also, significant differences occurred between the spacecraft at many of the boundaries making it impossible to use multispacecraft timing analysis. Indeed there were only two major boundaries in the interval which we could analyze in this way. [40] Near the start and end of interval 3 (Figure 1), two enhancements in temperature occurred, associated with deflections of the plasma velocity, that were consistent with the signatures of HFA cavities seen in intervals 1 and 2 (Figure 1). We were able to estimate the orientation of the boundary Cluster crossed as it entered the first HFA-like disturbance at 0355 UT. We obtained a normal of [0.10, 0.89, 0.44] with a GSE frame velocity of 230 km/s, i.e., the boundary was convected antisunward in the GSE frame. This boundary was deflected from the expected bow shock plane by 80, and, unlike the HFAs in earlier intervals, had a large Y GSE component. [41] The second HFA-like disturbance occurred from 0358 to 0359 UT. Between the two HFAs, there was an enhancement in density without a large temperature increase, with values near those downstream of the bow shock crossing at around 0328 UT. We therefore interpret the two boundaries of this region as an outward and then inward shock crossing. This shock pair might have been the edge of an HFA, the cavity of which did not pass over the spacecraft, or they might have been the bow shock moving outward and inward as a result of HFA disturbances. We were able to estimate the orientation of the outward shock crossing of this pair to be [0.55, 0.40, 0.73] with a velocity of +70 km/s in the GSE frame. Therefore the shock 8of10

9 was propagating sunward in the GSE frame, as expected for a shock encounter. This normal was from a model bow shock normal [Peredo et al., 1995]: the range of this value is a result of timing uncertainties due to magnetic field fluctuations within the shock profile at the four spacecraft. [42] Comparison of this shock normal with the normal calculated for the HFA entry boundary at 0355 UT showed that they differed by about 50, suggesting that the shock encounter was unlikely to be explained by a simple reencounter with that HFA as described in section 3.1 for the event in Figure 2, although the shock pair might have resulted from another HFA which the spacecraft did not encounter. Alternatively the shock pair might have been the Earth s bow shock, significantly perturbed in orientation as a result of the HFA disturbances. We cannot distinguish between these two possibilities. In addition we cannot determine whether the shock pair encountered by Cluster in between the two HFA-like disturbances formed part of a contiguous bow shock, or whether they had detached from the main bow shock as a result of the interaction with the two HFAs. [43] In summary, this sequence of HFA-like signatures shows the complexity of response which can be generated by changes in the upstream solar wind conditions and we plan to examine the interval further in a later paper, concentrating in particular on the particle signatures of the events in more detail. 4. Discussion and Summary [44] In this paper we have presented the first four spacecraft observations of hot flow anomalies and illustrated through several case studies that with Cluster we can estimate the orientation of the edges of the HFAs, and better characterize the motion of the plasma throughout the structure. With this extra information we are able to derive a more complete picture of the HFA. In this paper we used Cluster data when the tetrahedron scale was 100 km, and even at these small separations we find significant differences between the spacecraft during wave activity inside the HFA, suggesting that the scale lengths in the interior of the HFA are of order of the ion gyro-radius or smaller, and smaller than the ion inertial length. [45] We have presented data from one day which contained several HFA signatures, and discussed three intervals in detail. Although all three intervals contained disturbances consistent with them being HFAs, they had significantly different signatures, probably related to both their varying levels of development and differences in the TD bow shock interaction. It was possible to estimate the orientation of the discontinuity which generated the events in two of the cases, and show that the direction of the motional electric field was consistent with previous observations, simulations and theory [Burgess, 1989; Thomas et al., 1991; Thomsen et al., 1993; Schwartz et al., 2000; Lin, 2002]. [46] One of the HFAs ( UT) appeared to be a well developed event filled with hot isotropic ions. During the first part of the HFA a very large flow deflection was observed, with plasma flowing approximately in the positive Z GSE direction, with a small positive X GSE component, i.e., sunward. Later the plasma flow turned southward briefly. This was consistent with expansion of the structure perpendicular to the discontinuity plane as it was carried from south to north over the spacecraft. The earlier HFA ( UT) was unusual in that the core contained two distinct ion populations: a reduced density solar wind beam, and a population of hot ions streaming away from the bow shock. This is not a stable ion distribution and its presence can be interpreted as an indication that this HFA was at an early stage in its evolution [Thomsen et al., 1988]. We expect two ion populations to evolve rapidly to a single, hot population, through interaction with waves generated by the unstable distribution [e.g., Gary, 1991]. [47] Using data from the four Cluster spacecraft we were able to calculate the orientations and motion of the compression regions and shocks bounding the first two events. The first event had a weak compression propagating earthward, and a shock propagating against the solar wind, consistent with being driven by expansion of the HFA. The deflection of the bulk velocity moment vector from the solar wind direction showed two characteristics. It appeared to be dominated by expansion of the HFA near the shock, but was directed along the discontinuity plane near the centre of the HFA. We were able to combine our estimates of the normals for the compression, the shock and the underlying discontinuity, with the velocity deflection information, to deduce a sketch of the three-dimensional shape of the HFA which was consistent with an expanding sheet, at least during the part of the HFA evolution when it contained two ion populations. [48] The three cases that we have presented demonstrate that complex, time varying HFA signatures can be generated. The first HFA passed over the spacecraft as the discontinuity tracked southward across the bow shock, but Cluster then reencountered the compression region at the northern edge, which we either interpret as a signature of the HFA changing its expansion rate, or a ripple in the TD changing the HFA motion briefly. The final event consisted of two HFA encounters separated by a shock pair. The first shock normal was significantly deflected from a model bow shock normal, suggesting that HFAs can result in anomalous shock motion as well as affecting their local environment. [49] The details of HFA structure that we have been able to deduce from measurements made with small tetrahedron scales, together with future observations when the tetrahedron scale is larger, 5000 km, will allow us to study HFA morphology. We can also test our results against current simulation models [e.g., Lin, 2002], especially the first event where we have the most complete picture of the shape of the HFA. [50] Previous studies have shown that HFAs can generate significant signatures within the magnetosheath and on the ground [e.g., Sibeck et al., 1999]. The results from Cluster regarding the orientation and direction of motion of the HFA might help us interpret these other HFA signatures. [51] In order to explore the way in which HFAs accelerate particles we will examine the kinetics of the bulk plasma and high-energy particles. Also, in several regions we see that there are significant differences in the magnetic field signatures seen at the four spacecraft, even though the spacecraft are only 100 km apart. The detailed structure of 9of10

10 these regions and their relation to energetic particles will be the subject of a future paper. [52] Acknowledgments. The authors would like to thank Andrew Fazakerley and Steve Schwartz for providing us with electron moments in order to calculate Mach numbers for shocks associated with some of these HFAs. Cluster FGM data analysis is supported at Imperial College by PPARC; T. S. Horbury is supported by a PPARC Advanced Fellowship. Cluster CIS analysis at CESR is supported by a CNES grant. The authors would like to thank David Sibeck and the participants of the UK Cluster Workshop on Hot Flow Anomalies, held at Queen Mary University of London on 9 January 2003, for their useful discussions on the events described in this paper. The workshop participants were Steve Schwartz, David Burgess, Olivier Moullard, Tony Allen, Michael Balikhin, Simon Walker, Andrew Buckley, Tobia Carozzi, William Wilkinson, Malcolm Dunlop, and Chris Owen. [53] Lou-Chuang Lee thanks David Burgess and Michelle F. Thomsen for their assistance in evaluating this paper. References Balogh, A., et al. (2001), The Cluster Magnetic Field Investigation: Overview of in-flight performance and initial results, Ann. Geophys., 19, Burgess, D. (1989), On the effect of a tangential discontinuity on ions specularly reflected at an oblique shock, J. Geophys. Res., 94, Fuselier, S. A., M. F. Thomsen, J. T. Gosling, S. J. Bame, C. T. Russell, and M. M. Mellott (1987), Fast shocks at the edges of hot diamagnetic cavities upstream from the Earth s bow shock, J. Geophys. Res., 92, Gary, S. P. (1991), Electromagnetic ion/ion instabilities and their consequences in space plasmas: A review, Space Sci. Rev., 56, Hoppe, M. M., C. T. Russell, L. A. Frank, T. E. Eastman, and E. W. Greenstadt (1981), Upstream hydromagnetic waves and their association with backstreaming ion populations: ISEE 1 and 2 observations, J. Geophys. Res., 86, Johnstone, A. D., et al. (1997), PEACE: A plasma electron and current experiment, Space Sci. Rev., 79, Lin, Y. (2002), Global hybrid simulation of hot flow anomalies near the bow shock and in the magnetosheath, Planet. Space Sci., 50, Øieroset, M., D. L. Mitchell, T. D. Phan, R. P. Lin, and M. H. Acuña (2001), Hot diamagnetic cavities upstream of the Martian bow shock, Geophys. Res. Lett., 28, Onsager, T. G., D. Winske, and M. F. Thomsen (1991), Interaction of a finite-length ion beam with a background plasma: Reflected ions at the quasi-parallel bow shock, J. Geophys. Res., 96, Paschmann, G., G. Haerendel, N. Sckopke, E. Möbius, H. Lühr, and C. W. Carlson (1988), Three-dimensional plasma structures with anomalous flow directions near the Earth s bow shock, J. Geophys. Res., 93, 11,279 11,294. Peredo, M., J. A. Slavin, E. Mazur, and S. A. Curtis (1995), Three-dimensional position and shape of the bow shock and their variation with Alfvénic, sonic and magnetosonic Mach number and interplanetary magnetic field orientation, J. Geophys. Res., 100, Rème, H., et al. (2001), First multispacecraft ion measurements in and near the Earth s magnetosphere with the identical Cluster ion spectrometry (CIS) experiment, Ann. Geophys., 19, Safránková, J., L. Prech, Z. Nemecek, D. G. Sibeck, and T. Mukai (2000), Magnetosheath response to the interplanetary magnetic field tangential discontinuity, J. Geophys. Res., 105, 25,113 25,121. Schwartz, S. J. (1998), Shock and discontinuity normals, Mach numbers, and related parameters, in analysis methods for multi-spacecraft data, report, edited by G. Paschmann and P. W. Daly, Int. Space Sci. Inst., Bern. Schwartz, S. J., et al. (1985), An active current sheet in the solar wind, Nature, 318, Schwartz, S. J., R. L. Kessel, C. C. Brown, L. J. C. Woolliscroft, M. W. Dunlop, C. J. Farrugia, and D. S. Hall (1988), Active current sheets near the Earth s bow shock, J. Geophys. Res., 93, 11,295 11,310. Schwartz, S. J., G. Paschmann, N. Sckopke, T. M. Bauer, M. Dunlop, A. N. Fazakerley, and M. F. Thomsen (2000), Conditions for the formation of hot flow anomalies at Earth s bow shock, J. Geophys. Res., 105, 12,639 12,650. Sibeck, D. G., et al. (1999), Comprehensive study of the magnetospheric response to a hot flow anomaly, J. Geophys. Res., 104, Sibeck, D. G., T.-D. Phan, R. Lin, R. P. Lepping, and A. Szabo (2002), Wind observations of foreshock cavities: A case study, J. Geophys. Res., 107(A10), 1271, doi: /2001ja Sonnerup, B. U. Ö., and L. J. Cahill Jr. (1967), Magnetopause structure and attitude from Explorer 12 observations, J. Geophys. Res., 72, Thomas, V. A., D. Winske, M. F. Thomsen, and T. G. Onsager (1991), Hybrid simulation on the formation of a hot flow anomaly, J. Geophys. Res., 96, 11,625 11,632. Thomsen, M. F., J. T. Gosling, S. A. Fuselier, S. J. Bame, and C. T. Russell (1986), Hot, diamagnetic cavities upstream from the Earth s bow shock, J. Geophys. Res., 91, Thomsen, M. F., J. T. Gosling, S. J. Bame, K. B. Quest, C. T. Russell, and S. A. Fuselier (1988), On the origin of hot diamagnetic cavities near the Earth s bow shock, J. Geophys. Res., 93, 11,311 11,325. Thomsen, M. F., V. A. Thomas, D. Winske, J. T. Gosling, M. H. Farris, and C. T. Russell (1993), Observational test of hot flow anomaly formation by the interaction of a magnetic discontinuity with the bow shock, J. Geophys. Res., 98, 15,319 15,330. A. Balogh, T. S. Horbury, and E. A. Lucek, Blackett Laboratory, Imperial College, Prince Consort Road, London, SW7 2BW, UK. (a.balogh@ic. ac.uk; t.horbury@ic.ac.uk; e.lucek@imperial.ac.uk) I. Dandouras and H. Rème, Centre d Etude Spatiale des Rayonnements, Toulouse F-31028, Toulouse Cedex 4, France. (iannis.dandouras@cesr.fr; henri.reme@cesr.fr) 10 of 10

11 Figure 3. Schematic of the first HFA event projected onto the X-Z GSE plane. We interpret the HFA as bubble expanding under internal pressure. The form of the bubble is constrained by the following information: the spacecraft location (filled circle) relative to a model bow shock surface, the estimated discontinuity plane (heavy dashed line), the velocity perturbation vectors (faint lines), plotted assuming that the discontinuity tracks southward at 110 km/s, and the orientations of the compression and shock at the edges of the event. Figure 4. Two cuts through Cluster 3 CIS ion distributions, in the X-Z GSE plane (Y GSE = 0), showing (a) the ion population before the spacecraft entered the HFA at 0335:51 UT and (b) the heated ion population flowing sunward and southward within the HFA at 0336:27 UT. The log of the particle flux is indicated by the color scale, with red and orange regions indicating higher flux levels. Figure 6. Cut in the X-Z GSE plane through the ion distribution recorded at 0341:40 UT within the core of the second HFA. There is a single, hot ion distribution with a northward component. The log of the particle flux is indicated by the color scale, with red and orange regions indicating higher flux levels. 5 of 10, 6 of 10, and 8 of 10