Cluster observations of hot flow anomalies with large flow

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, , doi:1.129/212ja1824, 213 Cluster observations of hot flow anomalies with large flow deflections: 2. Bow shock geometry at HFA edges Shan Wang, 1 Qiugang Zong, 1,2 and Hui Zhang 3 Received 1 August 212; revised 29 October 212; accepted 9 December 212; published 31 January 213. [1] Case and statistical studies of the bow shock geometry at hot flow anomaly (HFA) edges have been performed based on 87 HFAs with large flow deflections observed by the Cluster C1 spacecraft from 23 to 29. The results suggest that HFAs can be formed at both quasiparallel and quasi-perpendicular shocks. In an accompanying paper, we show that the ions might be near-specularly reflected at the bow shock and interact with the solar wind to form HFAs. The guiding center of specularly reflected ions will typically be swept downstream to the bow shock at quasi-perpendicular shocks. However, this study shows that in at least 13 of these 87 (15%) HFAs, both the leading and trailing edges are at quasi-perpendicular shocks. These HFAs show a high gyration velocity and a high fast magneto-sonic Mach number, increasing the gyro-radius and the possibility of pitch angle scattering, which might help the ions escape from the bow shock and move upstream. In addition, HFAs with both edges at quasi-perpendicular shocks are closer to the bow shock than those with both edges at quasiparallel shocks. This might help the reflected ions at a quasi-perpendicular shock interact with the incident solar wind immediately after the reflection and increase the possibility of HFA formation. Citation: Wang, S., Q. Zong, and H. Zhang (213), Cluster observations of hot flow anomalies with large flow deflections: 2. Bow shock geometry at HFA edges, J. Geophys. Res. Space Physics, 118, , doi:1.129/212ja Introduction [2] Hot flow anomalies (HFAs) are phenomena that are often observed near the bow shock [Schwartz et al., ; Facskó et al., 29]. Inside HFAs, the plasma flow is substantially deflected and the temperature increases [Schwartz, 1995; Zong and Zhang, 211]. When there is a tangential discontinuity interacting with the bow shock and the convective electric field on at least one side of the discontinuity is pointing inward, the electric field and the discontinuity would trap the reflected particles from the bow shock in the vicinity so that these particles can interact with the incident solar wind to form HFAs [Thomas and Brecht, 1988; Thomas et al., 1991; Thomsen et al., 1993; Zhang et al., 21]. Then the hot plasmas in the core region of the HFA expand outward, leading to the low number density and low magnetic field magnitude inside HFAs, while the number density and the magnetic field magnitude are often increased on HFA edges due to the compressions [Thomsen et al., 1988; Schwartz, 1995]. 1 Institute of Space Physics and Applied Technology, Peking University, Beijing, China. 2 Center for Atmospheric Research, University of Massachusetts Lowell, Lowell, MA, USA. 3 Geophysical Institute, University of Alaska Fairbanks, Fairbanks, AK, USA. Corresponding author: Qiugang Zong, Institute of Space Physics and Applied Technology, Peking University, China. (qgzong@gmail.com) 212. American Geophysical Union. All Rights Reserved /13/212JA1824 [3] In HFA studies, one controversial topic is whether HFAs are generated at quasi-parallel or quasi-perpendicular shocks [Zhang et al., 21]. The bow shock geometry where HFAs tend to be generated depends on how ions are reflected at the Earth s bow shock. According to Gosling et al. [1982], ions are near-specularly reflected at the bow shock and gyrate around the upstream magnetic field. If so, the ions may escape upstream near the quasi-parallel regions but have to gyrate back to the bow shock on the quasiperpendicular side. The backstreaming ions may further interact with the incident solar wind beam to form HFAs [Thomsen et al., 1988], while the quasi-perpendicular side of the bow shock is not likely to generate HFAs due to the lack of backstreaming ions. Most simulation and observational results confirmed this point by demonstrating that HFAs were only generated at quasi-parallel shocks. The simulations of Omidi and Sibeck [27] showed that HFAs were formed at the quasi-parallel side of an interplanetary magnetic field (IMF) tangential discontinuity intersecting the bow shock, while only solitary shocks appeared at the quasi-perpendicular side. This result was consistent with observational results of Facskó et al. [29] which show that 66% of the 124 HFAs were observed in the quasi-parallel region. Besides, observationally, Thomsen et al. [1988] found that HFAs tended to form near the transition region between the quasi-perpendicular and quasi-parallel shock which may provide larger-than-normal fraction of reflected ions, and Schwartz et al. [] found the tendency for the pre-hfa bow shocks to be more quasi-parallel and post- HFA bow shocks to be more quasi-perpendicular. Schwartz et al. [] also showed that few HFAs corresponded to 418

2 quasi-perpendicular shocks on both leading and trailing edges, while several HFAs corresponded to quasi-parallel conditions on both edges. However, simulation results of Thomas et al. [1991] and Lin [22] demonstrated that HFAs can be formed in the quasi-perpendicular shock region. [4] There are at least three kinds of nonspecular suprathermal distributions for backstreaming ions at the bow shock: field-aligned beams, intermediate ions, and diffuse ions. Field-aligned beams are often observed at quasi-perpendicular shocks [Kan et al., 1991]. The plasma velocity reverses along the magnetic field [Paschmann et al., 198], and the ion spectra show a sharp peak at an energy under 1 kev [Gosling et al., 1978]. Diffuse ions characterized by energy spectra extending from slightly above that of the incident solar wind (~1 kev) to above 1 kev [Kan et al., 1991; Ipavich et al., 1981] and the isotropic velocity distribution functions [Thomsen, 1985] often appear at quasi-parallel shocks. Near-specularly reflected ions might be a seed population for diffuse ions through multiple scattering processes and Fermi accelerations [Fuselier and Thomsen, 1982; Scholer, 199]. Characteristics of intermediate ions are between the field-aligned beams and diffuse ions, with a crescent velocity distribution [Thomsen, 1985]. In the regions upstream of the bow shock, there are also hydromagnetic waves associated with the backstreaming ion populations. Diffuse ions were observed to be associated with low-frequency (~.3 Hz) and large-amplitude (ΔB/B ~ 1) hydromagnetic waves; the reflected ions were accompanied by smallamplitude (ΔB/B ~.2) and higher frequency (.5 5Hz) whistler waves, and waves associated with intermediate ions are mixtures of the two wave types [Paschmann et al., 1979; Hoppe et al., 1981; Hoppe and Russell, 1983; Kan et al., 1991]. [5] In an accompanying paper, Wang et al. [212] identified 87 HFAs with large flow deflections from Cluster data and investigated characteristics of the flow deflection. In this paper, we perform case and statistical analysis of the bow shock geometry at these HFA edges. The bow shock geometry is determined by calculating the angle (θ Bn ) between the magnetic field and the bow shock normal. Ion spectra and the fluctuations of the magnetic field are used to help confirm our analysis. This paper is organized as follows. Section 2 introduces the data used in this study and the methods of identifying the bow shock geometry. Section 3 presents the case studies of four HFA events with different bow shock geometry at edges. In section 4, we analyze the uncertainties in the determination of the bow shock normal and the IMF orientations via comparing the results from different methods. The superposed epoch analysis results of HFAs with different bow shock geometry at edges are presented in this section. In section 5, we discuss the solar wind conditions and the event locations for HFAs with different bow shock geometry at edges to indicate the possible favorable conditions for the HFA formation at quasiparallel or quasi-perpendicular shocks. 2. Data and Analysis Methods 2.1. Data [6] Data used in this paper are from the Cluster-C1 spacecraft from 23 to 29. Plasma data are from the Hot Ion Analyzer (HIA) instrument in the Cluster Ion Spectrometry (CIS) package onboard Cluster [Rème et al., 21], and the data are used to select HFA events when the instrument is in MAG (magnetosheath or magnetosphere) mode in order to avoid the loss of the count in the large fields-of-view of particles inside HFAs [Dandouras and Barthe, 21]. Magnetic field data, with.2 s resolution, are from Fluxgate Magnetometer (FGM) on Cluster [Balogh et al., 21]. Hourly-averaged data in the number density and the solar wind velocity from the Omni web site are used in coordinate transformations. The HFAs used in this paper are the same with the 87 HFAs with large flow deflections discussed in an accompanying paper [Wang et al., 212]. [7] The locations of the HFA events and the bow shock are very important for the identification of the bow shock geometry; therefore, we determine and normalize the HFA locations and the bow shock positions according to the solar wind conditions for each event. The coordinate system is rotated into aberrated GSE coordinates to remove the effect of the Earth s aberration. We determine the Cluster-C1 bow shock crossing closest to each HFA event. The bow shock model of Farris et al. [1991] is chosen for the bow shock shape, but the distance from the bow shock surface to the Earth s center is rescaled according to the solar wind dynamic pressure at the bow shock crossing and at the HFA onset time. Then this new bow shock surface is taken as the bow shock position when the HFA is observed Determination of the Bow Shock Geometry [8] In order to determine the bow shock geometry, i.e., whether an HFA is formed at the quasi-parallel shock or at the quasi-perpendicular shock, we need to determine the angle (θ Bn ) between the magnetic field and the normal direction of the bow shock on both sides of the HFA. Multiple methods have been applied to determine the IMF orientation and the normal direction of the bow shock Determination of the IMF Orientation [9] Since there are hydromagnetic waves associated with different ion distributions in the region upstream of the bow shock [Paschmann et al., 1979; Hoppe et al., 1981], we choose intervals on the leading and trailing side of the HFA, and the average magnetic field in the intervals are used as the IMF direction at HFA edges. In addition, the averaging time interval on either side is shifted to the left and right by the same interval to estimate the uncertainty in the determination of the IMF orientations, three intervals on each side. The fluctuations in the magnetic field might be about.3 5 Hz under different bow shock geometry conditions [Kan et al., 1991; Paschmann et al., 1979], so the interval for averaging IMF is mainly from 1 to 3 s, containing at least one period of the fluctuations. The intervals are all within 4 min before and after the HFA onset time (the time with maximum velocity component perpendicular to the Sun-Earth line). There might be other magnetic structures, e.g., other HFA events, which are very close to the analyzed HFA; therefore, these time intervals should not be included in the determination of the averaging IMF. However, in some cases, the magnetic field changes a lot within several minutes but without clear HFA-like structures. These intervals are not excluded in the averaging interval selections since such conditions might be close enough to affect the HFA formation. 419

3 Determination of the Normal Direction of the Bow Shock [1] 1. N method. For each event, we design a surface with the shape of Farris et al. [1991] bow shock model and include the HFA location. Then the normal direction of this surface at the HFA location can be calculated, and this direction is used as the normal direction of the bow shock (^n). Along ^n, we trace from the HFA location to the normalized bow shock surface with the distance R trace. [11] 2. B method. With the average IMF direction in the averaging intervals on HFA edges, we trace along this direction from the HFA location to the bow shock surface and obtain an intersection point. Then the normal direction of the bow shock surface at this intersection point is regarded as the normal direction from the B method. Note that the determination of the normal direction by this method depends on IMF orientations. [12] 3. BSM method (the method of bow shock crossing with model). The Cluster bow shock crossing time ranges from several minutes to about 4 h from the HFA onset time, during which the spacecraft location does not change much. Therefore in this method, we calculate the normal direction with the shape of the bow shock model at the point of Cluster bow shock crossing (normalized according to the dynamic pressure at the HFA onset time). [13] 4. CP method (coplanarity method). For ideal collisionless shocks, the magnetic field upstream (! B u ), downstream (! B d ) to the shock, and the shock normal should be coplanar, and the magnetic field jump across the shock is also in this plane. So the normal direction of the shock can be determined as follows: ^n cp ¼! B u! B d! Bu! B d where B u and B d are average magnetic field upstream and downstream of the bow shock. [14] The first three methods are all based on the shape of the bow shock model but different in the selection of the point on the bow shock surface to calculate the normal direction. The statistical study of Horbury et al. [22] showed that the normal direction determined from the bow shock models and that from timing analysis can be relatively consistent: the difference in the normal direction determined by the two methods is less than 1 for nearly 8% of the 48 bow shock crossings in their study. Therefore, it might suggest that the bow shock normal is usually stable within 1 of the normal determined from the bow shock models, and the timing analysis method is accurate to about 1 [Horbury et al., 22]. The variations in the bow shock normal might be caused by surface waves and the shock front reformation [Lobzin et al., 27; Miao et al., 29]. Therefore, it is necessary to use magnetic field conditions in specific bow shock crossings to help estimate the uncertainties. Unfortunately, for the bow shock crossings near the 87 HFA events, nearly half of the crossings were not observed by all four Cluster spacecraft, which makes the timing analysis impossible. On the other hand, [Horbury et al., 22] showed that the method to determine the bow shock normal with the assumption of coplanarity is not so accurate (less than 2% of the normal vectors are within (1) 1 of the model normal). So we use coplanarity assumption to determine the bow shock normal but only as a reference for uncertainty estimates. [15] The coplanar condition of the shock might cause the degeneracy of the variance matrix of Minimum Variance Analysis (MVA) method since the variances in the shock normal direction and the direction perpendicular to the plane with B u and B d are both near zero. Thus, the normal direction from MVA method becomes invalid, but the L direction with maximum variances, which is perpendicular to the shock normal, remains a good vector [Sonnerup and Scheible, ]. Therefore, we only compare the L direction of MVA and the shock normal determined by other methods, and the determination of the bow shock normal will be regarded consistent if the difference between the two directions is close to Determination of θ Bn [16] With the direction of IMF and the bow shock normal, the angle between the two is defined as θ Bn. It is considered as a quasi-parallel shock if θ Bn 45 or θ Bn 135, and it is a quasi-perpendicular shock if 45 < θ Bn < 135. The ion spectra, the magnetic field fluctuations, and the ion velocity distribution functions (VDFs) have also been used to help identify the bow shock geometry. [17] The IMF direction from the intervals closest to the HFA onset on the leading and trailing edge and the normal direction from the N method are used as the main results in identifying the bow shock geometry, while θ Bn determined by other methods will only be used when discussing uncertainties. 3. Case Studies [18] In this section, we analyze four typical HFAs with different bow shock geometry on their sides HFA Event with Both Leading and Trailing Edges at Quasi-parallel Shocks ( Para-Para Event) [19] The HFA on 11 May 23 is an event under the quasi-parallel shock condition at both the leading and trailing edges (Figure 1). In short, such events are called Para- Para events. The left part shows the CIS ion spectra and the line plots of plasma and magnetic field data which show the characteristics of the HFA. UT and LT are the universal time and the local time, respectively. X(Y,Z) GSE are the positions of the spacecraft C1 in GSE coordinates and X(Y,Z) Norm are C1 positions in the aberrated GSE coordinates after the normalization. The red dashed line represents the onset time (2:43:4 UT) with maximum velocity component in the direction perpendicular to the Sun-Earth line, and the gray shadowed region represents the interval inside the HFA structure. In the event center, the velocity decreased from about 65 km s 1 to about 35 km s 1 (Figure 1g), and the temperature increased from about 2 MK to more than 1 MK (Figure 1h). The number density decreased from about 4cm 3 to less than 1 cm 3 at the lowest point (Figure 1i), and the magnetic field magnitude decreased from about 1 nt to about 2 nt (Figure 1d). [2] The black dashed lines in Figures 1a 1j represent the averaging intervals for the magnetic field on HFA edges. The intervals for the leading edge are 2:4:44 2:41:14 42

4 Figure 1. Para-Para HFA event on 11 May 23. Parameters on the left are in aberrated GSE coordinates. (a) Cluster CIS HIA ion spectra; (b) dynamic pressure; (c) Cluster FGM magnetic field components; (d) magnetic field magnitude; (e) V x ; (f) V y and V z ; (g) total velocity; (h) ion temperature; (i) number density; (j) plasma b. The red dashed line represents the event center with the maximum velocity perpendicular to the Sun-Earth line. The gray shadowed region represents the interval for the HFA. The black dashed lines represent the averaging intervals for the interplanetary magnetic field (IMF) conditions at HFA edges. The right panel shows the bow shock geometry identification from N method and the IMF averaging intervals closest to the HFA center. Red arrow: tracing from HFA to the bow shock; green arrow: bow shock normal; blue arrows: magnetic field direction. Black dashed lines are the bow shock positions. The upper panel is a part of the X-Y plane, and the lower part is a part of the X-Z plane. 1 and 2 represent the leading and trailing edges. UT, 2:41:14 2:41:44 UT, and 2:41:44 2:42:14 UT, and the intervals for the trailing edge are 2:43:44 2:44:14 UT, 2:44:14 2:44:44 UT, and 2:44:44 2:45:14 UT. The duration for the intervals at both the leading and trailing edges are 3 s. The shock normal determined by the N method and magnetic field averaged over the time interval closest to the HFA onset time are shown in Figure 1 (right), which are in the X-Y plane (upper part) and X-Z plane (lower part) in aberrated GSE coordinates, respectively. The red star represents 421 the location of the HFA, the red arrow represents the trace from the HFA location to the bow shock surface, the green arrow represents the bow shock normal, and the blue arrows represent the average IMF direction at the leading (labeled as 1 ) and trailing (labeled as 2 ) edges. It is clear that orientations of the bow shock normal and the magnetic field are similar. θ Bn is at the leading edge and at the trailing edge with the N method, indicating a quasi-parallel shock geometry at both the leading and trailing edges of the HFA.

5 [21] The bow shock geometry at HFA edges has also been determined via other methods described in section 2, and results from different methods are consistent. From different methods, θ Bn at the leading edge ranges from to 169.4, and θ Bn at the trailing edge ranges from to The difference between the bow shock normal determined by the BSM method and the L direction of MVA method is 76.4, which can be regarded as close to 9. Therefore, the results of all these methods show that this HFA is a Para-Para event. [22] The identification of the bow shock geometry has been further confirmed by the ion spectra, the magnetic field fluctuations, and the ion VDF. The ion spectra (Figure 1a) show a wide increase in the energy from slightly above 1 kev, which is the typical solar wind beam energy, to the uppermost energy of the instrument (about 4 kev) at both the leading and trailing edges for the HFA, which are the characteristics for the spectra of diffuse ions in the foreshock region near quasi-parallel shocks [Paschmann et al., 198; Kan et al., 1991]. Besides, the magnetic field (Figure 1c) shows low frequency (about 15 s period) and large-amplitude (about 8 nt peak-to-peak) fluctuations, which might be hydromagnetic waves that are usually associated with the diffuse ions in the foreshock region. Figure 3 (left) shows the VDF in the vicinity of this HFA, i.e., on the leading side (Figure 3a), at the HFA center (Figure 3b) and on the trailing side (Figure 3c). It is clear that the VDFs on both sides of this HFA contain nearly isotropic suprathermal ion distributions, which suggests that both sides of the HFA were located at quasi-parallel bow shock with a well-formed foreshock region. Therefore, the ion spectra, the magnetic field fluctuations, and the ion VDF confirm the quasi-parallel bow shock condition at both the leading and trailing edges of this HFA HFA Event with the Leading Edge at the Quasiparallel Shock and the Trailing Edge at the Quasiperpendicular Shock ( Para-Perp Event) [23] The HFA on 12 February 28 is an event with the quasi-parallel shock at the leading edge and the quasiperpendicular shock at the trailing edge (Figure 2). In short, such events are called Para-Perp events. In the event center, the velocity decreased from about 6 km s 1 to less than 35 km s 1 (Figure 2g), and the temperature increased from about 2 MK to about 2 MK at the highest point (Figure 2h). The number density decreased from about 3cm 3 to less than.3 cm 3 (Figure 2i), and the magnetic field decreased from about 3 nt to less than.2 nt (Figure 2d). [24] The averaging intervals for the magnetic field are represented by the black dashed lines. At the leading edge, the intervals are 23:5:45 23:6: UT, 23:6: 23:6:15 UT, and 23:6:15 23:6:3 UT with the duration of 15 s in each interval; at the trailing edge, the intervals are 23:8: 23:8:3 UT, 23:8:3 23:9: UT, and 23:9: 23:9:3 UT with the duration of 3 s in each interval. The shock normal determined by the N method and magnetic field averaged over the time interval closest to the HFA onset time are shown in Figure 2 (right). The magnetic field at the leading edge (blue arrow with the label 1) is closer to the bow shock normal (green arrow), while the magnetic field at the trailing edge (blue arrow with the label 2) is nearly perpendicular to the bow shock normal. θ Bn is at the leading edge and 64.4 at the trailing edge, indicating that the leading edge is at quasi-parallel shocks, and the trailing edge is at quasi-perpendicular shocks. [25] The identification results via most of the other methods show the same results. At the leading edge, θ Bn ranges from 145. to for all methods but CP method, from which θ Bn at the leading edge is from 52.7 to 57.9.Atthe trailing edge, θ Bn ranges from 59.2 to 73.1 for all methods but CP method, from which θ Bn at the trailing edge is from to The difference between the L direction of MVA and the bow shock normal determined by BSM method is Therefore, with all methods but CP method, we identify this HFA as a Para-Perp event. [26] The results have been further confirmed by the ion spectra, the magnetic field fluctuations, and the ion VDF. It is clear that the spectra (Figure 2a) shows increase in a wide energy range above the solar wind beam at the leading edge indicating the existence of the diffuse ions near the quasiparallel shock, while there is little difference with the solar wind beam with fewer suprathermal particles at the trailing edge. Besides, the magnetic field (Figure 2c) shows clear fluctuations with the amplitude of about 1 nt and the frequency of about.1 Hz at the leading edge, while the magnetic field at the trailing edge is smooth. Figure 3 (right) shows the ion VDF near and in this HFA. On the leading side (Figure 3d), besides the ion population close to the positive V perp1 axis which is the incident solar wind beam, there are intermediate ion distributions scattered into almost 18 in the negative V para plane which usually appear in the quasi-parallel shock region; however, on the trailing side (Figure 3f), there is only the solar wind beam close to the positive V perp1 axis which is probably near the quasiperpendicular shock. Thus, the ion spectra, the magnetic field condition, and the ion VDF suggest this HFA as a Para-Perp event. [27] Since the result can be confirmed through most methods, we may believe that the HFA on 12 February 28 is at the quasi-parallel shock at the leading edge and at the quasi-perpendicular shock at the trailing edge, while the bow shock normal determined from CP method in this event is not accurate enough to believe HFA Event with the Leading Edge at the Quasiperpendicular Shock and the Trailing Edge at the Quasi-parallel Shock ( Perp-Para Event) [28] The HFA on 1 March 25 is an event at the quasiperpendicular shock at the leading edge and at the quasiparallel shock at the trailing edge (Figure 4). In short, such HFAs are called Perp-Para events. In the event center, the velocity decreased from 65 km s 1 to about 36 km s 1 (Figure 4g), and the temperature increased from about 1 MK to about 1 MK (Figure 4h). The number density decreased from about 2 cm 3 to about.6 cm 3 (Figure 4i), and the magnetic field magnitude decreased from about 6 nt to less than 3 nt with clear compressions on the edges (Figure 4d). [29] The averaging intervals for the magnetic field are 8:36:4 8:37: UT, 8:37: 8:37:2 UT, and 8:37:2 8:37:4 UT at the leading edge with the duration of 2 s for each interval, and 8:38:3 8:39: UT, 8:39: 8:39:3 UT, and 8:39:3 8:4: UT at the 422

6 Figure 2. Para-Perp HFA event on 12 February 28. Formats are the same as in Figure 1. trailing edge with the duration of 3 s for each interval. The shock normal determined by the N method and magnetic field averaged over the time interval closest to the HFA onset time are shown in Figure 4 (right). It is clear that the magnetic field orientation (blue arrows) is more perpendicular to the bow shock normal (green arrow) at the leading edge and more parallel to the bow shock normal at the trailing edge. At the leading edge, θ Bn is 15.7 ; at the trailing edge, θ Bn is with this method. This indicates that this HFA is at quasi-perpendicular shock at the leading edge and at quasi-parallel shock at the trailing edge. [3] The bow shock geometry determined by other methods show consistent results. The range for θ Bn from different methods at the leading edge is from 93.6 to 129.5, and the range for θ Bn at the trailing edge is from to The difference between the L direction of MVA and the bow shock normal determined by BSM method is Therefore, multiple methods in determining θ Bn indicate that this HFA is an Perp-Para event. [31] Then we have also used ion spectra, magnetic field fluctuations, and the ion VDF to conduct further analysis. The ion spectra (Figure 4a) in the interval closest to the HFA center at the leading edge shows clear characteristics of the quasi-perpendicular shock without much increase in the energy higher than a few kev. The spectra in the other intervals at the leading edge show the increase in suprathermal particles, but from the results in determining θ Bn, we can see that the magnetic field direction does not change a lot. The spectra at the trailing edge for all the intervals show clear increase in suprathermal energies suggesting it at the quasi-parallel shock. The magnetic field (Figure 4c) at the leading edge is smooth, while the magnetic field at the trailing edge has strong low-frequency (~.3 Hz) fluctuations 423

7 Leading side 28212_ _24138 (a) (d) Vpara (km/s) Para Vpara (km/s) - Para log c/s HFA center 23511_2432 (b) (e) Vpara (km/s) Vpara (km/s) 28212_ Trailing side 28212_ _2443 (c) (f) Vpara (km/s) Para Vpara (km/s) - 1. Perp Figure 3. Ion velocity distribution functions (VDF) in the Vpara plane for the Para-Para HFA on 11 May 23 (left) and Para-Perp HFA 12 on February 28 (right). Vpara is along the magnetic field, and is in the V-B plane but perpendicular to the magnetic field. (a) The VDF on the leading side of the Para-Para case within the closest interval to determine the leading edge IMF conditions labeled in Figure 1; (b) the VDF in this HFA closest to the maximum velocity deflection point; (c) the VDF on the trailing side of this HFA within the closest interval to determine the trailing edge IMF conditions labeled in Figure 1. (d f) Formats are similar to those of Figures 3a 3c. with large amplitudes (over 5 nt). The ion VDF on the leading side (Figure 6a) only shows a solar wind beam distribution, while there are clear diffuse ions in the trailing side VDF (Figure 6c). All above also suggest this HFA as an Perp-Para event. [32] Therefore, we may believe that the HFA on 1 March 25 is at the quasi-perpendicular shock at the leading edge and at the quasi-parallel shock at the trailing edge HFA Event with both Leading and Trailing Edges at Quasi-perpendicular Shocks ( Perp-Perp Event) [33] The HFA event on 2 April 28 was a typical case with both its leading and trailing edges at quasi-perpendicular shocks (Figure 5). In short, we call such HFAs as PerpPerp events. In the event center, the velocity decreased from about 52 km s 1 to about 26 km s 1 (Figure 5g), while the 424

8 Figure 4. Perp-Para HFA event on 1 March 25. Formats are the same as in Figure 1. temperature increased from about.5 MK to about 11 MK (Figure 5h). The number density decreased from about 3cm 3 to less than.9 cm 3 (Figure 4i), while the magnetic field magnitude decreased from about 3.8 nt to about 1.8 nt and went back to about 4 nt (Figure 5d). Compressions are clear, especially on the trailing edge. [34] The averaging intervals for the magnetic field are 13:28:24 13:28:44 UT, 13:28:44 13:29:4 UT, and 13:29:4 13:29:24 UT at the leading edge with the duration of 2 s for each interval and 13:3:24 13:3:54 UT, 13:3:54 13:31:24 UT, and 13:31:24 13:31:54 UT at the trailing edge with the duration of 3 s for each interval. The shocknormaldeterminedbythenmethodandmagneticfield averaged over the time interval closest to the HFA onset time are shown in Figure 5 (right). The magnetic field (blue arrows) at both edges of the HFA are nearly perpendicular to the bow shock normal (green arrow). θ Bn is 1.8 at the leading edge and 91.2 at the trailing edge with this method. [35] Bow shock geometry identifications determined by other methods of determining the bow shock normal and IMF intervals show consistent results. θ Bn determined by different methods at the leading edge ranges from 98.1 to 124.3, and θ Bn at the trailing edge ranges from 9. to The difference from the L direction of MVA and the bow shock normal determined by the BSM method is Therefore, multiple methods in determining θ Bn indicate that this HFA is a Perp-Perp event. [36] The ion spectra, the magnetic field fluctuations, and the ion VDFs also help us to further confirm our identification. The ion spectra (Figure 5a) at the leading edge is discrete in high energy and does not have much difference with that of the solar wind beam at the trailing edge. These indicated few ions reflected from the bow shock, and there were quasi-perpendicular on both leading and trailing edges. Besides, the magnetic field (Figure 5c) only shows highfrequency (~.2 Hz) and small-amplitude (about.5 nt 425

9 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Figure 5. Perp-Perp HFA event on 2 April 28. Formats are the same as in Figure 1. peak-to-peak) waves, which might be associated with the reflected beams near the quasi-perpendicular shock. The ion VDFs on the leading side (Figure 6d) and trailing side (Figure 6f) both show the unique solar wind beam, and it became scattered only at the event center with two ion populations under the interaction with each other (Figure 6e). Therefore, we may believe that the HFA on 2 April 28 is under the condition of quasi-perpendicular shock at both the leading and trailing edges of the event. 4. Statistical Studies [37] From the case studies, we find that HFA events can appear at both quasi-parallel shocks and quasi-perpendicular shocks on their edges. In this section, we provide statistical results together with the uncertainty analysis Uncertainty Analysis [38] We have introduced four methods to determine the bow shock normal and three averaging intervals at either edge of the HFA for IMF conditions. Here we compare the results from different methods. [39] Figure 7 shows the uncertainties of the IMF directions and the bow shock normal directions. Figures 7a and 7b show the maximum angle difference ( θ IMF diff ) between the IMF directions from different averaging intervals at the leading or trailing edge, respectively. At the leading edge, the event numbers for θ IMF diff < 1,2, and 4 are 18, 47, and 79; at the trailing edge, the event numbers for θ IMF diff < 1, 2, and 4 are 27, 51, and 78. Therefore, the IMF conditions for most events are relatively stable with θ IMF diff < 4. Figures 7c 7g show the angle difference ( θ n diff ) between 426

10 Leading side 2531_ _13292 (a) (d) Perp (km/s) Vpara - (km/s) Vpara - Perp HFA center 2531_ _ (b) (e) log c/s 4. (km/s) Vpara - (km/s) Vpara Trailing side 2531_ _13325 (c) (f) 2. Para (km/s) Vpara - (km/s) Vpara - Perp Figure 6. Ion velocity distribution functions (VDF) for the Perp-Para HFA on 1 March 25 (left) and Perp-Perp HFA on 2 April 28 (right). Formats are the same as in Figure 3. the bow shock normal direction determined by different methods. The titles represent the methods introduced in section (B 1 and B 2 represent the normal direction from B method at the leading and trailing edges). It is clear that results obtained from those methods, which are dependent on the bow shock model (N, B, and BSM methods), do not show much difference: θ n diff in 84 events between the N method and the B1 method (Figure 7c), 82 events between the N method and the B2 method (Figure 7d), and all 87 events between the N method and the BSM method (Figure 7e) are less than 1. However, CP method brings much uncertainty to the determination of the bow shock normal. θ n diff < 2 in only 13 events (15%) between the BSM method and the CP method (Figure 5f). Horbury et al. [22] analyzed the bow shock normal with CP method in 48 clean quasi-perpendicular shocks, and only 19% of the 427

11 (a) Uncertainties of the IMF direction (b) (c) Uncertainties of the BS normal from different methods (d) (e) (f) (g) Figure 7. Uncertainties in identifying the bow shock geometry brought by different IMF averaging intervals and different methods of determining the bow shock normal. See text for details. events were within 1 of the model normal. The quasilinear condition for the magnetic field upstream and downstream of the quasi-perpendicular shock [Horbury et al., 22] and the fluctuations at the quasi-parallel shock might cause the CP method to be less accurate. Therefore, the CP method is only used as a reference for the determination of the bow shock normal in this paper. Although the normal direction of the shock from MVA method is invalid, the L direction in MVA method with maximum variations might be reliable [Sonnerup and Scheible, ]. Thus, we compare the angle difference between the L direction in MVA method and the normal direction from the BSM method (Figure 7g). The result is that 45 events (52%) have the difference between the two directions in the range of 8 1, and 77 events (89%) have the difference between the two directions in the range of 7 11, indicating that the L direction in MVA is almost perpendicular to the bow shock normal determined from other methods. This result might help confirm the reliability of the methods with the bow shock model. 428

12 [4] Figure 8 shows the result of θ Bn with uncertainties. In each panel, the black cross represents θ Bn determined by the N method and magnetic field averaged over the intervals closest to the HFA onset, and the green error bars represent the uncertainties. Figures 8a and 8b show θ Bn with the uncertainties brought by IMF orientations averaged over different intervals at the leading and trailing edge. Figures 8c and 8d show θ Bn with the uncertainties brought by the bow shock normal determination from all methods. The uncertainties from the CP method cause the error bars to be long. Figures 8e and 8f show θ Bn with all the uncertainties from the determination of the bow shock normal and IMF orientations over different intervals. Horbury et al. [22] showed that the bow shock normal from the model might be accurate within 1,andin this study more than half of the events have the difference between the model-determined normal and MVA-determined L direction within 1 to 9. Therefore, we may choose 1 as the uncertainty for θ Bn as shown in Figures 8g and 8h. Figure 8. θ BN with uncertainties from different methods. See text for details. 429

13 [41] The event numbers with different bow shock geometry considering different uncertainties are listed in Table 1. We can see that the IMF conditions might bring less uncertainty than the methods of the determination of the bow shock normal. Although only 17 events are consistent in the bow shock geometry identification considering all the uncertainties, there are still seven cases with at least one edge at the quasi-parallel shock and 12 cases with both edges at the quasi-perpendicular shock, respectively. This confirms that HFAs can be formed at both quasi-parallel and quasi-perpendicular shocks. [42] We use the ion spectra and the magnetic field fluctuations to help identify the bow shock, the result of which is absolutely consistent with those from the N method and IMF averaging intervals closest to the HFA center with 1 errors in θ Bn. Therefore, we may believe the bow shock geometry identifications with the error bars of Superposed Epoch Analysis [43] In this section, we provide the superposed epoch analysis of Para-Para events and Perp-Perp events determined by the N method and the IMF averaging intervals closest to the HFA center with the error bars of 1. Therefore, the criteria for quasi-parallel shocks is equivalent to θ Bn 35 or θ Bn 145, and the criteria for quasi-perpendicular shocks is 55 < θ Bn 125. There are 1 and 13 cases in the two groups, respectively. The epoch for the superposed epoch analysis is defined as the time when the velocity component perpendicular to the Sun-Earth line reaches maximum, and the interval for the superposed epoch analysis is 2 s. The red lines in the middle represent the median value of the parameters, and the upper and lower bounds of the gray region are the 75% and 25% values. We can see that in the event center, they both show typical characteristics of HFAs with the velocity decreasing, the temperature increasing, the number density decreasing, and the magnetic field magnitude decreasing. [44] However, it shows that the number density at background in Para-Para events (Figure 9B) is higher than that in Perp-Perp events (Figure 9b). The median value of the number density for Para-Para events is about 3 cm 3 at background and about 2 cm 3 for Perp-Perp events. The temperature in Para- Para events (Figure 9I) appears to be higher than that in Perp- Perp events (Figure 9i) at both the background and the HFA center. From the background solar wind to the HFA center, the median temperature of Para-Para events increases from about 2 MK to 2 MK, while the median temperature of Table 1. HFA Event Numbers With Different Bow Shock Geometry From Different Methods BS Geometry Para- Para Para- Perp Perp- Para Perp- Perp In Total N method, closest IMF intervals N method, all IMF intervals All methods for ^n, closest IMF intervals All methods for ^n and all IMF intervals N method with the uncertainties of In the titles of the shock geometry, Para-Perp represents the cases with the leading side at the quasi-parallel shock and the trailing side at the quasi-perpendicular shock. Titles in other types are similar. IMF, interplanetary magnetic field. Perp-Perp events increases from less than 1 MK to about 12 MK. From the magnetic field data, we can see that the magnetic field near Para-Para events (Figures 9F 9H) have larger fluctuations than those near Perp-Perp events (Figures 9f 9h) at both edges. This is consistent with the wave characteristics in different bow shock geometry: large-amplitude and low-frequency waves are associated with the diffuse ions in the foreshock region near the quasi-parallel shock, while small-amplitude and high-frequency waves are associated with the reflected beams that are often near the quasi-perpendicular shock. [45] Figures 9D and 9d show the velocity (V r ) perpendicular pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi to the Sun-Earth line, with the absolute value of Vy 2 þ V z 2 and the sign of V y. At epoch, the third quartile of V r is about 24 km s 1 for Para-Para events and about 2 km s 1 for Perp-Perp events; the median V r for Para- Para events is about 28 km s 1, larger than that for Perp-Perp events with the value of about 22 km s 1. Then we check the HFA locations for these events. For Para-Para events, 8 out of 1 events (8%) are located in the morning side of the subsolar point with negative Y values in the aberrated GSE coordinates; for Perp-Perp events, 7 out of 13 events (52%) are located in the afternoon side. Therefore, the Para-Para events might be observed in the morning side with higher possibilities, while Perp-Perp events might be observed in the afternoon side with slightly higher chances. This might be due to the Parker spiral structure of IMF. 5. Discussion [46] Previous observational and simulation studies [e.g., Facskó et al., 29; Omidi and Sibeck, 27; Schwartz et al., ; Thomsen et al., 1988] provided evidence that HFAs tend to be associated with a quasi-parallel shock on at least one edge of the structure. Only the simulation results of Thomas et al. [1991] and Lin [22] showed that HFAs could be generated in the quasi-perpendicular regions. On the other hand, our statistical study in an accompanying paper showed that the ions interacting with the solar wind beam to form HFAs might be near-specularly reflected at the bow shock. Since the near-specularly reflected ions gyrate around the magnetic field, the guiding center goes upstream at the quasi-parallel side and goes downstream at the quasi-perpendicular side [Gosling et al., 1982]. In addition, Onsager et al. [199]pointed out that the nearspecularly reflected ion beam can stay coherent only for a fraction of the gyroperiod before being scattered and dispersed. Therefore, it may be easier for the reflected ions at quasi-parallel shock to interact with the incident ions to form HFAs than those at quasi-perpendicular shock. [47] However, our observations show that at least 13 HFA events were observed at quasi-perpendicular shocks at both the leading and trailing edges. Therefore, we need to understand how the near-specularly reflected ions at quasiperpendicular shocks can interact with the upstream solar wind beams instead of being directly guided back to the bow shock. The gyration velocity can be determined according to the following relation [Gosling et al., 1982]: V g ¼ j2v i cosθ vn sinθ bn j (2) where V i is the incident solar wind velocity, θ vn is the angle between! V i and the bow shock normal ^n, and θ bn is the angle 43

14 between the upstream magnetic field and the bow shock normal (Figure 1 in Gosling et al. [1982]). For each HFA, we select a 1 min interval within 1 3 min of the HFA center where the variations in the velocity components are minimum, and the average velocity in this interval is used as! V i. Besides, the average number density (N b ), temperature (T b ), and magnetic field magnitude (B b ) in this interval are used as the upstream conditions to determine the fast magneto-sonic mach numbers (M f ) for each event. [48] Here we only compare the results for Para-Para events (1 cases) and Perp-Perp events (13 cases) identified via N method and the nearest IMF averaging intervals to the HFA center with the error of 1, and results are further confirmed by the ion spectra and magnetic field fluctuations. The calculated median V g and median V g /V i of the Para-Para events is 761 km s 1 and 1.3, while the median V g and median V g /V i of the Perp-Perp events are 867 km s 1 and 1.6. In Perp-Perp events, V g have been checked to point Para-Para events (1 cases) Perp-Perp events (13 cases) (A) (B) (C) (D) (E) (F) (G) (H) (I) Figure 9. Superposed epoch analysis results of 1 Para-Para HFAs (left) and 13 Perp-Perp HFAs (right). Parameters are in aberrated GSE coordinates. The time with maximum velocity component perpendicular to the Sun-Earth line is set to be epoch, which is labeled by the blue dashed line. The yellow shadowed region represents the interval for HFAs. Red solid line: median value; boundary of the gray region: 75% (upper boundary) and 25% (lower boundary) values. (A, a) Dynamic pressure; (B, b) number density; (C, c) V x ; (D, d) V r ; (E, e) total velocity; (F, f) B x ;(G,g)B r ; (H, h) magnetic field magnitude; (I, i) ion temperature. 431

15 upstream, and this may help the ions escape the bow shock right after the reflection. Besides, the median B b are 6. nt and 4.8 nt, for Para-Para and Perp-Perp events, respectively. Therefore, the high gyration velocity and relative low magnetic field magnitude provide large gyro-radius and help the ions to escape upstream before being guided back to the bow shock. In Para- Para events, M f rangesfrom2.91to5.7withthemedianvalue of 3.9, and M f in Perp-Perp events ranges from 3.66 to 6.39 with the median value of The high Mach number (M f > 2) near all of these HFAs, especially in Perp-Perp events, is a favorable condition for near-specular reflections [Gosling et al., 1989], and it also helps the development of the Alfvén waves, which may further lead to the pitch angle scattering of the reflected ions [Onsager et al., 199]. The pitch angle scattering may also cause the ions at the quasi-perpendicular shocktoescape[möbius et al., 21]. [49] In addition, our statistics in the tracing distance R trace from the HFA locations to the bow shock surface show that Perp-Perp events tend to be closer to the bow shock than Para-Para events. R trace for Para-Para events ranges from.57 to 2.81 R E with the median value of 1.5 R E, and R trace for Perp-Perp events ranges from.9 to 2.82 R E with the median of.52 R E. Therefore, the close distance from the bow shock might help the reflected ions interact with the upstream solar wind soon after the reflection before being guided back to the downstream of the bow shock. 6. Conclusions [5] We have analyzed 87 HFAs with large flow deflections. The bow shock geometry at both the leading and trailing edges of the HFAs have been identified through multiple methods. The results determined by the N method and the IMF averaging intervals closest to the HFA center is used as the main results. The results might be accurate within 1, and they are also confirmed through checking the ion spectra, the magnetic field fluctuations, and the ion VDF. We find that HFAs can be observed under the condition of either a quasi-parallel or a quasi-perpendicular shock at HFA edges. Para-Para events (1 cases) show higher number density and higher temperature in the background solar wind, and higher temperature at the event center than Perp-Perp events (13 cases) in statistics. The higher gyration velocity, the lower background magnetic field magnitude, and the closer distance from the bow shock to the HFA locations in Perp-Perp events might help the reflected ions escape from the bow shock or interact with the upstream solar wind very soon after the reflection. The higher M f for Perp-Perp might also help develop the pitch angle scattering and Alfvén waves, which might help the ions escape from the bow shock. 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