Cluster observations of the dusk flank ... - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, A10201, doi:10.1029/2012JA017703, 2012

Cluster observations of the dusk flank magnetopause near the sash: Ion dynamics and flow-through reconnection Nelson C. Maynard,1 Charles J. Farrugia,1 William J. Burke,2 Daniel M. Ober,3 Forrest S. Mozer,4 Henri Rème,5,6 Malcolm Dunlop,7 and Keith D. Siebert8 Received 8 March 2012; revised 27 July 2012; accepted 15 August 2012; published 2 October 2012.

[1] Compared to the dayside, dynamics on the flanks of the magnetopause are poorly understood. To help bridge this knowledge gap we analyzed Cluster plasma and field measurements acquired during a 90-min period on 20 November 2003 when Cluster crossed the magnetopause four times in the vicinity of the sash. MHD simulations provide a context for Cluster observations. Crossings were between the magnetosheath and an S-shaped plasma sheet, rather than to the open-field lobes of the magnetotail. Cluster encountered two regions of MHD-breaking differences between perpendicular ion velocities and E B convection. Ion adiabatic expansion parameter (d i) calculations show that ion gyrotropy was not broken during an episode of strong Alfvén wave activity in the magnetosheath. However, gyrotropy was broken (d i > 1) during the fourth magnetopause crossing. In the magnetosheath, ion guiding-center motion was maintained but inertial effects associated with temporally varying electric fields are probable sources of velocity differences. Regarding the magnetopause crossing, the generalized Ohm’s law limits possible sources for breaking ion gyrotropy to inertial forces and/or electron pressure gradients associated with a nearby reconnection event. We suggest that Cluster witnessed effects of a temporally varying and spatially limited, flow-through reconnection event between open mantle field lines from the two polar caps adding new closed flux to the LLBL at the sash. Future modeling of flank dynamics must consider inertial forces as significant drivers at the magnetopause and in the adjacent magnetosheath. Citation: Maynard, N. C., C. J. Farrugia, W. J. Burke, D. M. Ober, F. S. Mozer, H. Rème, M. Dunlop, and K. D. Siebert (2012), Cluster observations of the dusk flank magnetopause near the sash: Ion dynamics and flow-through reconnection, J. Geophys. Res., 117, A10201, doi:10.1029/2012JA017703.

1. Introduction [2] The dayside magnetopause’s position is determined by force balance between the magnetosphere magnetic field and the dynamic pressure of the solar wind. Coupling through magnetic merging between the interplanetary magnetic field (IMF) and the magnetospheric magnetic field is the primary driver of convection patterns in the magnetosphere and 1 Space Science Center, University of New Hampshire, Durham, New Hampshire, USA. 2 Institute for Scientific Research, Boston College, Chestnut Hill, Massachusetts, USA. 3 Air Force Research Laboratory, Kirkland AFB, Albuquerque, New Mexico, USA. 4 Space Sciences Laboratory, University of California, Berkeley, California, USA. 5 UPS-OMP, IRAP, University of Toulouse, Toulouse, France. 6 CNRS, IRAP, Toulouse, France. 7 Rutherford Appleton Laboratory, Chilton, UK. 8 Applied Research Associates, Inc., Nashua, New Hampshire, USA.

Corresponding author: N. C. Maynard, Space Science Center, University of New Hampshire, Morse Hall, 8 College Rd., Durham, NH 03824, USA. ([email protected]) ©2012. American Geophysical Union. All Rights Reserved. 0148-0227/12/2012JA017703

ionosphere [Dungey, 1961]. Merging may occur at magnetopause locations where adjacent magnetospheric and magnetosheath field lines are anti-parallel [Crooker, 1979] or have anti-parallel components with the residual serving as a guide field [Sonnerup, 1974]. The first option generally locates coupling near the cusp, while the second nearer the subsolar magnetopause. During episodes of northward IMF BZ, merging occurs on magnetic flux that maps to the poleward boundary of the cusp [Maezawa, 1976]. [3] In contrast to magnetic merging in a region of stagnated flow like the sub-solar magnetopause, Siscoe et al. [2002] discussed a mode of magnetic merging that can develop in fast flowing plasma. Flow-through reconnection (FTR) is asymmetric with respect to plasma flowing through a merging X-line. One exhaust direction adds to the flow-through velocity. The opposite exhaust bucks against the incoming flow, slowing it down and possibly creating a stagnation region. Decelerated flows from the upstream side of an active merging site [e.g., Aggson et al., 1984] are also a signature of flow-through-reconnection. This mode must be considered in the analysis of merging events that occur away from the sub-solar stagnation point. [4] Viscous coupling occurs through the low latitude boundary layer (LLBL) [e.g., Sonnerup, 1980; Lotko et al.,

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MAYNARD ET AL.: DUSK FLANK MAGNETOPAUSE DYNAMICS

1987]. Early satellite measurements indicate that the LLBL accounts for 100 nA/m2. Crossings M1 and M4 had the strongest positive JY values. During crossing M2, JY values were also positive, but at about half the intensity of the other two. Current densities measured during crossing M3 were very small. The magnetopause was expanding in response to the fivefold density decrease. Also noteworthy is the strong variability of current densities in the X and Y directions detected between the times of lines M2 and M3 while Cluster was in the magnetosheath. During parts of this interval, calculated r• B increased, but remained small in comparison with the estimated r B.

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Figure 5. (a–c) The Z, Y, and X components of the current densities in GSM coordinates, calculated from r B. Traces give the magnitude of (d) r • B and (e) |B| calculated at the locations of all four spacecraft. [22] Figures 6a, 6b, and 6c separate the components of J into contributions parallel (red) and perpendicular (black) to local magnetic fields. The large and variable magnitudes of the red traces demonstrate that, away from magnetopause boundaries (dashed vertical lines), the currents were mostly parallel to B. For later comparisons, Figures 6d, 6e, and 6f show the components of Hall currents in electric field ([J B]/ne) units. We note here that the primary intervals in which Hall terms were the large occurred between lines M1– M2 and lines M3–M4, where the presence of higher energy ions (Figure 3) suggest that Cluster returned to the magnetospheric boundary layer at the magnetopause current layers highlighted by lines M1 and M3. [23] Energy flow is an important indicator of magnetopause electrodynamics. The component of the wave Poynting flux (dS) parallel to the local magnetic field is given in Figure 6g. We calculated dS by subtracting from the spinperiod values of the Poynting flux a 45-s sliding average of those values. This removes the DC background and highlights electromagnetic energy flow due to wave activity. The strongest values of d Sk occurred where the parallel currents were

large and at magnetopause crossing M4. Enhanced values of dSk (Figure 6g) were also observed between dashed lines M2 and M3. They peak within the negative excursions of BZ bounded by the green and blue arrows and dotted vertical lines in Figure 3. Note that dS is primarily directed in the +Y and – X directions indicating energy flow tailward along the flank. Figure 6h plots E • J for the interval. Negative (positive) E • J values indicate transfers of energy from the magnetic field to the particles (and vice versa). Places where BZ was negative (Figure 2e) were areas of energy transfer to the particles, which is confirmed by similarly located enhancements of ion flux and energy in the energy spectrogram of Figure 3. These particles have quasi-parallel distributions in the pitch angle spectrogram. Note that at magnetopause crossings M1 and M2, d Sk and the energy transferred to the particles was less than that observed during negative BZ excursions.

4. Discussion [24] The previous section provides a host of Cluster measurements acquired during a 90-min period leading up to the magnetic superstorm of November 2003. Cluster’s location

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Figure 6. (a–c) The X, Y, and Z components of current densities perpendicular (black) and parallel (red) to local B. (d–f) The X, Y, and Z components of (J B)/ne in units of mV/m. (g and h) The parallel component of the wave Poynting flux vector and the calculated values of E • J, respectively. near the northern flank of the magnetotail allowed it to monitor magnetospheric responses to three significant changes in the solar wind’s dynamic pressure. Plasma and field data indicate that Cluster crossed the magnetopause four times in response to pressure changes during that interval. MHD simulations suggest that when in the magnetosheath, Cluster was located adjacent to the sash rather than to the magnetotail lobe. Here we reflect on the physical principles underlying this rich set of observations. This section divides into three parts that consider (1) properties of interfaces between the sash and adjacent magnetosheath, (2) complex ion dynamics found near these interfaces, and (3) observations at crossing M4 which suggest close proximity to a flowthrough reconnection structure. 4.1. Sash-Boundary Layer/Magnetosheath Interfaces [25] We have identified particle and magnetic field transitions at lines M1 through M4 in Figures 2–4 as magnetopause

crossings. Changes in the ion energy and pitch angle distributions (Figure 3) have the characteristics of transitions between magnetosheath and magnetospheric boundary layers. Located behind the Earth near the magnetosheathmagnetosphere interface, Cluster’s boundary crossings exhibit characteristics that differ from those typically found at the sub-solar magnetopause. Across the dayside boundary plasma densities and magnetic fields vary in opposite senses, characteristic of slow-mode structures. Cluster often observed densities and magnetic fields that changed in the same senses across the magnetopause, characteristic of fast-mode structures [e. g., Völk and Auer, 1974; Wu et al., 1993; Kivelson and Russell, 1995]. [26] Figure 7 shows ISM results that help identify plasma and field properties expected at and near the dusk flank of the magnetopause just prior to the large density decrease at line M3. All panels show simulated quantities in the Y-Z plane at X = –5.5 RE. Note that in this ISM simulation the Earth’s

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Figure 7. ISM simulation results in the Y-Z plane at X = – 5.5 RE. (a and b) Ion energy densities with purple/red (green/black) representing high (low) values. (c) The X component of ion velocities with brown (blue) colors representing positive (negative) values. (d) The magnitude of the magnetic field with white/ purple (green/black) representing high (low) values. Note the dark green color of the sash. (e) The X component of the magnetic field with brown (blue) colors representing positive (negative) values. Arrows indicate the directions of the magnetic field vectors in the Y-Z plane. (f ) The X component of ion velocities with arrows indicating the direction of current-density vectors in the Y-Z plane. Long arrows highlight the bow shock, magnetopause, sash, lobe, plasma sheet, and the locus of the last closed field lines traced from both the northern and southern hemisphere polar caps. The double-ended arrow marks the approximate direction of the normal obtained via CVA analyses. dipole axis is fixed in the Z direction, and thus does not distinguish between GSE and GSM coordinates. The differences are important in the present analyses. Near the time of magnetopause crossing M4, Cluster’s location at (YGSM, ZGSM) ≈ (12.9, 0.3) RE indicates a much closer proximity to the magnetospheric equatorial plane than its corresponding (YGSE, ZGSE) ≈ (11.6, 5.3) RE coordinates might suggest. Last closed field line boundaries, traced from both polar ionospheres, appear as irregular red or blue lines. Inside this irregular structure field lines are closed and trace through the plasma sheet to the northern and southern auroral ionospheres. [27] Outside the boundary, but still within the magnetosphere, open field lines with BX positive (negative) attach to Earth in the northern (southern) hemisphere. Some of these thread through the low-density lobes, others through the higher-density mantle and high-latitude boundary layer. At some point all open field lines trace through the magnetosheath and bow shock into the solar wind until that connection is cut off by reconnection in the magnetotail or sash to form new pairs of closed and interplanetary field lines.

[28] In Figure 7b, a region of high ion energy density curls upward from the plasma sheet following the reversal of BX from positive to negative (Figure 7e). Note also that the plasma sheet itself tilts northward (southward) on the dusk (dawn) flank (Figure 7a). This allows southern lobe field lines and closed field lines from the southern polar cap (all with negative BX) to appear above the equator on the dusk side (see Figure 7e). The last closed field line boundary on the outer side of this extension maps to the southern hemisphere. A similar feature on the dawn side extends below the equatorial plane and maps to the northern hemisphere. As seen in Figure 7d, the plasma sheet with these extensions forms a “cross-tail S” structure. The extensions are regions of low magnetic fields (green color). White et al. [1998] showed that they extend tailward along the flank like a “sash.” The magnetosheath VX penetrates through the boundary (Figure 7c), but with decreasing efficiency deeper into the boundary layer. [29] As a spacecraft crosses from the magnetosheath to the sash or the cross-tail S extension of the plasma sheet |B| decreases (Figure 7d). Plasma densities also decrease. In the vicinity of the sash we expect to encounter a down-tail

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Table 3. Triangulations: Unit Vector Components of the Normal and Properties

Line 1 Line 2 Line3f Line3e Line 4

Time

kx

ky

kz

Vk

la

ab

Pressure

10:09:50 10:17:10 10:30:03 10:43:37 10:45:42 11:09:40

0.188 –0.205 –0.180 –0.197 0.164 –0.196

–0.430 0.395 0.414 0.271 –0.434 0.432

0.883 –0.895 –0.892 –0.942 0.886 –0.880

4.8 7.7 18.0 59.0 12.8 8.0

113 72 68 76 114 61

91 90

decrease increase BZ change

89 110

decrease increase

a

Angle (deg) between the triangulation normal and the minimum variance normal. Angle (deg) between triangulation normal and B.

b

extension of the low latitude boundary layer (LLBL) in which the high-density and low-energy fluxes of the magnetosheath transition to high-energy, low-density plasma sheet populations of the plasma sheet [e.g., Lotko et al., 1987]. Note that Figures 7d and 7a show oppositely directed B and ion energy density variations at the interface between the lobe regions and the magnetosheath at high latitudes northward of the sash, similar to those regularly observed on the dayside. [30] Throughout the studied interval BX (Figure 2c) remained negative in the magnetosphere because of the tilt of the plasma sheet and cross-tail S, and in the magnetosheath because of the draping of the IMF. VX also remained negative except for the interval between crossings M1 and M2 (Figure 4a). We conclude that at crossing M1 Cluster transitioned from the magnetosheath through the boundary layer to the closed field line region of the cross-tail S extension. However, it remained on magnetic field lines tied to the southern auroral region and equatorward of the neutral line in the cross-tail S extension. Consistent with the ion observations presented in Figure 3, Cluster returned to the magnetosheath at crossing M2. [31] Currents measured near lines M1, M2 and M4 are strongest in the +Z direction (Figure 5a), consistent with the large changes in BX (Figure 2c). Arrows in Figure 7f indicate that the directions of currents in the Y-Z plane were primarily in the Z direction near Cluster’s location. This is consistent with the direction of Chapman-Ferraro currents along the magnetopause and the closure of the cross-tail currents as well as Region 1 field-aligned currents seen above the equatorial plane in the near-tail dusk flank in MHD simulations [see Siscoe et al., 2000, Plates 1 and 3]. No dominant currents developed near line M3 that had magnitudes similar to those observed at the other magnetopause crossings. We note that the magnetosphere was expanding as a result of the fivefold density decrease, and we might expect the magnetopause currents to be spatially spread out and therefore less intense. [32] Ion spectral data (Figure 3) indicate that an additional crossing from the magnetosphere to the magnetosheath occurred near 10:05 UT (at the P1 particle boundary). The isotropic, high-energy ion fluxes detected prior to 10:05 UT transitioned to magnetosheath fluxes that were highly fieldaligned in the anti-parallel direction. JZ was positive and significant from 10:00 to 10:05 UT (Figure 5a) consistent with the spacecraft being located within the magnetopause boundary layer. The gradual transition of BX from near zero to large negative values suggests that Cluster moved through the boundary layer slowly.

[33] We now explore the character of the discontinuities and the magnetosheath region between crossings M2 and M3. The timings of the boundary crossings by each of the 4 Cluster satellites, allowed use of triangulation techniques to determine normal-incidence velocities at the transitions associated with lines M1–M4. The triangulation method is also referred to as a constant velocity analysis (CVA) [Russell et al., 1983]. Normal directions and velocities obtained via the CVA method are listed in Table 3. The analysis near 10:30 UT marks the time of the largest variation in Bz (Figure 2e). At line M3 the values for M3f are for the beginning of the decrease in |B|, while those of M3e correspond to its end. At all crossings the velocities were several km/s (Table 3), most strongly in the Z direction. The double ended arrow in Figure 7b indicates the approximate orientation of the CVA normal direction. The values of the angle between the CVA normal and B are given in the next-to-last column of Table 3. For crossings M1, M2 and M3e it was very close to 90 . The motion of magnetic field changes was nearly tangent to the magnetopause as well as normal to B. This direction, along with boundary crossings being associated with solar wind pressure changes, suggests that the tail lobes flatten (balloon) with increasing (decreasing) solar wind pressure. [34] After transforming into the plasma’s rest frame, which was traveling tailward between 200 and 300 km/s with respect to Cluster, we obtain velocities between the sonic and Alfvén speeds, but well below those of fast-mode waves. However, |B|, |V |, and n variations had the same sense as fast mode waves. Because the phase velocity was small in the plasma’s rest frame, observed variations cannot be interpreted as signifying the presence of standing fast wave structures. [35] Minimum variance analyses [e.g., Sonnerup and Scheible, 1998] are often used to distinguish between tangential or rotational discontinuities. They assume that the observed structures are locally planar. Ideally tangential discontinuities have normal components Bk and Vk that are identically zero. Tangential discontinuities can have large variations in |B|. By contrast, rotational discontinuities have only small to no variation in |B| and a significant but small normal component Bk that is related to merging rates within active reconnection sites. Discontinuities that have small normal components but small variations in |B| were classified as “either.” Discontinuities that have large normal components and large variations in |B| are inconsistent with MHD tangential and rotational discontinuities [e.g., Neugebauer et al., 1984; Knetter et al., 2004]. Teh et al. [2011] used ideal MHD reconstruction techniques [Sonnerup and Teh, 2008] to show that three solar wind discontinuities that

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Table 4. Minimum Variance Analyses: Normal Direction and Properties Interval

kX

kY

kZ

Ratio

BK

Standard Deviation

10:00–10:50 10:10–10:45 10:00–10:43 10:00–10:30 10:50–11:30 10:55–11:15

0.2458 0.1501 0.2216 –0.2492 0.5250 0.6198

0.9693 0.9883 0.9750 –0.9683 0.8257 0.7702

–0.0098 0.0281 –0.0141 –0.0187 –0.2063 –0.1502

5.83 6.67 9.39 14.37 3.16 2.47

19.7 31.2 24.7 –24.6 –19.8 –27.0

9.6 9.0 8.1 6.8 5.8 6.3

Knetter et al. [2004] had identified as “either” contained magnetic islands that violate the assumption of planar structures. These events had large angles between the CVA and minimum variance normals. [36] Separate minimum variance analyses were performed for the intervals 10:00 to 10:50 UT and 10:50 to 11:30 UT. Vector directions for the minimum variance normals are given in Table 4, along with the ratio of the middle-to-least eigenvalues, the normal components of B, and their standard deviations. We performed nested analyses on the first interval with the best ratios of middle to least variance directions ranging up to 14.37. In all analyses a large, but statistically significant normal to the plane of maximum variance (Bk) was found. These values were very large, varying between 19 and 31 nT. The minimum variance normal in each case was close to the Y direction, which was at a large angle to the normal direction determined by CVA triangulation. A nested analysis in the second interval (last line of Table 4) had a poor ratio of the intermediate-to-minimum variance directions. We include it for reasons that are explained in section 4 below. [37] The angles between the triangulated and minimumvariance normals (l) are given for each case in the seventh column of Table 3. The values were close to either (90 –20) or (90 + 20) and were similar to values found in the examples presented by Teh et al. [2011]. They suggested that large angle between the two normals is caused by a minimum variance analysis that focused on an axial (or ‘guide field’) in a reconnection geometry that had relatively small variations, while the field variance in the normal direction taken from CVA was enlarged consequent to a spacecraft encounter with a magnetic island. In the present case this cannot be the complete story. Here the direction of maximum variance in E was approximately aligned with the minimum variance in B, similar to results obtained near merging sites on the sub-solar magnetopause. A large normal electric field is required to convect magnetic field lines in the plane of the discontinuity, which in this case was primarily in the –X direction. Even so, the convective velocity (green) was highly variable and less than the measured perpendicular ion velocity (Figure 4a). Also, the proximity of the sash favors anti-parallel reconnection. In the magnetosheath the IMF side of the magnetic field line from an active upstream merging site must be pulled by magnetic tension away from the draped configuration in the direction of the IMF clock angle (see the direction of magnetic field arrows in the Y-Z plane of Figure 8e). [38] The detection of field-aligned currents between lines 2 and 3 on the magnetosheath side of the boundary suggests that Alfvén waves were present (Figures 6a and 6b). Strong correlations of BZ versus BY and VZ versus VY, observed over

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the whole interval, had fitted slopes of –0.9 and –1.0. Matsuoka et al. [2000] previously reported observing Alfvén waves in the magnetosheath near the magnetopause. Their event and statistical analyses showed that the waves were always propagating downtail in the direction of the plasma flow. The waves satisfied the Alfvenic relation by correlating the perturbations of field and flow perpendicular to the background magnetic field: DB? = – (mor)1/2DV?. Their suggested source of the waves was either the magnetopause or the bow shock. We also tested this relationship for each component in the interval from 10:17 to 10:44 UT. The 397 points fit to a line with slope of 1 with correlation coefficients of 0.82 and 0.81 in the Y and Z directions. This provides strong evidence that Alfvén waves were dominant across this interval. The GSM components of the wave Poynting flux (not shown) were strongest in the –X and +Y directions, indicating energy flow was directed down-tail and away from the magnetopause. These variations were strong in the field-aligned direction (Figure 6g). Proximity to the sash, a potential reconnection site, suggests a source for the waves. Field-aligned currents are expected to flow along the separatrices connected to active merging sites. The outer separatrices from an upstream merging site extend downstream into the magnetosheath near the magnetopause and the location of Cluster. Field-aligned currents are carried by obliquely propagating Alfvén waves [Siscoe, 1983] and have significant dSk. Changes in IMF clock angle modulate the location of the sash and, hence, those of associated merging sites [Siscoe et al., 2001]. This, coupled with a timedependent process provides ample reason for a continuing mix of interacting Alfvén waves in the magnetosheath adjacent to the sash. In the present instance the active merging sites were located upstream of Cluster, as evidenced by a tailward-directed wave Poynting flux. 4.2. Ion Dynamics [39] Data presented in Figure 4 indicate that the E B/|B|2 convection velocity (VC) and the component of ion velocity perpendicular to the local magnetic field were mismatched over large portions of the interval, indicating that the ions were not always fully coupled to the magnetic field. Parker [1996] treated B and V as primary variables with E and J as secondary for maintaining consistency with Maxwell’s equations. The primary driving forces for V are particle pressure (thermal momentum flux), the Maxwell stress tensor and the Reynolds stress tensor. Since the solar wind’s velocity was relatively constant (Figure 1) over the studied interval, the thermal momentum flux changed only with the density. In the magnetosheath V was regulated by the momentum flux as modified by the bow shock and by requirements for the Maxwell stress tensor associated with draped field lines. In the steady state, E? = –Vi B and J = r B/m0. Hence, variations in perpendicular components of E and J primarily reflect changes in B. [40] To help understand the VC and Vi? comparisons of Figure 4 and investigate causes of their differences, it is useful to compare values of the associated electric fields. In Figure 8 we show (in black) the differences of the measured spin-fitted electric fields obtained from the 3–4 sensor pair on C1 (with the assumption of E • B = 0) and the perpendicular electric field calculated from Vi B using Cluster 1 CIS/ HIA and magnetometer data. When making the comparisons

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Figure 8. Comparisons between E + (Vi B) (black line) and E + (Vi B) – (J B)/ne (red points) for (a–c) the three GSM components and (d) the vector-sum perpendicular differences. (e) The ratio of the perpendicular electric to magnetic force (di) experienced by thermal particle in the fluid’s rest frame. This parameter measures the degree to which ions are coupled to the magnetic field [Scudder et al., 2008].

in electric field units, the differences are the magnitudes of the left hand side of the generalized Ohm’s law [e.g., Vasyliunas, 1975]. " # me ∂~ J ~ ~ ~ ~ ~ ~ ~ ~ þ r⋅ JV þ VJ E þ V B ¼ hJ þ 2 ne ∂t i $ 1h r ⋅ Pe ~ J ~ B ne

ð1Þ

In ideal MHD, ions are frozen to the magnetic field and righthand side of equation (1) is exactly equal to zero. Differences from zero measure the degree to which ions are decoupled from the magnetic field. Sources of the decoupling are represented by the terms on the right side of the equation. Terms in the first set of brackets represent inertial effects. The

last two terms arise from electron pressure gradients and Hall effects. The first term on the right side represents anomalous resistivity. Since the variations in the velocity differences do not follow those of the currents (Figure 5), we ignore this term. [41] Note that the electric fields were large and variable in the magnetosheath between lines M2 and M3 and of larger magnitude in the magnetosheath after line M4, exceeding 50 mV/m (Figures 2f, 2g, and 2h). The differences between the measured and calculated electric field components as well as differences of the total perpendicular electric fields are shown in Figures 8a, 8b, 8c, and 8d. The differences are largest in the Y and Z components (Figures 8b and 8c). Difference values between 0 and 5 mV/m are typical with occasional differences ranging up to 10 mV/m. The largest

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difference is >20 mV/m near line M4. Note too that the scale in Figure 8d is 0 to 40 mV/m. [42] We measured the Hall or J B/ne term (see Figures 6d, 6e, and 6f ). Note that it is small in the magnetosheath regions, but of comparable magnitude to the differences in the sash and boundary layer regions between crossings M1 and M2 and crossings M3 and M4 (orange highlight below Figure 8d). In each of the first four panels of Figure 8 we have subtracted the Hall term from the velocity differences and overlaid combined values as red points. Note that between lines M1 and M2, especially in Figure 8b, the values, after the subtraction of the Hall term, are greater (not less) and of opposite sign to the original differences. The largest difference values occurred where field-aligned currents (Figure 6) and electric fields (Figure 2) were most variable, especially between lines 2 and 3. On this basis we conclude that the Hall term is not the principal source of the deviations from ideal MHD. All remaining differences must be attributed to the inertial terms or the electron pressure gradient terms in equation (1). [43] Before continuing our discussion of possible sources of the deviations between Vi and VC, it is useful to introduce the adiabatic expansion parameter, di,e = ri,e /L. The symbols ri,e and L represent the thermal gyroradii of either ions or electrons and the dominant spatial scale lengths of their respective variations. As such, di,e measures how well the plasma species are tied to magnetic field lines. For conditions with di,e ≪ 1, guiding center theory describes the particle motion, and the MHD approximation to the generalized Ohm’s law applies. A particle species is said to be demagnetized if di,e > 1 [Macmahon, 1965; Vasyliunas, 1975; Scudder et al., 2008; Maynard et al., 2011]. Based on fieldline-resonance-ordering considerations, Scudder et al. [2008] also demonstrated that d is more accurately connected to the ratio of the perpendicular electric to magnetic forces experienced by a thermal ion or electron in the plasma’s rest frame. d i;e ≡

E? þ Ui;e B w?i;e B

ð2Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where w?i;e ≡ 2kT?i;e =mi;e represents the mean thermal speeds of ions or electrons. [44] Quantity d i calculated from the above equations is shown in Figure 8e. In the magnetosheath after line M4 and between lines P1 and M1, di < 0.2, indicating that the ions were reasonably well tied to the magnetic field and guiding center theory remains applicable. In the areas identified as boundary layer (orange line at the top of Figure 8e) values ranged between 0 and 0.5. Here we find indications that the terms on the right hand side of equation (1) begin to become significant. In the magnetosheath near 10:22 UT, and just after line M3, di approached 1.0. The largest value occurred near line M4 where di exceeded 2.0, clearly signifying a demagnetization of the ions. With the exception of these very short intervals, the guiding center approximation was applicable. [45] The region between lines M2 and M3, which we have identified as magnetosheath is characterized by large and variable field-aligned currents, the strongest in the X direction (Figures 6a, 6b, and 6c). We argued above that Alfvén waves were present, acting as carriers of the field-aligned

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currents. Perpendicular electric fields are also large and variable. The larger values of di in this interval coincide with the strongest field-aligned currents and electric field variations (Figure 2). In contrast, Figure 4 shows that: (1) this is a region of relatively constant parallel ion flow velocities (red traces), and (2) the measured V?X (black) is larger than the more variable VCX (green). The first indicates that the chargedparticle carriers of the observed field-aligned currents must be electrons. Combining the second with observed values of di between 0.2 and 0.8 suggests that the ions were experiencing (F B)/qB2 motions, other than the convective VC = (E B)/B2 motions, within the guiding center approximation. Inertial drifts from time varying electric fields provide a possible source. ~ inertial V

0 ~. 1 dE ~ B dt A B ¼ m@ qB2 B2 ¼

. ~. i m h d~ E dE ~ ~ ~ ~ ⋅ B B B ⋅ B 4 dt dt qB

ð3Þ

[46] If we assume that E and its time variations are perpendicular to the main field then " # . m d~ m ∂~ E ~ E ~ ~ V inertial ¼ 2 dt ¼ qB2 ∂t þ V Vc rE qB

ð4Þ

Note that if the perceived time varying electric field is inductive r E = (∂B/∂t) then k dE = -wdB, or |dE| = Vph|dB|. Here Vph represents the phase velocity of the wave in the plasma rest frame. In the MHD approximation Vph can represent VA, VFast or VSlow. We have presented evidence for the presence of Alfvén (intermediate mode) waves in this region. [47] The driving forces for Vi in the magnetosheath are the particle pressure (thermal momentum flux) and the Maxwell stress tensor. E and J are secondary variables and react to V and B. Given the large variations in both E and J, and the presence of Alfvén waves, we suggest that inertial terms from time varying E and J are the primary source of the differences from zero of the left hand side of equation (1), allowing VC to differ from Vi. This allows for the presence of non-MHD drifts within the guiding center framework for long periods, without breaking ion gyrotropy, consistent with the observed values of d i. 4.3. Flow-Through Reconnection [48] We return to consider events leading up to Cluster’s M4 crossing into the magnetosheath. The large solar wind density decrease observed by ACE had the effect of expanding the magnetopause beyond Cluster’s location at the time of crossing M3. Cluster’s return toward the magnetosheath, starting 10 min later coincided with a gradual increase in the solar wind density (Figure 1a) that recompressed the magnetosphere. Also of significance for Cluster’s return to the magnetopause were the large Z component of the solar wind velocity’s and a steady increase from about from 30 to 90 km/s in the –Y direction, allowing significant transverse components of the dynamic pressure to affect the magnetospheric-boundary location (Figures 1k and 1j). Magnetic field structures encountered near the M4 crossing

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were more complex than those observed during crossings M1 and M2 that were dominated by changes in BX. Crossing M4 also provided the only example with di > 1, indicating local ion demagnetization. [49] Before developing a physical interpretation of Cluster measurements acquired near this magnetopause crossing it is useful to recall three relevant studies. First, Siscoe et al. [2001] suggested that the sash is a locus of anti-parallel merging. Second, Siscoe et al. [2002] discussed a mode of magnetic reconnection in which an active merging site remains stationary in fast flowing plasmas, that they called flow-through reconnection (FTR). Third, Eriksson et al. [2004] analyzed plasma and field measurements acquired during two Cluster crossings into the magnetosphere near the sash to test the anti-parallel merging hypothesis of Crooker [1979] and Siscoe et al. [2001]. In one crossing Cluster data supported an anti-parallel interpretation; in the second case a weak component-reconnection interpretation appeared more plausible. Eriksson et al. [2004] made no mention of FTR. This omission is intelligible. Siscoe et al. [2002] identified FTR in their analysis of an ISM simulation with a purely northward IMF. The simulation yielded a steady state merging line forming near the noon meridian poleward of the cusp [Maezawa, 1976]. Siscoe et al. [2002] made no mention of FTR near the sash. However, there seem to be no a priori reasons that either forbid FTR formation near the sash or render FTR incompatible with either anti-parallel merging or component reconnection with a small guide field. In the following we briefly review criteria for FTR formation and argue that they are met in our reported Cluster measurements. [50] Siscoe et al. [2002] identified four characteristic features that specify FTR structures. [51] 1. The motional electric field obtained from the ion velocity (Ei = –Vi B) differs from the convective electric field E: i.e., ion flows are decoupled from the magnetic field. They referred to the difference between E and Ei as the dissipation electric field (Ediss). In fact, Ediss represents sum of all the terms on the right side of equation (1) and is the same as the difference field shown in Figure 8. Note that their ISM simulations had an explicit resistivity proportional to J as a source for Ediss that acted to stabilize the X-line. [52] 2. The magnetic field between the anti-parallel magnetic field lines about to merge is weak. A tongue of low magnetic field strength was found in the simulation extending sunward (upstream) from the X-line. [53] 3. (a) Sunward convective velocities and Poynting fluxes were seen in the low-field tongue. (b) However, in the steady state simulation the magnetosheath plasma velocity, accelerated tailward along streamlines from the sub-solar stagnation point pressure gradients, was in the opposite direction, a “distinctly non-MHD-like situation.” [54] 4. Tailward flowing plasma penetrated the magnetopause and tended to pull the X-line downwind (Figure 7c). Vik is not part of the left side of equation (1): hence, the name “flow-through.” [55] Magnetic field and ion flux measurements identify the regions that Cluster passed through while approaching the magnetopause crossing at the time of line M4. To aid in the discussion of those data, Figure 9a contains a schematic representation of the event from the perspective of an observer looking tailward at the Y-Z plane at X = –5.5 RE. Large arrows indicate the orientations of the Y and Z axes

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in GSE (black) and GSM (red) coordinates. The cartoon incorporates information from Figure 7 to show the relative positions of the lobes, mantle, cross-tail S configuration of the plasma sheet, LLBL and sash. The irregular blue arrow schematically suggests a temporal path for Cluster’s progression through these regions. It passed from the lobe to the plasma sheet, staying on the southern side of the current sheet (BX < 0), and then moved into the sash/LLBL approaching a merging site and consequently exiting to the magnetosheath. The small curved arrows at the magnetosheath interface indicate that open field lines from both hemispheres must be present and meet in the sash for reconnection to be accomplished, purple equatorward and red poleward of the sash. Figure 9b provides an expanded view of an FTR X-line adapted to our scenario. Solid lines represent magnetic field lines of the four required typologies: red – open to the magnetosheath from NH; purple - open from SH; black – closed interconnecting both hemispheres; and green – interplanetary/ magnetosheath only). Orange arrows represent plasma velocities. Again, the blue dashed line represents our concept of Cluster’s trajectory relative to the FTR structure. The L, M, and N vectors represent the boundary normal coordinate system that we describe below. [56] Consistent with this interpretation, Figures 9c and 9d show ISM-traced magnetic field lines from points every 0.05 RE along a line from Y = 9.5 to 12.5 RE with Z = 5.5 and X = –5.5 RE. The simulation is the same as that used in Figure 7. Red (purple) traces are open lines that map to the northern (southern) hemisphere mantle locations. The black traces represent newly closed field lines in the sash from a reconnection point close to but tailward of X = –5.5 RE. This is similar to the reconnection configuration schematically represented in Figure 9b, but is based on ISM-simulated magnetic field line tracings. [57] The blue trajectory in Figure 9b for magnetopause crossing M4 does not cross the “merging X” above or below the separator, but slides horizontally along the structure, sampling both exhaust regions. This is consistent with Cluster never encountering the positive BX expected in the NH mantle, lobe, and above the center of the plasma sheet current layer. Consequently, what we would expect to be the maximum variance direction of B in a merging configuration will be either the intermediate direction or close to the minimum variance direction. We used the (i, j, k) transformation matrix from the last minimum variance analysis in Table 4 to rotate the E and B data from GSM coordinates to that frame. It was obvious from inspection of the results that a further rotation of 20 about the maximum variance axis (i) would concentrate the variations in E almost completely into one axis. We label the combined transformation axes L, M, and N, with N the direction of maximum variance of E. Normally, the axis of maximum variation in E is also equivalent to the axis of minimum variation in B. The transformation matrix from GSM is given by

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L ¼ ð0:4630; 0:2044; 0:8624ÞðX ; Y ; Z ÞGSM M ¼ ð0:8074; 0:3043; 0:4028ÞðX ; Y ; Z ÞGSM N ¼ ð0:3657; 0:9304; 0:3139ÞðX ; Y ; Z ÞGSM

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Figure 9. (a) Cartoon representation of the configuration of the magnetic tail at X = – 5.5 RE showing the relative locations of the plasma sheet and cross-tail S, LLBL, sash, and mantle and lobe open field lines. (b) Schematic representation of Cluster’s trajectory (blue dashed line) relative to the FTR structure encountered near line M4. Black lines are closed. Purple (red) lines are open, connecting from the southern (northern) hemisphere to the magnetosheath. Green lines have both ends in the magnetosheath (eventually tracing to the IMF. The boundary-normal coordinate directions L, M, and N used in Figures 10 and 11 are noted. P2, P3, P4, and M4 mark their phenomenological locations along the Cluster trajectory in the cartoon. (c and d) Y-Z and X-Y planes showing traced magnetic field lines in both directions from points every 0.05 RE along a line from Y = 9.5 to 12.5 RE with Z = 5.5 and X = –5.5 RE The simulation is the same as in Figure 7. The open-closed boundary (OCB) in the plane is shown by the intersection of the last closed field lines, traced from the northern and southern ionospheres, with the plane. The color code for field lines is the same as in Figure 9b. [58] Figure 10 presents expanded ion spectral and pitch angle data of Figure 3, the magnitude of B, and the components of B and E in the (L,M,N) system around crossing M4. Note that color bars are different in Figures 10a and 10b from their analogs in Figure 3. The sensitivity was increased to emphasize ion structuring throughout this region. Three ion boundaries (P2, P3, and P4) are highlighted. The first two are the same as P2 and P3 in the previous figures. Coming from open southern hemisphere lobe field lines with low densities, Cluster encountered tailward-streaming fluxes at P2. Note the beginning of the weaker fluxes that extended to the top of the sensor’s energy range. The tailward streaming and velocity dispersion of the ions and the large and negative BX are consistent with open southern hemisphere mantle field lines that drape over the dusk flank, eventually crossing into the magnetosheath. At P3 the ions changed to a basically perpendicular distribution with a raised lower energy boundary. We interpret this to be an entry onto closed field lines of the LLBL associated with the cross-tail S extension of the plasma sheet, but staying on field lines tied to the southern hemisphere. In Figure 9b, P3 indicates the entry to closed field lines. At the time of P4 the ions sampled by Cluster became more isotropic and heated, with significant fluxes above 10 keV. E • J was positive indicating energy flow to the particles (Figure 6h). This is also the point of entry

into a depression in |B|, which ends at crossing M4 (criterion 2 for FTR). In Figure 9b the region between P4 and crossing M4 is close to the center of the X and the radiating separatrices. After crossing M4 the ion distribution transitioned to that of the magnetosheath, emphasizing perpendicular pitch angles but with significant parallel fluxes. Fluxes of high energy ions fell below the sensor’s level of sensitivity after this time. [59] In the (L,M,N) system N is the direction of maximum variance of E (Figure 10i) which we assume to also be the minimum variance of B in a full crossing of the discontinuity. For relating the transformed quantities to those presented in earlier figures, the principal contributions to the L, M, and N axes come from GSM components Z, X, and Y, respectively. The largest component of B is BM (Figure 10e). It is greater than –90 nT and relatively constant except for a decrease in magnitude between line P4 and M4. BM never reversed polarity consistent with the trajectory in Figure 9b. Note that EM was essentially zero until after M4 (Figure 10h). The M and N axes form the “merging X” (Figure 9b). The separator, or out of plane component, then would be along the L axis. Should a guide field exist, it would be along the L axis. This is also the axis of the component of E which is tangential to the boundary and is related to the merging rate. From the geometry of Figure 9b, BN must reverse at the separator along

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Figure 10. (a and b) Expansion of the energy and pitch angle ion spectrograms from Figure 3 near the time of magnetopause crossing 4. The range of the color bars (in log c/s) has been changed from (2.4–7.2) to (2.1–6.7) in the energy spectrogram and from (0.3–5.4) to (0.5–4.2) in the pitch angle spectrogram to emphasize spectral details. Particle boundary P4 is added to mark the transition to isotropic fluxes. (c–f) Magnetic field magnitude and components in boundary-normal coordinates L, M, and N. (g–i) Electric field components in boundary-normal coordinates. the proposed trajectory. Figure 10f shows that BN changed from near –18 nT at line P4 to +10 nT at line M4, consistent with the curvature of the magnetic field lines near the separator. Note the large fluctuations in BN between P4 and M4 with a 20 to 30 s period, indicative of a time varying process. [60] Figures 11a–11d display (in black) the three components and magnitude of Vi in (L,M,N) coordinates from 10:55 to 11:15 UT. The convective velocities are overlaid in red. Values of d i are shown in Figure 11e. At M4 d i exceeds 2 indicating demagnetization of the ions (FTR criterion 1). Because BM is the dominant component of B, VCM must be small. Except for a brief excursion to near zero in the sunward exhaust region between lines P4 and M4 in Figure 11b, ViM is large and negative and is the parallel or flow-through velocity (FTR criterion 4). ViL (Figure 11a) closely matched

the convective velocity in the plane of the boundary, which is driven by EN (Figure 10i). [61] Associated with the changes near M4 are large increases in the parallel wave Poynting flux (S), initially anti-parallel on the inward side of the boundary, and then parallel (Figure 6g). They occurred at the termination of the depression in |B| prior to entry into the magnetosheath. BX approached zero near the end of this depression (Figure 2c). SX (not shown) was positive at this time (FTR criterion 3a), and di reached its maximum value. Field-aligned currents were also associated with the boundary (Figure 6). As discussed relative to the magnetosheath observations between crossings M2 and M3, they are expected to flow near the separatrices of active merging sites. [62] We have suggested that axis L is the separator in our coordinate system. The separator would be the axis of a guide

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Figure 11. (a–d) The three boundary-normal components and magnitude of the ion velocity (black). Also, the inferred components of the E B convective velocities (VC) in boundary normal coordinates are plotted in red. (e) Values of di are shown on the same time scale for comparison. field in component merging scenarios. Here BL is variable and significant over most of the time interval. In the early part of the depressed magnetic field region between P4 and M4 BL ranges from 15 to 30 nT. However, at M4 when d i exceeds 2 and gyrotropy is broken, BL becomes small or slightly negative (Figure 10d). It is the only location where we could identify non-gyrotropic ions and is consistent with a small or non-existent guide field and anti-parallel merging. The configuration is far from static. We suggest that both anti-parallel and small-guide-field component merging may exist in close proximity, compatible with FTR. Evidence of this can be seen in Figure 11b. Away from the immediate vicinity of line M4, EN and BL combine into a convective velocity in the M direction. VCM remains numerically smaller than ViM, leaving a parallel flow-through component. [63] ViM (Figure 11b) varied from near zero to –500 km/s in the tailward exhaust region with the total velocity reaching 600 km/s (Figure 11d). The orange arrows in Figure 9b indicate the velocities in the different regions. The plane of

the rotational discontinuity contains the L and M axes. In this plane VC did become positive between lines P4 and M4 and was more positive (sunward) than Vi (FTR criterion 3). That difference was the strongest near line M4 where Vi turned sharply negative and VC remained near zero (FTR criterion 3b). This large difference corresponds to where d i reached a value of 2. This measure of decoupling of the ions from the magnetic field meets FTR criterion 1. Note that Vi in the LM plane remained negative throughout all regions, consistent with both FTR criterion 4 and the penetration of the negative magnetosheath velocity into the closed and open magnetosphere boundary layer (see also Figure 7c). Velocities remained sub-Alfvénic except for the brief spike at line M4 which resulted in an Alfvénic Mach number of 1. [64] Observations at the time of line M4 suggests that reconnection was temporally varying and between open field lines from each polar mantle coming into close proximity in the sash. The products of reconnection are closed field lines being added to the LLBL at the sash and newly reconnected

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IMF field lines that are accelerated down-stream in the magnetosheath flow pattern. Data plotted in Figure 8 indicate demagnetization of local ions and our discussion narrows the causes for breaking gyrotropy to the inertial and electron pressure gradient terms in the generalized Ohm’s law. This is not a large-scale steady state event. The geometry of sliding along the merging X rather than a full crossing of an exhaust region excludes performance of a successful Walèn test, as was done by Eriksson et al. [2004] for their crossings. However, the M4 event has many properties similar to those found in the simulation results of Siscoe et al. [2002], and, with d i, we were able to show breaking of ion gyrotropy. Thus we regard the reported measurements as indicating that Cluster encountered a temporally and spatially variable FTR event.

5. Summary and Conclusions [65] Data presented above show that Cluster crossed the magnetopause in the vicinity of the sash at each of the dashed lines. The transition between the magnetosheath and a magnetospheric boundary layer provided access to higher temperature plasma sheet ions. Observed ion distributions and ISM simulations indicate that the boundary crossings were from the magnetosheath to the S-shaped plasma sheet, rather than to a lobe of the magnetotail. In the boundary layer Cluster detected weak magnetic fields characteristic of the sash. It did not observe positive BX values that characterize the northern lobe of the magnetotail. Pressure balance across the discontinuity is between the lower-density, highertemperature plasma sheet fluxes against the colder, higher density fluxes of the magnetosheath. Since the primary ion motion was essentially tangential to the boundary, the ion thermal pressures must contribute significantly to force balance. Calculated phase speeds indicate that correlated decreases in |V|, |B| and n observed while crossing into the sash cannot be interpreted as fast-wave structures. [66] In the magnetosheath region encountered between crossings M2 and M3 Cluster measured strong and variable field-aligned currents as well as strong evidence for the presence of Alfvén waves. Here too the perpendicular ion velocities (Vi?) differed significantly from the convective velocities (VC), indicating that the ions were not strongly tied to local magnetic field lines. We suggest that sources for the observed Alfvén waves and field-aligned currents were upstream reconnection sites associated with the sash. The corresponding outer separatrices should extend downstream within the magnetosheath near the magnetopause to the locations of Cluster. The excursion into the magnetosheath after crossing M4 did not manifest signatures of large fieldaligned currents or differences between VC and Vi?, consistent with Cluster being located beyond outer separatrices of any nearby reconnection sites. [67] Compared with the highly structured VC and fieldaligned currents observed between crossings M2 and M3, the ion velocity was relatively constant. With a variable IMF and a slowly varying V driven by the solar wind thermal momentum flux, E and J are primarily driven by changes in B and adjust to variations of B that are more local. Except for a few brief moments, ion gyrotropy was not broken. In the context of the generalized Ohm’s law and guiding center constraints, we suggest that inertial terms associated with

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time varying electric fields and field aligned currents are the most probable source of the VC, Vi? differences. [68] Our analysis indicates that crossing M4 provides an example of a Cluster encounter with nearby flow-through reconnection between open mantle field lines from each hemisphere, creating new closed field lines that are added to the LLBL at the sash. [Siscoe et al., 2002]. The breaking of ion gyrotropy, the decrease in flow velocity to near zero and subsequent increase to near 600 km/s down-tail implies that Cluster traversed reconnecting magnetic field lines very near the diffusion region. We have narrowed possible sources of the breaking of ion gyrotropy to the inertial terms or electron pressure gradients in the Ohm’s law. The process is both temporally varying and spatially limited. [69] Acknowledgments. We thank Elizabeth Lucek, the FGM team, and the ESA Cluster Active Archive for use of the Cluster magnetometer data, Mats Andre for use of the Cluster electric field data, Charles Smith and David McComas for use of the ACE magnetic field and particle data. We would like to acknowledge helpful conversations with B. U. Ő. Sonnerup and J. D. Scudder. The ISM was developed under sponsorship of the Defense Threat Reduction Agency, Dulles, Virginia. ISM computations were performed on computers at AFRL. NCM and FSM received NASA support under Cluster grant NNX09AE41G-1/14. C.J.F. acknowledges NASA grant NNX10AQ29G. W.J.B. received support in part from the Air Force Office of Scientific Research, through task 2311SDA5 under AF contract FA8718-10-C-0001 with Boston College. D.M.O. received support through AFOSR Task 11RV04COR. M.D. was partly supported by Chinese Academy of Sciences (CAS) visiting professorship for senior international scientists grant 2009S1-54. [70] Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper.

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