Characteristics of the Flank Magnetopause: THEMIS Observations
CCharacteristics of the Flank Magnetopause: THEMISObservations
S. Haaland , A. Runov , A. Artemyev , and V. Angelopoulos Birkeland Centre for Space Science, University of Bergen, Bergen, Norway, Max-Planck Institute for Solar SystemsResearch, ,Göttingen, Germany, Department of Space Physics, University of California, Los Angeles, CA, USA, SpaceResearch Institute, Russian Academy of Science, Moscow, Russia
Abstract
The terrestrial magnetopause is the boundary that shields the Earth's magnetosphere on oneside from the shocked solar wind and its embedded interplanetary magnetic field on the other side. In thispaper, we show observations from two of the Time History of Events and Macroscales Interactions duringSubstorms (THEMIS) satellites, comparing dayside magnetopause crossings with flank crossings near theterminator. Macroscopic properties such as current sheet thickness, motion, and current density areexamined for a large number of magnetopause crossings. The results show that the flank magnetopause istypically thicker than the dayside magnetopause and has a lower current density. Consistent with earlierresults from Cluster observations, we also find a persistent dawn-dusk asymmetry with a thicker and moredynamic magnetopause at dawn than at dusk.
1. Introduction
The terrestrial magnetospause is a current sheet separating the magnetosphere, dominated by the geo-magnetic field and hot plasma on one side and the shocked solar wind with its embedded interplanetarymagnetic field (IMF) on the other side. The magnetopause plays a key role for the transfer of electromag-netic energy, mass, and momentum from the solar wind into the magnetosphere. It is also host to a numberof plasma phenomena and processes, of which magnetic reconnection is perhaps the most intriguing (for arecent update, see, e.g., Burch et al., 2016). The terrestrial magnetopause has therefore been the subject ofextensive investigation (see, e.g., reviews in De Keyser et al., 2005; Hasegawa, 2012, and references therein).Conceptually, the magnetopause can be regarded as a Chapman-Ferraro current sheet (Chapman & Ferraro,1931; Ferraro, 1952), in which solar wind ions and electrons are deflected in opposite directions by the mag-netic gradient in the transition zone between the solar wind and the geomagnetic field. In this theory, thethickness of the current sheet is dictated by the local gyro radii of the ions forming the current and wouldideally be 1 gyroradius thick. In reality, this picture is too simple, since there is plasma and magnetic fieldon both sides of the boundary. Observations have shown that the real magnetopause thickness is typicallyseveral ion gyroradii (Berchem & Russell, 1982; Kaufmann & Konradi, 1973; Paschmann et al., 2018).Due to the focus on processes, in particular those responsible for transfer of momentum and energy acrossthe magnetopause and the associated impact on magnetospheric dynamics, most of the attention has beenon the dayside magnetopause near the Sun-Earth line. Although the flanks of the magnetopause have tradi-tionally received less attention, their configuration and dynamics are critical for understanding the transportof magnetosheath plasma to the magnetotail (Wing et al., 2014).In this paper, we use observations from two of the THEMIS (Time History of Events and Macroscales Interac-tions during Substorms—see Angelopoulos, 2008) satellites to follow up on results from the Cluster missionpresented in Haaland et al. (2014), Haaland et al. (2017), and De Keyser et al. (2017) where observationalsupport and possible explanations for a dawn-dusk asymmetry in magnetopause parameters were presented.In particular, we investigated whether this dawn-dusk asymmetry in magnetopause thickness and velocityis present also in the THEMIS observations. We also discuss the result in context of the more recent sur-vey based on Magnetospheric Multiscale Mission (MMS) magnetopause crossings presented in Paschmannet al. (2018).
RESEARCH ARTICLE
Key Points: • Observations from THEMIS are usedto characterize the magnetopause• The flank magnetopause is thickerthan the dayside magnetopause• A dawn-dusk asymmetries exists inmany magnetopause parameters
Correspondence to:
S. Haaland,[email protected]
Citation:
Haaland, S., Runov, A., Artemyev, A.,& Angelopoulos, V. (2019).Characteristics of the flankmagnetopause: THEMIS observations.
Journal of Geophysical Research: SpacePhysics , , 3421–3435. https://doi.org/10.1029/2019JA026459Received 1 JAN 2019Accepted 30 APR 2019Accepted article online 6 MAY 2019Published online 30 MAY 2019©2019. The Authors.This is an open access article under theterms of the Creative CommonsAttribution-NonCommercial-NoDerivsLicense, which permits use anddistribution in any medium, providedthe original work is properly cited, theuse is non-commercial and nomodifications or adaptations are made. HAALAND ET AL. 3421 ournal of Geophysical Research: Space Physics
Figure 1.
THEMIS orbits during October–December (top row) and April–June (bottom row) of the initial (2007–2009)phase of the mission. The dayside is covered during July–September. In this paper, we utilize measurements fromTHEMIS C (cyan color) and B (yellow color) to characterize the magnetopause, with emphasis on the flanks. Orbits ofTHEMIS A, D, and E are shown in dark blue color, but they rarely cross the magnetopause during this time intervaland are not used in this study.
This paper is organized as follows: In section 2, we present the data basis and provide a brief introductionto the key THEMIS instruments used in this study. Section 3 describes the methodology used to calculatesome of the macroscopic parameters of the magnetopause. Section 4 presents the statistical results based onthe analyzed data set. Finally, section 5 summarizes the results.
2. Observations
THEMIS was launched on 17 February 2007 to study the time evolution of magnetospheric substorms(Angelopoulos et al., 2008). The orbits of the five spacecraft were initially configured so that the inner probes(A, D, and E) covered the region around the flow braking region in the magnetotail just outside geosyn-chronous orbit and regularly lined up with probe C (apogee around 20 R E ) and probe B (apogee around 30R E ) on each side of the near-Earth X-line expected to be formed around 25 R E downtail during substorms. Asa consequence of this configuration and the precession around the Earth, probes B and C will cross the dawnmagnetopause flank around October to December, and the dusk flank around April to June as illustrated inFigure 1.The magnetopause characteristics presented here are based on magnetic field and plasma measurementsfrom THEMIS probes B and C during the period August 2007 to December 2009 and thus encompass threeseasons with dawn crossings and two seasons with dusk crossings. Our data set also contains a number ofdayside crossings for comparison. Starting in late 2009, the orbits of the spacecraft were lifted and eventuallybecame the ARTEMIS mission (Angelopoulos, 2011), and thus unsuitable for dayside magnetopause studies.We note that this orbit phasing is almost opposite to that of Cluster, which crossed the dawn flank aroundMay–July and dusk around October–December. Another contrast to the Cluster mission is the orbit;THEMIS has an ecliptic orbit, and the magnetopause crossings take place at low latitudes whereas Clusterhas a polar orbit. As pointed out by, for example, Panov et al. (2008), the high-latitude magnetopause canhave very different characteristics compared to the low-latitude magnetopause. We also note that the years2007 to 2009 correspond to solar minimum, whereas MMS phase 1 (years 2015 to 2017) results correspond toHAALAND ET AL. 3422 ournal of Geophysical Research: Space Physics high solar activity. THEMIS observations can therefore provide an important complement to the knowledgegained from earlier missions like ISEE and more recent missions like Cluster and MMS. To determine macroscopic parameters, and characterize the magnetopause, we use plasma data from theElectrostatic Analyzer (ESA—described in detail in McFadden et al., 2008a) and magnetic field measure-ments from the Fluxgate Magnetometer (FGM—see Auster et al., 2008). The instrumentation is identicalfor all THEMIS spacecraft.The ESA instrument is designed to measure ion and electron distribution functions over the energy rangefrom a few electron volts up to 25 keV for ions and 30 keV for electrons. Full 3-D distributions, from whichmoments are calculated onboard, utilize the spacecraft spin, and has a resolution of approximately 3 s. Inthis paper, we primarily use the onboard ion moments (designated MOM in the THEMIS data archives) butconsult ion and electron spectra for initial identification of potential magnetopause crossings.The FGM instrument can measure magnetic fields with up to 64 samples per second, but in this study, weuse data with 0.25-s resolution (FGL) to determine magnetopause duration and 3-s spin resolution data(FGS) joined to the ion moments to establish the proper coordinate system and to calculate magnetopausethickness and motion (see section 3.4).
The position of the dayside magnetopause is essentially dictated by the balance between the solar windpressure on one side and the magnetic pressure set up by the geomagnetic field on the other side. At theflanks, the magnetosheath thermal pressure also contributes significantly to the pressure balance. The solarwind velocity and density and thus the dynamic pressure exerted by the solar wind can be highly variable. Inaddition, local instabilities can excite surface waves that propagate along the flanks (e.g., Kivelson & Chen,1995). Consequently, the magnetopause at any location is in continuous motion.In this study we have used time shifted IMF and solar wind parameters (King & Papitashvili, 2005) and geo-magnetic disturbance indices downloaded from CDAWEB (Coordinated Data Analysis Web—see https://cdaweb.sci.gsfc.nasa.gov) to monitor these external influences on the magnetopause. Magnetic reconnec-tion is modulated by magnetic shear, that is, the difference between the upstream magnetosheath field andthe geomagnetic field. Near noon, the time-shifted IMF from OMNI is probably a good representation ofthe upstream magnetic field, but at the flanks, there can be significant field line draping (e.g., Sibeck et al.,1990).
3. Methodology
The procedure to identify and characterize the magnetopause crossings builds on our experience withCluster (Haaland et al., 2014) and MMS (Paschmann et al., 2018) and basically consists of the followingsteps:1. Identify potential magnetopause crossings by visual inspection of quick-look plots of key parameters.Thereafter, download magnetic field and plasma data for a time period around these potential magne-topause traversals.2. Establish the current sheet orientation and a local LMN coordinate system.3. Apply an automated identification of the magnetopause crossing time and duration.4. Determine magnetopause velocity from a Minimum Faraday Residue (MFR) analysis, and calculatecurrent sheet thickness and current density.5. Check quality of analysis and store key parameters in database if deemed to be a proper magnetopausecrossing.6. Statistically analyze the records in the database.These steps are described in some details in the following sections.
First, we consult the THEMIS mission quick-look WWW pages (at the time of writing, these are avail-able from http://themis.ssl.berkeley.edu/index.shtml). These pages provide low-resolution overview plotsof key parameters from the THEMIS mission. We found the plots showing 2-hr overviews of fields, on-boardmoments, and spectra to be most useful for our purpose. Figure 2 shows an example of a quick-look plotHAALAND ET AL. 3423 ournal of Geophysical Research: Space Physics
Figure 2.
Example of quick-look plots used for the initial identification of potential magnetopause crossings. In this2-hr overview of field and plasma data from THEMIS C on 25 November 2007, a number of magnetopausecrossings take place and are manifested as abrupt changes in field and plasma parameters. The panels show (a)magnetic field, (b) plasma density, (c) plasma temperature, (d) ion velocity, (e) electron velocity, (f) electron energyspectrum, and (g) ion energy spectrum. (but reproduced with higher graphics resolution and slightly modified for this paper) with a number ofmagnetopause crossings.In the figure, which shows a number of inbound and outbound crossings (i.e., transitions between themagnetosphere and the magnetosheath due to oscillatory motion of the magnetopause) between 02:15 and03:10 UT on 27 November 2007, the magnetic rotations are easily discernible in panel (a). In the plasmamoments, the transitions are characterized by sharp jumps in plasma density (panel b) and temperature(panel c) as the spaceraft traverses either from the hot, low density magnetospheric plasma regime to theHAALAND ET AL. 3424 ournal of Geophysical Research: Space Physics
Figure 3.
Positions of magnetopause crossing positions used in this study. Black dots show dayside crossings, wheredayside is defined as crossings within a magnetic local time (MLT) sector between 08 and 16. Dusk crossings(blue symbols) are defined as crossings in MLT sectors 16 to 20, and dawn crossings (red symbols) are defined aspositions with MLT 04 to 08. The average radial distance to the dayside crossings is around 11 R E , while the radialdistance to both set of flank crossings is around 16 R E . turbulent magnetosheath, characterized by higher densities and lower temperatures, or vice versa. The flowvelocity (ions shown in panel d, electrons in panel e) is typically very low inside the magnetosphere. In themagnetosheath, the flow is often very turbulent near the dayside magnetopause and more laminar withhigher flow velocities toward the flanks of the magnetopause.The transitions from the hot magnetospheric regime to the magnetosheath is also seen in the ion and elec-tron spectra (panels f and g, respectively). The spectra are often useful to distinguish between magnetopausecrossings and discontinuities in the magnetosheath or solar wind, which sometimes can have magneticrotations and jumps in the plasma moments, which can be mistaken for magnetopause crossings. The spec-tra are also useful to identify crossing times in cases with low magnetic shear, for example, cases withnorthward IMF.After having identified potential magnetopause crossings by visual inspection of quick-look plots, we down-load and plot calibrated magnetic field and plasma data for a 30-min interval around the potential crossingtimes for each event. In total, data for 2094 time intervals with potential magnetopause crossings in the years2007–2009 were downloaded. For each event, we also store the solar wind dynamic pressure, the IMF, andgeomagnetic indices. After a second visual inspection of plots of the 30-min interval high-resolution data,we discarded some of the events—either because they proved to be magnetosheath or solar wind disconti-nuities or due to data gaps in some of the measurements. This step reduced the total number of events to1,297 events, whereof 1,083 crossings from THEMIS C and 214 crossings from THEMIS B.Figure 3 shows the positions (projected onto the XY GSE plane) of the 1,297 crossings. “Dawn” is defined ascrossings taken at magnetic local times (MLT) earlier than 08, and “dusk” is defined as those with MLT after16. Since our observations have one extra dawn season (autumn of 2007), we have 554 dawn crossings, 398crossings at dusk, and 365 dayside crossings available for analysis.Due to its lower apogee and shorter orbital period, there are more magnetopause traversals by THEMIS Cthan from THEMIS B. The total number of identified THEMIS magnetopause traversals (and eventually thenumber crossings suitable for the statistical analysis) is significantly lower than the number of crossings inHAALAND ET AL. 3425 ournal of Geophysical Research: Space Physics the Cluster results reported by (Haaland et al., 2014; 6,370 crossing during a 10-year period) or the number ofMMS crossings in the database constructed by (Paschmann et al., 2018; 2,446 crossings from MMS1 during2015–2017). When interpreting these numbers, one should keep in mind the short period (2007–2009) andthat THEMIS' primary objective was to investigate magnetospheric substorms. In contrast, Cluster was ded-icated to study outer magnetospheric boundaries whereas the prime objective of MMS was to study daysidemagnetopause reconnection. The lower number of crossings from THEMIS is thus primarily due to thespacecraft orbit and total observation time—not magnetopause identification or detection issues.
From the downloaded magnetic field data, we first construct a LMN coordinate system (Russell & Elphic,1978) for each event. This coordinate system is constructed by performing a minimum variance analysis(MVAB—see, e.g., Sonnerup & Scheible, 1998) of spin resolution magnetic field measurements over a 5-mininterval around the identified crossing. The resulting eigenvectors form a rotation matrix with the threeorthogonal unit vectors L (orientation of maximum variance), M (orientation of intermediate variance), and N (orientation of minimum variance). We use this rotation matrix to rotate the high-resolution (four samplesper second) magnetic field, which is used to find the crossing time and crossing duration described in thenext section.The L axis will typically be well defined since the maximum variance direction is largely governed by themagnetic field inside the magnetosphere. The N axis is typically perpendicular to the magnetopause currentsheet. Since THEMIS has a near ecliptic orbit, the N axis will also typically point in the eclipticic plane, butwith opposite Y GSE components at dawn and dusk. We enforce a positive Z
GSE orientation of the L direction,and an outward pointing N direction. The M axis completes the right-hand system. Magnetopause crossing time and duration are determined from the L component of the high-resolutionmagnetic field. As in Paschmann et al. (2018), we smooth the magnetic field measurements using a 3-sboxcar average filter in order to eliminate the effect of small-scale structures inside the main current sheet.Crossing times and durations of the traversals are based on a one-dimensional (1-D) Harris sheet approach(Harris, 1962), in which the current sheet thickness is defined by a 76% change in magnetic field. We definethe crossing time as the midpoint (50% level) of the full B L transition, and the duration as the interval wherethe magnetic field changes from 12% to 88% of its asymptotic values. The procedure, which is similar tothe one we applied on Cluster observations (Haaland et al., 2004, 2014) and later on MMS observations(Paschmann et al., 2018), is illustrated in two examples below. Figure 4 shows approximately 2.5 min of measurements from THEMIS C during a dayside magnetopausecrossing on 8 September 2008, around 23:40 UT. The magnetic field rotation and changes in plasma density,flow velocity, and temperature are all used to classify and characterize the crossing.Panel (a) shows the high resolution L , M , and N components and the magnitude of the magnetic field. Thecrossing time, that is, the time where B L has reached its 50% level (herafter labeled t to be consistent withearlier papers), is indicated by a vertical dashed orange line through panels (a) to (d). Starting at this time,the automated routine then starts searching the boxcar filtered magnetic field forward and backward in timeuntil the times of the 12%, respectively, the 88% level of B L , are reached. These times, t and t , markedby red dashed lines, define the beginning and end of the current sheet. The time interval between them, t cs = | t − t | is the current sheet crossing duration (25 s in this case), which we later use to determine thethickness of the current sheet.In this example, the magnetic field rotation is fairly well defined, but neither smooth nor monotonousdespite our 3-s boxcar filtering. This is typical for almost all of the crossings observed—clean Harris sheetlike transitions are rare. The fluctuations in the current sheet indicate either internal spatial structures insidethe current sheet or back-and-forth motion of the magnetopause. With a single spacecraft, it is obviouslynot possible to distinguish between spatial and temporal variations. An accelerating magnetopause impliesa deviation from our simple 1-D, stationary model and thus introduce an uncertainty in our determinationof velocity and thickness.We note that the flow velocity (shown in panel c) is enhanced in this case, in particular in the Y and Z components, as the spacecraft crosses the current sheet. This is most likely a signature of reconnectionHAALAND ET AL. 3426 ournal of Geophysical Research: Space Physics Figure 4.
Illustration of current sheet crossing times, durations, and analysis intervals for a dayside magnetopausecrossing on 8 September 2008 around 23:40 UT. Panel (a), 0.25-s resolution magnetic field in LMN coordinates and thetotal magnetic field. The thick black curve shows a 3-s boxcar averaged version of the B L component, which we use todetermine duration, and the dashed black horizontal line shows where B L has reached 50% of its rotation. Panel(b), plasma density. Panel (c), plasma velocity. Panel (d), plasma temperatures. In panels (a) to (d), green vertical linesshow the start and stop of time interval (t MFRu to t
MFRd ) used for the HT and MFR analysis, described in section 3.4.The orange vertical line shows the crossing time t ; red vertical lines show the current sheet duration defined as 76% ofthe total B L transition. Panel (e), XY GSE projection of spacecraft position (red hexagon) with estimated positions of themagnetopause (MP) and the bow shock (BS) based on Fairfield (1971). Panel (f), as panel (e), but ZX
GSE projection. associated jetting and will be discussed further in section 4.2. We also note that neither the density (panel b)nor the temperature (panel d) immediately reach magnetospheric values after the crossing. This indicatesa boundary layer just inside the magnetosphere, possibly formed by the observed reconnection (e.g., Phanet al., 1997; Scholer & Treumann, 1997).
Figure 5 shows another example—this time 2.5 min of measurements from an outbound crossing of thedawn magnetopause tailward of the terminator (GSE position [ − − −
6] R E ) on 25 November 2007. Themagnetic field rotation (panel a), along with an increase in density (panel b) and a decrease in temperature(panel d) as the spacecraft leaves the hot and tenuous plasma regime of the magnetosphere and enters themore turbulent magnetosheath region, is readily apparent also in this event.As with the above dayside event, there are indications of a boundary layer just inside the magnesphere. Wenote an enhanced density in combined with a reduction in temperatures in the time interval 01:58:06 to01:58:31 UT. We are not able to directly relate this to any clear reconnection signatures in the form of plasmajetting though, but the bipolar B M signature may indicate the passage of a magnetic structure.The flow velocity in the magnetosheath (panel c, right part) exceeds 500 km/s and is primarily in the − X GSE direction as expected for this location. This value is very close to the velocity one would expect from recon-nection jets. The local Alfvén velocity, V A = B ∕ √ 𝜇 𝜌 , where B is the observed magnetic field and 𝜌 is themass density, is also around 500 km/s in this case. High flow velocities are more common at the flanks thanat the dayside. It is therefore often difficult to identify reconnection signatures in the form of distinct velocityenhancements. For comparison, the solar wind velocity around this time is just above 600 km/s.HAALAND ET AL. 3427 ournal of Geophysical Research: Space Physics Figure 5.
Similar to Figure 4, but for a THEMIS C dawn flank crossing on 25 November 2007.
Compared to Figure 4, this crossing has a shorter duration (t cs is ∼
16 s), but as we will show in the nextsection, the magnetopause normal velocity is much higher, so the magnetopause is significantly thicker thanin the above dayside example.
To determine the velocity, V MP of the magnetopause current sheet, we apply the MFR (see Khrabrov &Sonnerup, 1998a; Terasawa et al., 1996) method, which returns a frame of reference in which the residualtangential electric field is minimized. MFR also returns a set of eigenvectors that can be used to estimatethe orientation (boundary normal, ⃗ n ) of the magnetopause current sheet as well as a set of eigenvalues thatcan be used to assess the quality of the determination.As a check, we also perform a deHoffmann-Teller (HT—see, e.g., Khrabrov & Sonnerup, 1998b; Paschmann& Sonnerup, 2008) analysis, in which the minimization is performed on the electric field, to get the framevelocity. To get the normal velocity from HT analysis, the frame velocity is projected along a suitable bound-ary normal, in this case the boundary normal, ⃗ n , obtained from a constrained minimum variance of themagnetic field (MVAB0).For both methods, we neglect kinetic effects and assume that the magnetohydrodynamic approximation isvalid so that the electric field can be derived from the ion bulk velocity, that is, ⃗ E = − ⃗ V × ⃗ B . Provided thatour model of the magnetopause as a stationary magnetohydrodynamic structure is valid, the frame velocity(from either MFR or HT) represents the magnetopause velocity. As in Paschmann et al. (2018) the MFR,HT, and MVAB analyses all use a longer time interval, t MFR = | t MFRu − t MFRd | (where the subscripts u and d refer to upstream and downstream), in this case three times the duration of t cs . In Figures 4 and 5 thisinterval is indicated by vertical green lines. The consistency between the MFR and HT velocities, as well aseigenvalues of the analyses, is used to assess the quality of the velocity calculation.The magnetopause thickness, d , can be calculated from the normal component of velocity and duration: d = ( ⃗ V MP · ⃗ n ) ∗ t cs . With the thickness known, the magnitude of the current density can be estimated fromthe jump in magnetic field across the current layer: 𝜇 J = Δ B ∕ d ≃ Δ B L ∕ d . Using this simplified version ofAmpéres law, no detailed information about current direction is possible, though, and one only gets a singlevalue representing the average current density across the entire magnetopause current sheet.HAALAND ET AL. 3428 ournal of Geophysical Research: Space Physics Using the above method, we found a velocity of 17 km/s, a thickness of 430 km (6.5 ion inertial lengths),and a current density of approximately 100 nA/m for the dayside example in Figure 4. For the dawn eventshown in Figure 5, we found a normal velocity of 180 km/s, a thickness of 2,700 km (34 ion inertial lengths),and a current density of approximately 11 nA/m . Before proceeding to the statistical analysis and characterization, we perform a quality check of the cal-culations and results. As with any experimental data, there are uncertainties in the measurements, theunderlying model as well as statistical spread in the data that need to be considered and handled. We there-fore filter the data once more before calculating statistical moments. Table 1 provides details about thedefinition we have used and filtering we performed on the 1297 events.1. Measurement uncertainties in the FGM data are probably negligible for this study. Assessments anddetails are given in Auster et al. (2008). Likewise, we assess that uncertainties in the ESA measurements(discussed in some detail in section 3 of McFadden et al., 2008b) do not strongly influence our results.There will be cases where the energy range of the instrument or spacecraft charging combined with thepresence of heavy ions or cold ions skew the plasma moments. The plasma bulk velocity, which is mostcritical for our study, is less affected than the plasma density or temperature. Density and temperatureenter the calculations of the ion inertial length and as a pressure correction in the deHoffmann-Tellercalculations (seem e.g., Blagau et al., 2015), respectively.2. Determination of the LMN coordinate system relies on a simple, near 1-D stationary current sheet asthe underlying model and uses MVAB to establish the coordinate system. The L direction and thus theB L component used to determine the crossing duration are typically well defined. Error estimations forMVAB (see, e.g., equation 8.23 in Sonnerup & Scheible, 1998) are performed as part of our analysis chainand indeed confirm a well-defined L direction in the large majority of cases. However, one should havein mind that these are purely statistical uncertainty estimates.3. Our definition of thickness as a 76% change in the B L component is fairly objective, but a potential dis-advantage is that this definition does not always work well for cases with low magnetic shear. There willalso be cases (in particular on the dayside) where the magnetosheath magnetic field magnitude is largerthan the magnetospheric field.4. As noted in section 3.3, internal structures in the magnetopause current sheet or an accelerating mag-netopause also imply a deviation from our simple 1-D, stationary model. Nonconstant motion meansless accuracy in the velocity determination and thus a less accurate determination of the magnetopausethickness and velocity.5. The magnetopause crossing duration and thus the number of samples used for analysis vary from eventto event. As in Paschmann et al. (2018), we first determine the duration of the current sheet crossing fromthe magnetic field profile, t cs , then use a longer interval t MFR for the MFR and HT analyses. This ensuresplasma samples from both upstream and downstream of the current sheet, but obviously with a variablenumber of samples. This procedure is obviously open to discussion for a number of cases, but with a largecollection of events it is not feasible nor necessarily any better to individually optimize the results foreach event.6. Determination of magnetopause velocity using the MFR technique also assumes a stationary plasmastructure. Error estimates for MFR and HT analysis build on the same principle as the above MVABerror analysis. For a detailed assessment of the errors, we refer to the papers by Khrabrov and Sonnerup(1998c), Sonnerup and Scheible (1998), and Sonnerup et al. (2006). In the statistical analysis, we discardall events where MFR fails completely, for example, due to missing data or where the frame determinationis deemed to be unreliable, for example, eigenvalue ratio 𝜆 ∕ 𝜆 ≤ ). As in Haaland et al. (2014), eventswith calculated current sheet thickness less that 150 km, or more than 10,000 km, are also discarded toavoid outliers.7. Since our analysis chain requires both magnetic field and plasma data, we are only able to includea fraction of the ≈ ournal of Geophysical Research: Space Physics Table 1
Definitions of Dawn, Dusk, and Dayside Regions and Filter Criteria Used to Discard Records Where ReliableMagnetopause Parameters Could Not Be Determined
Quality/criteria Allowed range RemarksDawn crossings MLT ≤
08 See Figure 3.Dusk crossings MLT ≥ | Y GSE | ≤ R E .MFR ( 𝜆 ∕ 𝜆 ) ≥ CS ≥ MFR ≥
18 sec; Ensures minimum 5 plasma samples.Shear angle ≥ ◦ Identical to Paschmann et al. (2018).
Note.
The magnetic shear angle (angular difference between upstream and downstream magnetic field—taken at t
MFRu and t
MFRd , respectively) criteria is only used for the current density calculations to enable comparison with the resultsfrom Paschmann et al. (2018).
Important for all of the above potential sources of uncertainties is that the same criteria has been used forall observations, so there should be no bias in the selection. Nor should there be any significant dawn-duskasymmetries in instrument response. As we will see below, the statistical spread, which is a measure of thetrue variability in nature, is probably larger than any of the above uncertainties.
4. Results
After having performed the above analyses and quality checks for the 1,297 events, we end up with acollection of 576 magnetopause traversals, with key parameters, such as crossing times and duration, mag-netopause velocity, current sheet thickness, current density, and a set of measurements at the upstream anddownstream of the magnetopause for each event. To characterize the magnetopause and look at specificquestions, for example, dawn-dusk asymmetries, we analyze this collection statistically.
Table 2 summarizes the results of the statistical analysis of the collection of events. Here we show averagesof distributions of the various key magnetopause parameters for dusk ( >
16 MLT), dawn ( <
08 MLT), andthe dayside (08-16 MLT) locations. For comparison, we also list some key figures from the recent MMSbased study by Paschmann et al. (2018). To check for any significant influence and bias due to externalconditions, we calculated corresponding averages of geomagnetic activity indices, IMF values, and the solarwind dynamic pressure. Some of these averages are shown in rows 7–10.As in Haaland et al. (2014) and Paschmann et al. (2018), we use median as a measure of average whencharacterizing the distributions. As opposed to mode, the median is unique and robust. Mean values willtypically be somewhat higher due to tails in the various distributions, but the dawn-dusk asymmetries arealso existent if we use mean to characterize averages. The standard error, 𝜎 = s ∕ √ N , where s is the standarddeviation and N is the number of crossings, gives an indication of the spread in the data. The ion inertiallengths (a measure of the scale at which ions become demagnetized) given in the table are calculated as Λ i = d ∗ √ N i ∕ , where N i is the upstream (magnetosheath side) ion density.Despite differences in instrumentation and epoch (around solar minimum for THEMIS vs. around solarmaximum for MMS and over several years for Cluster), the overall results in Table 2 are largely consis-tent with earlier Cluster and MMS results. THEMIS observations indicate that the dayside magnetopause isthinner than at the flanks, and there is a dawn-dusk asymmetry in thickness and velocity.If we express the thickness in terms of ion intertial lenghts (row 3), we observe an even larger dawn-duskasymmetry with the dawn magnetopause flank being almost 80% thicker than the dusk flank. The mainreason for this is the much larger average upstream density at dawn (N dawn ≃
7) than at dusk (N dusk ≃ ournal of Geophysical Research: Space Physics Table 2
Key Magnetopause Parameters Based on THEMIS B and C Measurements (Columns B–D, Rows 2–7) and CorrespondingSolar Wind and Disturbance Parameters (Rows 6–9)
B C D EParameter Dawn Dusk Dayside MMS Dayside a b ±
99 1,149 ±
144 642 ±
72 7053 Thickness ( 𝛬 i ) 14.9 8.0 8.3 12.64 Velocity Vn MFR (km/s) 66.7 ± ± ± HT (km/s) 67.4 ± ± ± ) 16.7 ± ± ± c ± ± − ± d − ± ± ± − d ± ± ± d
10 Dst (nT) − ± − ± − ± − d Note . For comparison, dayside values in column E are based on numbers from Paschmann et al. (2018). Values givenare medians. Standard errors (see text) are given for THEMIS-based thicknesses, velocities, and current densities, andstandard deviations are given for IMF, Pdyn, and Dst. a | Y GSE | ≤ R E . b Depending on parameter investigated. c Peak current derived from high-resolution electron and ionmoments. Average currents were much lower. As in Paschmann et al. (2018), we used only included events with shearangle ≥ ◦ to calculate the current. d Not explicitly listed in Paschmann et al. (2018) but calculated from their database.
From the velocities (rows 4 and 5), we infer a more dynamic dawn flank magnetopause—also consistentwith the earlier Cluster results. For individual events, the velocities derived from HT and MFR analyses candiffer, but the overall consistency show that the dawn-dusk asymmetry in velocity is real. These results arerobust in the sense that adjustments in the filter criteria (Table 1) do not change the overall results.Current densities derived from THEMIS (row 6, columns B–D) are averages across the magnetopausecurrent sheet, based on difference in magnetic field upstream and downstream, and thus not directly com-parable to curlometer-derived results from Cluster or currents based on the high-resolution ion and electronmoments from MMS. For both these missions, it was possible to derive current density profiles and givepeak current density. In particular, note that Paschmann et al. (2018) only give peak currents based onhigh-resolution (150-ms cadence) plasma moments—their averages are much lower. In the present THEMISdata set, the average jump in magnetic field is smaller for the dusk flank than for dawn, thus giving almostidentical current density estimates despite a thinner dusk current sheet. The higher jump at dawn is primar-ily due to a higher upstream (magnetosheath) magnetic field at dawn, suggesting dawn-dusk differences inmagnetosheath properties rather than intrinsic properties of the magnetopause itself as an explanation.
The most pronounced observational manifestation of magnetic reconnection in space is plasmajetting—accelerated plasma flows from an active reconnection site. As discussed in section 3.3 and illus-trated in Figures 4 and 5, reconnection jetting is easier to identify at the dayside magnetopause than at theflanks. At the dayside, the upstream (magnetosheath) plasma flow is usually more stagnant (lower | V | inour overview plots), so that jetting (with velocities up to the local Alfvén speed) emerges as significant flowvelocity enhancements around the crossing time. Toward the flanks the magnetosheath flow has a highervelocity, and accelerated magnetosheath flows with velocities higher than the solar wind can also exist undernorthward IMF (Erkaev et al., 2011; Lavraud et al., 2007). Reconnection associated jetting at the flanks istherefore difficult to detect by visual inspection.A more quantitative approach to check for reconnection is to do a Walén test (Walén, 1944) or a Q-test(Sonnerup et al., 2018)—both describing the proportionality between the change in flow velocity and theAlfvén velocity across the magnetopause. A high correlation between these two quantities are expected inrotational discontinuities (RDs) associated with reconnection. Earlier studies, for example, Chou and Hau(2012), Paschmann et al. (2005), and Haaland et al. (2014), have classified events with a well-defined HTframe (HT correlation coefficient ≥ . ) and a Walén regression line slope ≥ ournal of Geophysical Research: Space Physics As part of the processing chain, we perform a Walén test of all crossings and record the regression slope andHT correlation coefficient in. Ideally, one would do the Walén only for the outer (i.e., the magnetosheathside of the magnetopause current sheet) part since this is where one would expect to see the RD. How-ever, this would have required individual treatment and optimization of each event. In addition, the limitedtime resolution of the plasma moments would have restricted such an approach for many of our eventssince there would have been too few values to correlate in a number of cases. We have therefore done theWalén test using plasma and field data the same time interval, t MFR , as that used for the MFR, HT, andMVAB analysis.In our data set, a well-defined HT frame could be established for 111 crossings at dusk and 276 crossings atdawn. Only 18, respectively, 14 of these crossings, had Walén regression slopes above 0.5. These fractions ofcases indicating an RD-like magnetopause are comparable to the results reported by Chou and Hau (2012)and only slightly higher than the Cluster results in Haaland et al. (2014). For comparison, the MMS daysidestudy by Paschmann et al. (2018) found Walén slopes above 0.5 in around 30% of the cases.It should be emphasized that we did not perform any optimizations such as tuning the analysis intervals,correct for pressure anisotropy (Blagau et al., 2015), or correct for any effects of composition or cold plasmainfluence (e.g., Wang et al., 2014). It is also possible that the underlying assumptions (i.e., stationarity, near1-D structure) for the Walén test are less frequently satisfied at the flanks due to surface waves and turbulentstructures inside the magnetopause current sheet. A more concise treatment of each individual event anda higher time resolution in the plasma data would probably have revealed more cases with reconnectionsignatures than the survey like method used in this study.
Our investigation of THEMIS magnetopause crossings, summarized in Table 2, reveals a dawn-dusk asym-metry in thickness and motion similar to that reported in Haaland et al. (2014). So why is there a dawn-duskasymmetry in these key parametres?
External influences, like the very different nature of the bow shock at dawn and dusk, result in differ-ences in the upstream magnetosheath properties at dawn and dusk (e.g., Dmitriev et al., 2003). In theChapmann-Ferraro (CF) picture, a difference in magnetic field and temperature at dawn and dusk willlead to different particle gyro radii at the two flanks, and thus different thicknesses. However, given thatthe simple CF picture of the magnetopause is an oversimplification (and probably even more so at theflanks), quantitative effects of magnetosheath asymmetries on corresponding asymmetries in magnetopausethickness are difficult to assess.Walsh et al. (2012) and Dimmock et al. (2016), both using THEMIS data partly overlapping with thetime interval used in our investigation, found significant dawn-dusk asymmetries with larger densitieson the dawnside than on the duskside. Similar results have also been reported earlier by, for example,Paularena et al. (2001), using observations from the Interplanetary Magnetospheric Explorer 8 (IMP 8) satel-lite and Nˇemeˇcek et al. (2002) using INTERBALL observations. Our observations are no exception—averageupstream plasma moments are different at dawn and dusk also in our data set and largely explains the largedifference in the thickness expressed in terms of ion inertial lengths.None of the above studies were able to identify a single parameter such as the Alfvén Mach number, plasmavelocity, or the IMF strength that could exclusively account for the asymmetry observed in magnetosheathproperties. The reason for a dawn-dusk asymmetry in density and temperature thus does not seem to havea simple explanation, and Nˇemeˇcek et al. (2002) concluded that the results “bring more questions thananswers.”
Recently, De Keyser et al. (2017), inspired by earlier theoretical works by Sestero (1964), used a 1-D kineticVlasov-Maxwell model to determine the structure of the magnetopause current layer as function of IMFdirection. They noted that the electric field profiles across the magnetopause, that is, the combination of theconvection electric (E
CONV = − ⃗ V magnetosheath × ⃗ B magnetosheath ), and the CF charge separation field (E CF ) werealways different at the two flanks.The difference in electric field profiles was present regardless of IMF direction, even for cases where theIMF was draped along the flow direction on both sides (and thus E CONV =0), but is perhaps best illustratedby considering a southward IMF case: Due to the absence of strong flows inside the magnetosphere, theHAALAND ET AL. 3432 ournal of Geophysical Research: Space Physics electric field there will be negligible or zero. On the magnetosheath side, however, there is usually a strongtailward flow, so E
CONV is nonzero and will have a component opposite to E CF at one flank, and along E CF at the other flank.Consequently, magnetosheath ions will be accelerated at dawn and penetrate deeper into the current sheetwhile electrons will be decelerated and penetrate less deep. Inside the current sheet, there will be a largerseparation between ions and electrons and thus a thicker magnetopause current sheet. At dusk, the situ-ation will be opposite; ions and electrons will pulled together and result in a thinner current sheet. Thedifference of such ion-electron decoupling at dawn and dusk flanks should result in different intensities ofHall (polarization) electric fields (Roth et al., 1996) that affect the magnetopause structure (e.g., Artemyevet al., 2017and references therein). Motion of the magnetopause is controlled by a combination of direct solar wind variations, (i.e., mainlychanges in the solar wind dynamic pressure) and surface waves like, for example, Kelvin-Helmholtz (KH)waves. At the flanks, the latter probably plays a larger role. One theory (see, e.g., Fadanelli et al., 2018; Kavosi& Raeder, 2015, and references therein) is that waves are exited by local instabilities at the dayside andpropagate toward the flanks. Local conditions such as density and velocity shear determine wave parameterssuch as wavelengths and wave growth rate.At present, there does not seem to be a clear consensus about whether surface waves are more frequent onthe dawn or dusk flank, however (e.g., Dimmock et al., 2017). Simulations (e.g., Nykyri, 2013) indicate thatthe dawn flank possesses more favorable conditions for KH wave growth. Observations (e.g., Taylor et al.,2012), however, seem to indicate the KH waves are more frequent at the dusk flank.
5. Summary
Based on visual inspection of field and plasma parameters from the THEMIS B and C probes, we identified1,297 potential magnetopause traversals during the period August 2007 until December 2009. Measurementsfrom these intervals were downloaded and analyzed.We used a Harris sheet approach and defined the magnetopause current sheet crossing duration as theinterval where the B L component of magnetic field rotated from 12% to 88% of its asymptotic values. Theframe velocity of the magnetopause was determined from MFR analysis and deHoffmann-Teller analysis offield and plasma data. Reliable crossing durations and magnetopause velocities could be determined for 538crossings, whereof 240 at dawn, 182 at the dayside, and 116 at dusk.Although the number of classified flank crossings is far lower than those of Haaland et al. (2014) weobserve a similar pattern; the dawn magnetopause is thicker and more dynamic than the dusk flank. Themedian thickness at dawn was found to be 14,00 km, corresponding to approximately 15 ion inertial lengths.The median velocity at dawn was found to be around 67 km/s. At dusk, the current sheet thickness wasfound to be 1,150 km, corresponding to eight ion inertial lengths. The median velocity at dusk is around50 km/s.We are not able to identify a single, unique mechanism or process responsible for the asymmetry inthickness, but note that a dawn-dusk asymmetry in plasma parameters exists already in the upstream mag-netosheath plasma. Nor are we able to identify any single mechanism able to explain the more dynamicnature of the dawn flank magnetopause.Using the Walén test as a measure, we found that only about 8% of the flank crossings had signatures ofreconnection (Walén slopes ≥ ournal of Geophysical Research: Space Physics References
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Research efforts by S. H. weresupported by the Norwegian ResearchCouncil under Grant 223252; Work ofA. R., A. A., and V. A. was supportedby NASA Grant NNX16AF84G andNASA contract NAS5-02099. A. A. alsoacknowledge Russian Foundation forBasic Research, Grant 8-02-00218. Wewould like to thank the followingpeople specifically: C. W. Carlson andJ. P. McFadden for the use of ESA dataand K. H. Glassmeier, U. Auster, andW. Baumjohann for the use of FGMdata provided under the lead of theTechnical University of Braunschweigand with financial support through theGerman Ministry for Economy andTechnology and the GermanAerospace Center (DLR) undercontract 50 OC 0302. Calculations inthis paper have made use of the QSASscience analysis system, provided byImperial College, London. THEMISdata used in this publication are freelyavailable from http://themis.ssl.berkeley.edu/data/themis/.
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