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Plasma sheet climatology: Geotail observations and LFM model comparisons
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Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 1351–1360 www.elsevier.com/locate/jastp
Plasma sheet climatology: Geotail observations and LFM model comparisons Timothy Guilda,, Harlan Spencea, Larry Kepkoa, Michael Wiltbergerb, Charles Goodricha, John Lyona,c, W. Jeffrey Hughesa a
Center for Space Physics, 725 Commonwealth Avenue, Boston University, Boston, MA 02215, USA b NCAR/HAO, 3450 Mitchell Lane, Boulder, CO 80301, USA c Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755, USA Available online 24 August 2004
Abstract We present a statistical comparison of plasma sheet properties from Geotail measurements and from the Lyon–Fedder–Mobarry (LFM) global magnetohydrodynamic (MHD) model. We compare more than three years of Geotail data with 10 consecutive days of simulation results driven by real solar wind data. Both studies have statistically similar solar wind inputs and a plasma sheet definition that follows from criteria that are widely used in the literature. We map the average plasma pressures, fields, and flows as functions of XY ðGSMÞ position within the equatorial plasma sheet. The comparisons show a persistent dawn–dusk asymmetry in the statistical patterns of plasma flows and electric fields in both the Geotail and the simulation results. Geotail observes a less rapid fall-off of thermal pressure with downtail distance than is seen in the simulation. The Geotail dataset suffers from an orbital bias, but we show the dawn–dusk asymmetry persists after accounting for the bias. Overall, our study finds similar statistical plasma pressures, magnetic pressures, and perpendicular flows in Geotail measurements, and the LFM MHD regions of the plasma sheet. r 2004 Elsevier Ltd. All rights reserved. Keywords: Plasma sheet; Plasma convection; Numerical modeling; Model validation
1. Introduction The Earth’s plasma sheet is a dynamic region of the magnetosphere that under certain conditions couples the stored energy in the magnetic lobes to the inner magnetosphere. This coupling is especially noticeable during geomagnetic substorms, when lobe magnetic energy is converted to kinetic and thermal energy in the plasma sheet. The energy released during substorms can Corresponding author. Tel.: +1-617-353-7406; fax: +1617-353-6463. E-mail address: [email protected] (T. Guild).
enhance the dynamics and energetics of the plasma in the near-Earth region, causing near-Earth space technological disruptions known as space weather. Despite the importance of the plasma sheet to energy coupling, our relatively limited understanding of the region is largely based on two types of analysis, each of which yields differing pictures of the plasma sheet. Previous studies of the plasma sheet have largely used two analysis methods: individual event analysis and long baseline time averages. The former method enables studies of localized plasma sheet dynamics (cf Baumjohann et al., 1990; Angelopoulos et al., 1992, 1994), while the latter provides a global, statistical picture of the
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plasma sheet (cf Baumjohann et al., 1989; Angelopoulos et al., 1993; Huang and Frank, 1994; Kaufmann et al., 2002). Wing and Newell (1998) inferred plasma sheet properties from high time resolution ionospheric observations, achieving global coverage with a shorter time baseline than the previously mentioned studies. Long baseline temporal and spatial averaging leaves only trends and obscures dynamics. Those trends, however, can illuminate underlying magnetospheric physics, which are often masked by the time-dependent dynamics. For example, studies have shown that slow, steady magnetospheric convection exists globally, but localized, bursty high-speed flows dominate net transport (Angelopoulos et al., 1992). Meteorological analogies between terrestrial and space ‘climate’ and ‘weather’ can provide an ideological structure within which to frame our study. This study examines the global ‘climatology’ of the Earth’s plasma sheet, because having only a handful of spacecraft available for the study limits us to a time-averaged depiction of it. Global magnetohydrodynamic (MHD) simulations can augment sparse data coverage. In principle, they can provide a theoretical framework to fill in the coverage gaps and present a global picture of an event. Prior to applying the simulations in this manner, they must be ‘‘validated’’ in a climatological sense. Similar statistical features in the observations and simulations provide a necessary but not sufficient condition for model validation. In this study, we collect a large statistical sample of plasma sheet measurements from Geotail and simulation points from the Lyon–Fedder–Mobarry (LFM) MHD model, bin all parameters in the equatorial plane, and compare the resultant maps. Thus, we attempt to validate the LFM model in a climatological sense and to identify potential model improvements.
2. Observations We use observations from the Low Energy Particle (LEP) (Mukai et al., 1994) and Magnetic Fields (MGF) (Kokubun et al., 1994) Experiments aboard the Geotail spacecraft. We analyzed data from January 1995 to April 1998 while Geotail was in a 10 by 30RE equatorial orbit and use these data to obtain statistical properties of the near-Earth plasma sheet. We linearly interpolate the 12-s ion plasma moments (LEP) and the 3-s magnetic field (MGF) data to a common 12-s resolution time base. The measured plasma properties determine the plasma sheet encounters, in a similar fashion to previous studies (cf Baumjohann et al., 1989; Huang and Frank, 1994). We define a plasma sheet sample as a measurement where the local plasma b40:5, ðb ¼ PTH =PMAG Þ and the ion temperature T i 41 keV. We further require that Geotail was located tailward of X GSM ¼ 10RE .
To limit potential orbital biasing of our dataset in the Z direction, we further restrict our plasma sheet data points to be within 3RE of the position of the neutral sheet, ZNS , as defined by the empirical model of Hammond et al. (1994). The Hammond et al. (1994) neutral sheet model is based on a functional fit to a large dataset of average magnetic field measurements, and is parameterized by the solar wind dynamic pressure. For each measured plasma sheet point, we calculate the Z distance between Geotail and the model neutral sheet. Fig. 1 shows the data set coverage, projected into the XY , XZ NS , and YZ NS planes (in Figs. 1a–c, respectively), where Z NS ¼ ZACTUAL ZNS;MODEL . The figure shows all measured points where the three plasma sheet criteria are satisfied. We include the jZ NS jo3RE cutoffs (shown as gray lines) in the XZ NS and YZ NS planes. We obtain the solar wind inputs to the magnetosphere during the measured plasma sheet passes from the Solar Wind Experiment (SWE) (Ogilvie et al., 1995) and Magnetic Fields Investigation (MFI) (Lepping et al., 1995) instruments on the WIND spacecraft. We linearly interpolate the WIND data to the Geotail time resolution, smooth with a 20-min boxcar average filter, and ballistically propagate the data to the position of the Earth. The X GSM position and velocity of each averaged time series point determines its propagation time. We resample the resultant solar wind time series, averaging any parameters that arrive in the same time bin. We then select only those propagated solar wind points corresponding in time with Geotail plasma sheet measurements for the solar wind dataset. Our Geotail dataset consists of 797,830 points.
3. Simulations The corresponding statistical MHD study uses simulation results from the LFM global MHD model (Lyon et al., 2004). The LFM model solves the 3D timedependent single fluid MHD equations in a modified spherical simulation domain roughly stretching from þ304X SM 4 300RE , and from approximately þ100 to 100RE in the Y SM and Z SM directions. The fixed computational grid places the highest resolution in regions of a priori interest to the solar wind/magnetosphere system. The magnetospheric MHD simulation takes solar wind input as the upstream boundary condition and couples to a simple 2D height-integrated ionospheric model below the two RE magnetospheric inner boundary condition. Lyon et al. (2004), Fedder et al. (1995) and Wiltberger (1998) contain detailed information about the computational method of the LFM model. We analyze 10 continuous days when the simulation was driven by the real solar wind inputs of 11 September 1999 through 21 September 1999 with a time cadence of
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Fig. 1. Spatial coverage of the Geotail plasma sheet dataset. We plot projections of all Geotail measurements where the plasma sheet criteria are satisfied in the XY ; XZNS , and YZNS projections. The ZNS coordinate is defined as ZNS ¼ ZACTUAL Z NS;MODEL . The jZ NS jo3RE limits (gray lines) are included in parts (b) and (c) which exclude measurements far from the model neutral sheet.
of the LFM study, where the translucent surface bounds the volume of the MHD-identified plasma sheet according to the three aforementioned criteria. We take only those points within 3RE of the Hammond et al. (1994) neutral sheet model position, collapse this volume to the XY plane, and the cumulative set of all MHDplasma sheet points at all time steps over the 10-day interval comprise the MHD plasma sheet study. Even though it includes only 10 days, our MHD study consists of 15,744,526 points, approximately 20 times more than are included in the Geotail study.
4. Analysis Fig. 2. View from dusk of the noon–midnight plane of a representative time step in the LFM simulation, showing the gray plasma sheet boundary in the MHD domain. The background color scale is in logðnÞ, where n denotes the plasma density, the top upstream vector shows the IMF direction, and the lower upstream vector shows the solar wind direction. The color scale ranges from 0.01 (blue) to 10 (red) particles per cubic centimeter, and three (white) GSM axes are shown with tick marks every 10RE .
1:5 min. We identify the plasma sheet in the simulation domain with the same criteria as with the Geotail dataset, yielding a volume of points at each time step in the simulation. Fig. 2 shows one representative time step
4.1. Methodology Gross plasma sheet dynamics are closely related to solar wind energy input into the magnetosphere (cf Bargatze et al., 1985). Accordingly, meaningful statistical comparisons between the Geotail observations and the LFM model results require that the solar wind input to both datasets be similar. Ideally, comparisons should be of exactly the same time and positions with identical solar wind drivers. Unfortunately, Geotail achieves sufficient statistical coverage only after many years of operations, and it is impractical to simulate these same 3:5 years for direct comparison. Because we are constrained by computing resources, we select a shorter interval of simulation results for comparison. By doing
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so, we assume that the range of conditions experienced by Geotail in 3 years is approximated by conditions in the 10-day interval. Fig. 3 shows histograms of the solar wind parameters measured by WIND during Geotail plasma sheet encounters (solid line), and the solar wind inputs to the simulation (dashed line). It shows input distributions of the geoeffective quantities logðPRAM Þ, logðnÞ, jV SW j; BY ; BZ , and also DST . With the exception of n and jV SW j, all parameters show similar histogram shapes for both the Geotail and LFM studies, and both peak histogram values for each parameter correlate to within 8% of that parameter’s distribution range. The MHD solar wind dataset is characterized by higher speeds and proportionally smaller density than the Geotail dataset, which includes a greater balance of high- versus low-speed streams. Figs. 3e and f reveal that the simulated magnetosphere encounters larger BZ southward IMF values more often, and those input drivers (large-BZ and large V X ) yield larger negative DST values more often. These BZ and DST distributions show that the simulated magnetosphere is more greatly driven when compared to the statistical Geotail magnetosphere. However, neither set exhibits evidence for strong persistent storm conditions. 4.2. General features of the Geotail results For the Geotail study, we generate maps of the plasma parameters and fields as 2D functions of position
within the equatorial plasma sheet. Figs. 4a–c show maps of the median thermal pressure, magnetic pressure, and perpendicular flow velocity (flow perpendicular to the instantaneous magnetic field) in each 3 3RE cell. A vector length of 5RE corresponds to 100 km/s flow. We find that the thermal and magnetic pressures fall off with radial distance from the Earth, and the median flow is consistently Earthward, but the cross-tail flow is asymmetrically divided in the dawn–dusk direction. Our dataset shows stronger flows on the duskside of the plasma sheet. The results shown in Fig. 4 qualitatively agree with similar studies previously published. Spence et al. (1989), Kistler et al. (1992), and Huang and Frank (1994) investigated statistical properties of the central plasma sheet as a function of downtail distance, and found a plasma pressure fall-off with distance similar to the Geotail thermal pressure curve of our Fig. 5. Angelopoulos et al. (1993) examined plasma sheet flow patterns in the equatorial plane, and found that preferentially duskward ion flows were consistent with particle drift velocities. Hori et al. (2000) extended the investigation of Angelopoulos et al. (1993) by deriving the plasma drifts from observations. Our average flow pattern has such a dawn–dusk asymmetry. Wing and Newell (1998) mapped ionospheric plasma observations out to the plasma sheet using an assumption of isotropy, and found equatorial distributions of pressure, density, and temperature that are qualitatively similar to those results of our dataset. Our Geotail thermal pressure
Fig. 3. Solar wind parameter distributions during the Geotail plasma sheet passes (solid lines) and in the simulation interval (dashed lines). We show histograms of the logðnÞ; logðPRAM Þ; jV j; BY ; BZ , and DST . The Y -axes of each plot are independently scaled, and the peak of the Geotail (LFM) histograms typically have 105 ð 103 Þ samples.
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Fig. 4. Comparison of the median value of Geotail (top row) and LFM (bottom row) plasma sheet samples of thermal pressure (first column), magnetic pressure (middle column), and perpendicular flows (last column). Note that the LFM thermal pressure (d) falls off much steeper than the data (a). In addition, the Geotail magnetic pressure shows a dawn–dusk asymmetry (b), and the LFM (f) median perpendicular flow magnitudes are much ð 5xÞ higher than those in the Geotail data (c).
distribution exhibits an overall peak close to the inner boundary, but a detailed analysis (not shown) indicates that a peak at the midnight meridian is evident at all distances down the tail. This result is consistent with previous studies by Angelopoulos (1996) and Wing and Newell (1998), and has been interpreted as a statistical manifestation of bursty bulk flows. Additionally, the variances of our Geotail measurements within each bin are larger than or equal to the median value in that bin, consistent with the velocity measurements and variances of Angelopoulos et al. (1993). Overall, the pressures and flows determined from our dataset are generally consistent with those from the aforementioned studies, even though they used different satellites, methods, and differing criteria to identify plasma sheet samples. 4.3. Geotail-LFM comparisons Assuming that the Geotail study is representative of the average state of the plasma sheet, we now repeat the same analysis using the LFM MHD model for comparison. The statistical maps derived from the LFM simulation are shown in Figs. 4d–f. The Geotail (top row) and LFM (bottom row) color scales are the same for each parameter, and each 5RE flow vector corresponds to 100 km/s flow. Comparisons of the
thermal and magnetic pressures from both studies (Figs. 4a, d are the thermal and b, e are the magnetic pressure comparisons) show that both peak at local midnight nearest the Earth, and at nearly the same pressures ( 0:3 nP thermal, 0:18 nP magnetic). The LFM model exhibits a much steeper radial thermal pressure gradient than the Geotail results. There is also a dawn–dusk asymmetric magnetic pressure distribution seen in the Geotail data that is not present in the simulation results. Fig. 5 explores the pressure distributions of Fig. 4 in more detail. We plot profiles of thermal and magnetic pressures for the observations and the model along the X GSM -axis. The median thermal pressure at a given distance downtail always exceeds the corresponding magnetic pressure, as would be expected in a high-b plasma sheet and according to our plasma sheet selection criterion. Both data and model thermal pressures agree in magnitude at the earthward edge of the grid, but the LFM thermal pressure falls off much more steeply with downtail distance. At X GSM ¼ 30RE , the model underestimates the observed thermal pressure by a factor of approximately four. In contrast, the magnetic pressure distributions of both studies remain similar throughout the range of downtail distances.
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that E SW differences may partially reconcile the relative flow amplitude differences. We normalize the model and data flow vectors and plot both on the same grid in Fig. 6 to better illustrate direction discrepancies. We plot the Geotail (LFM) flows in red (blue), on the same equatorial 3 3RE grid. The normalized vector fields have a peak velocity of 50 km/s (displayed as a vector with a length of 2:5RE ). Large (Dy 50 1) equatorial flow direction discrepancies occur in the pre-midnight sector of the near earth plasma sheet, and along the tailward edge of the plasma sheet region. A trend for larger values of Dy with increasing Y GSM is apparent. Generally, the MHD flows are strongly earthward directed, more so than observed flows. Some caution is warranted though. Flow speed and flow direction may well be correlated. Weak average flows indicate smaller average cross-tail electric fields, meaning that gradient-curvature drifts (generally
Fig. 5. Thermal and magnetic pressure profiles along the X GSM -axis extracted from the median equatorial plots of the Geotail and LFM plasma sheet studies (Fig. 4). The thermal pressures of the model and data are similar near the earth ðX GSM ¼ 12RE Þ, but diverge as they are compared further down the tail. By X GSM ¼ 30RE , the model underestimates the thermal pressure of the data by a factor of approximately four.
Fig. 4b suggests that the distribution of median magnetic pressure measured by Geotail is not dawn–dusk symmetric. The magnetic pressure falls more rapidly with distance in the pre-midnight sector than the post-midnight sector. This feature is not present in the LFM results. Note that the thermal pressure distribution (Fig. 4a) shows no such spatial asymmetry in the opposite sense, as would be required in a statistical, pressure-balanced configuration. We explore and explain this apparent discrepancy in Section 5. Figs. 4c and f display the median perpendicular flow velocity of the Geotail measurements and the LFM plasma sheet samples. A 5RE flow vector corresponds to 100 km/s flow in both figures. The magnitudes of flow vectors in each study differ significantly. The median flow speed in the equatorial plane is 11 km=s ð 54 km=sÞ for the Geotail (LFM) study. A larger energy input to the LFM magnetosphere could cause this difference, as alluded to in Section 4.1. According to Figs. 3e and c, the simulation encounters larger BZ southward and substantially faster solar wind more often. Consequently, the net solar wind electric field energizing the simulation systematically exceeds that during the Geotail intervals. We do not attempt to relate the magnetospheric energy input to the median flow magnitudes in the plasma sheet, other than to argue
Fig. 6. Comparison of the perpendicular flow directions only, where the magnitude of the vectors are normalized to the peak flow in each study. Geotail (LFM) median flow vectors are plotted in red (blue). Aside from the far flanks (where the MHD plasma sheet samples magnetosheath plasma directed antisunward), large (50 1) direction discrepancies occur in the premidnight sector and along the tailward-most edge of the plasma sheet considered ðX GSM ¼ 30RE Þ.
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east–west) are accentuated, at least on the duskside. Energy dependent gradient-curvature drift effects are not present in the LFM solution to the ideal MHD equations, and the directions of the flows in the model presumably correspond to flows around a magnetized obstacle.
5. Discussion Our study finds similar statistical plasma pressures, magnetic pressures, and perpendicular flows in Geotail measurements, and the LFM MHD regions of the plasma sheet. We can crudely estimate the reproducibility in these quantities by sorting the same plasma sheet datasets according to the IMF BY observed upstream. We assume that the upstream IMF BY polarity does not have a drastic effect on the plasma sheet pressure or flow morphology. The resultant equatorial maps of thermal pressure, magnetic pressure, and perpendicular flows for IMF BY 40 and BY o0 are qualitatively similar (not shown). Median flow directions, though not magnitudes, are also qualitatively similar if we divide our Geotail and LFM studies according to DST 4 15 nT and DST o 15 nT (not shown). This and other such sorting demonstrates that the average features of these maps are robust and not dominated by one or a few data points. General features of both studies also exhibit peculiar differences. One curiosity is the presence of a statistical dawn–dusk total pressure gradient. This interest prompts us to look closer at our method and datasets. Previous studies have interpreted statistical dawn-todusk plasma sheet flow asymmetries as the effects of plasma drifts (E B, corotation, and diamagnetic) in the near-Earth plasma sheet (Angelopoulos et al., 1993; Spence and Kivelson 1993; Wing and Newell, 1998; Hori et al., 2000; Wang et al., 2001). Our Geotail observations also reveal statistical dawn–dusk asymmetries in the perpendicular flows as well as in equatorial maps of magnetic pressure. However, before drawing physical conclusions based on these asymmetries, we more carefully explore the possibility of orbital bias in our Geotail data set. Fig. 1c shows the distribution of Geotail plasma sheet measurements in the YZ NS plane. To minimize orbital bias, we included only those points within 3RE of the Hammond et al. neutral sheet model (within the gray lines in Figs. 1b and c) in the statistical analysis presented thus far. Despite this attempt to remove bias, note the incomplete coverage on the dusk side of the YZ NS plot within 3RE . Narrowing the Z NS limits would exclude too much Geotail data from our study, and our statistical coverage would suffer. This dawn–dusk data coverage bias could cause some of the
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asymmetries found in the plasma parameters and flows in the previous section. 5.1. Tsyganenko comparison reveals sampling bias In order to determine if the spatial distribution of Geotail measurements leads to a corresponding asymmetry in measured parameters, we compute the magnetic field from the Tsyganenko (1996) magnetic field model (Tsyganenko and Stern, 1996) at each point Geotail measured the plasma sheet in our study. The upstream solar wind values of PRAM ; BY ; BZ , along with the DST index parameterize the Tsyganenko (1996) model field. We selected these solar wind inputs from WIND observations ballistically propagated to the Earth when each Geotail measurement was taken in the plasma sheet, and the DST value concurrently with each Geotail measurement. The Tsyganenko (1996) model does not include a partial ring current, and thus is dawn–dusk symmetric in the equatorial plane (Tsyganenko, 2002). Plotting the median Tsyganenko input parameters (PRAM ; BY ; BZ , and DST ) as functions of position within the plasma sheet reveal no dawn–dusk asymmetry in the model inputs (not shown). Therefore, a map of the field values of a completely symmetric model sampled equally across the plasma sheet should show no dawn–dusk asymmetry. Fig. 7 shows the sampling of the Tsyganenko (1996) model at the Geotail positions. It displays the median BX component of the magnetic field as measured by Geotail (a) and as computed from the Tsyganenko model (b). We use the BX component, as it is a sensitive tracer of distance from the neutral sheet. Both data and model exhibit similar patterns of median BX values, especially on the dusk side. There are more positive BX values on the duskside than on the dawnside of both the data and model maps. The similarity of these distributions suggests that a portion of the observed dawn–dusk asymmetry could be due to orbital biases. 5.2. Unfolding the sampling bias The perpendicular flow distribution also exhibits a strong dawn–dusk asymmetry in the equatorial plane, with the observed duskside flows being stronger. As Figs. 1c and 7 suggest, our Geotail dataset samples positions within the plasma sheet at different latitudes and magnetic topologies as a function of cross-tail location. Geotail most often measures the duskside plasma sheet at high latitudes, but measures the dawnside plasma sheet more probably near its center. Maps of field components indicate, on average, that the largest component is BX on the duskside (Fig. 7), but BZ dominates on the dawnside (not shown). Because convective flow amplitudes likely depend on distance from the plasma sheet center owing to the variation of
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Fig. 7. Comparison between the median BX magnetic field components as measured by Geotail (a) and as computed from the Tsyganenko 96 model (b). Consistently, more positive BX values are apparent on the dusk side of the plasma sheet in both plots. This suggests that a portion of the observed dawn–dusk asymmetry could be due to orbital biases.
jBj along a flux tube, an orbital bias in latitude introduces an apparent gradient in flow speed. However, if we assume that magnetic field lines are equipotentials, then equatorial maps of jEj ¼ jv Bj will normalize high- and low-latitude flow magnitudes sampled at different distances from the center of the plasma sheet. Other studies have shown the value of exploring the electric field in addition to the velocity field (e.g. Schoedel et al., 2001). Fig. 8 compares equatorial plots of the median jEj calculated from the measured VGEOTAIL and BGEOTAIL (Fig. 8a), and the jEj computed from the LFM model (Fig. 8b). Note the scale of jEj calculated from the LFM model exceeds that calculated from Geotail measurements by a factor of two. Contrary to expectations, this amplitude factor is significantly less than the previously shown median flow amplitude ratio (see Fig. 4) that was closer to five. If the electric field normalizes flows at various distances from the neutral sheet, we would expect large flows measured at high-latitude to map to even larger flows near the neutral sheet. The jEj comparison in Fig. 8 shows that both distributions are asymmetric, with higher median values in the pre-midnight region. This is consistent with Fig. 4c, but now is a map of flux-tube averaged flow vectors in the equatorial plane, with the Geotail orbital bias effectively removed. Note that both electric field maps retain their dawn–dusk asymmetry, with the duskside jEj fields larger, consistent with our earlier conclusion of measuring stronger flows on the duskside of the plasma sheet. The origin of the higher jEj field in the on the
duskside of the LFM has not yet been explored, though one possible source of asymmetry, energy dependent plasma drifts, are not included in the single fluid ideal MHD equations and can be ruled out. Another possible source arises from ionospheric Hall conductance asymmetries mapping into the magnetosphere, demonstrated by Wolf (1970), and included in the LFM model. In addition, the LFM model result has the largest field values along the X GSM axis, indicative of fast, reconnection-induced flows originating on average between 20 and 25RE in the tail. Inspection of time-series visualizations of the LFM simulation corroborates this interpretation. The Geotail map exhibits a similar, suggestive large-field feature at X GSM ¼ 20RE , but further analysis is necessary to determine the robustness of the result.
6. Conclusions We performed a statistical study of flows and plasma properties in the near-Earth plasma sheet as measured by the Geotail spacecraft, and in the near-Earth simulation domain of the LFM global MHD model. While gross climatological similarities exist between the two, some differences require further analysis and explanation. We find a dawn–dusk asymmetry in the magnitude of the Geotail and LFM plasma flows, and a consistent difference in their flow directions, with stronger flows on the duskside. The model predicts a steeper thermal pressure gradient in the equatorial plane
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Fig. 8. Comparison between the median electric field magnitudes calculated from the measured v and B (a), and calculated from the LFM model (b). Note the LFM color scale maximum exceeds the Geotail color scale maximum by a factor of two, significantly less than the factor of approximately five difference in velocity magnitudes of Fig. 4. Both plots are dawn–dusk asymmetric, with larger jEj values predominantly on the duskside. The highest LFM jEj fields are associated with reconnection-induced flows along the X GSM axis.
than is observed, and the Geotail observations indicate a dawn–dusk magnetic pressure asymmetry. Previous studies interpreted the dawn–dusk asymmetry of the flow as the cumulative effect of plasma drifts in the nearEarth plasma sheet (Angelopoulos et al., 1993; Spence and Kivelson, 1993; Wing and Newell, 1998; Hori et al., 2000; Wang et al., 2001). Our results show a dawn–dusk sampling bias of the plasma sheet points used in the study, but normalizing all flows to the equatorial plane by considering jEj ¼ jv Bj still yields a small but persistent dawn–dusk asymmetry. This asymmetry is seen in the LFM simulation results. We suggest that flow magnitude differences may partially result from differing degrees of driving; the LFM data set was produced by stronger solar wind electric fields than were present during the Geotail observations. We anticipate that future work with more similar statistical MHD plasma sheet sampling will resolve this question. Finally, coupling to the Rice Convection Model (RCM, Harel et al., 1981) in the inner magnetosphere should serve to improve data/model comparisons of the magnitude and direction of plasma flows, particularly in the near-Earth magnetotail.
Acknowledgements We would like to thank H. Petschek, M.-C. Fok, T. Hori and A. Clark for useful discussions and suggestions. We would also like to express our gratitude to T.
Mukai for the LEP data, S. Kokubun for the MGF data, and the ISAS sponsored DARTS system for maintaining and delivering the Geotail data used in this study. We would also like to thank K. Ogilvie and R. Lepping for the plasma and magnetic field data from the WIND satellite. This material is based upon work supported by the National Science Foundation under Grant No. DGE-0221680, and in part by CISM, which is funded by the STC Program of the National Science Foundation under Agreement Number ATM-0120950.
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International Conference on Substorms (ICS-3). ESA, Paris, pp. 17–22. Bargatze, L.F., Baker, D.N., McPherron, R.L., Hones, E.W., 1985. Magnetospheric impulse response for many levels of geomagnetic activity. Journal of Geophysical Research 90, 6387–6394. Baumjohann, W., Paschmann, G.G., Cattell, C.A., 1989. Average plasma properties in the central plasma sheet. Journal of Geophysical Research 94, 6597–6606. Baumjohann, W., Paschmann, G.G., Luhr, H., 1990. Characteristics of high-speed ion flows in the plasma sheet. Journal of Geophysical Research 95, 3801–3809. Fedder, J.A., Lyon, J.G., Slinker, S.P., Mobarry, C.M., 1995. Topological structure of the magnetotail as a function of interplanetary magnetic field direction. Journal of Geophysical Research 100, 3613–3621. Hammond, C., Kivelson, M., Walker, R., 1994. Imaging the effect of dipole tilt on magnetotail boundaries. Journal of Geophysical Research 99, 6079–6092. Harel, M., Wolf, R.A., Reiff, P.H., Spiro, R.W., Burke, W.J., Rich, F.J., Smiddy, M., 1981. Quantitative simulation of a magnetospheric substorm 1. Model logic and overview. Journal of Geophysical Research 86, 2242–2260. Hori, T., Maezawa, K., Saito, Y., Mukai, T., 2000. Average profile of ion flow and convection electric field in the nearEarth plasma sheet. Geophysical Research Letters 27, 1623–1626. Huang, C.Y., Frank, L.A., 1994. A statistical survey of the central plasma sheet. Journal of Geophysical Research 99, 83–95. Kaufmann, R.L., Lu, C., Paterson, W.R., Frank, L.A., 2002. Three-dimensional analyses of electric currents and pressure anisotropies in the plasma sheet. Journal of Geophysical Research 107 doi:10.1029/2001JA000288. Kistler, L.M., Mobius, E., Baumjohann, W., Paschmann, G., Hamilton, D.C., 1992. Pressure changes in the plasma sheet during substorm injections. Journal of Geophysical Research 97, 2973–2983. Kokubun, S., Yamamoto, T., Acuna, M.H., Hayashi, K., Shiokawa, K., Kawano, H., 1994. The Geotail magnetic field experiment. Journal of Geomagnetism and Geoelectricity 46, 7–21. Mukai, T., Machida, S., Saito, Y., Hirahara, M., Terasawa, T., Kaya, N., Obara, T., Ejiri, M., Nishida, A., 1994. The low energy particle (LEP) experiment onboard the Geotail satellite. Journal of Geomagnetism and Geoelectricity 46, 669–692.
Lepping, R.P., Acuna, M.H., Burlaga, L.F., Farrell, W.M., Slavin, J.A., Schatten, K.H., Mariani, F., Ness, N.F., Neubauer, F.M., Whang, Y.C., Byrnes, J.B., Kennon, R.S., Panetta, P.V., Scheifele, J., Worley, E.M., 1995. The WIND magnetic field investigation. Space Science Review 71, 207–229. Lyon, J.G., Fedder, J.A., Mobarry, C.M., 2004. The Lyon–Fedder–Mobarry (LFM) global MHD magnetospheric simulation code. Journal of Atmospheric Solar Terrestrial Physics, this issue. Ogilvie, K.W., Chornay, D.J., Fritzenreiter, R.J., Hunsaker, F., Keller, J., Lobell, J., Miller, G., Scudder, J.D., Sittler, E.C., Torbert, R.B., Bodet, D., Needell, G., Lazarus, A.J., Steinberg, J.T., Tappan, J.H., Mavretic, A., Gergin, E., 1995. SWE, a comprehensive plasma instrument for the Wind spacecraft. Space Science Review 71, 55–77. Schoedel, R., Baumjohann, W., Nakamura, R., Sergeev, V.A., Mukai, T., 2001. Rapid flux transport in the central plasma sheet. Journal of Geophysical Research 106, 301–314. Spence, H.E., Kivelson, M.G., 1993. Contributions of the lowlatitude boundary layer to the finite width magnetotail convection model. Journal of Geophysical Research 98, 15487–15496. Spence, H.E., Kivelson, M.G., Walker, R.J., McComas, D.J., 1989. Magnetosphereic plasma pressures in the midnight meridian: observations from 2.5 to 35RE . Journal of Geophysical Research 94, 5264–5272. Tsyganenko, N.A., 2002. A model of the near magnetosphere with a dawn–dusk asymmetry 1. Mathematical structure. Journal of Geophysical Research 107, 1179 doi:10.1029/ 2001JA000219. Tsyganenko, N.A., Stern, D.P., 1996. Modeling the global magnetic field of the large-scale Birkeland current systems. Journal of Geophysical Research 101, 27187–27198. Wang, C.-P., Lyons, L., Chen, M., Wolf, R., 2001. Modeling the quiet time inner plasma sheet protons. Journal of Geophysical Research 106, 6161–6178. Wiltberger, M., 1998. Global magnetohydrodynamic simulations of magnetospheric substorms. Ph.D. Thesis, University of Maryland, College Park, MD. Wing, S., Newell, P.T., 1998. Central plasma sheet ion properties as inferred from ionospheric observations. Journal of Geophysical Research 103, 6785–6800. Wolf, R.A., 1970. Effects of ionospheric conductivity on convective flow of plasma in the magnetosphere. Journal of Geophysical Research 75, 4677–4698.
Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 1351–1360 www.elsevier.com/locate/jastp
Plasma sheet climatology: Geotail observations and LFM model comparisons Timothy Guilda,, Harlan Spencea, Larry Kepkoa, Michael Wiltbergerb, Charles Goodricha, John Lyona,c, W. Jeffrey Hughesa a
Center for Space Physics, 725 Commonwealth Avenue, Boston University, Boston, MA 02215, USA b NCAR/HAO, 3450 Mitchell Lane, Boulder, CO 80301, USA c Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755, USA Available online 24 August 2004
Abstract We present a statistical comparison of plasma sheet properties from Geotail measurements and from the Lyon–Fedder–Mobarry (LFM) global magnetohydrodynamic (MHD) model. We compare more than three years of Geotail data with 10 consecutive days of simulation results driven by real solar wind data. Both studies have statistically similar solar wind inputs and a plasma sheet definition that follows from criteria that are widely used in the literature. We map the average plasma pressures, fields, and flows as functions of XY ðGSMÞ position within the equatorial plasma sheet. The comparisons show a persistent dawn–dusk asymmetry in the statistical patterns of plasma flows and electric fields in both the Geotail and the simulation results. Geotail observes a less rapid fall-off of thermal pressure with downtail distance than is seen in the simulation. The Geotail dataset suffers from an orbital bias, but we show the dawn–dusk asymmetry persists after accounting for the bias. Overall, our study finds similar statistical plasma pressures, magnetic pressures, and perpendicular flows in Geotail measurements, and the LFM MHD regions of the plasma sheet. r 2004 Elsevier Ltd. All rights reserved. Keywords: Plasma sheet; Plasma convection; Numerical modeling; Model validation
1. Introduction The Earth’s plasma sheet is a dynamic region of the magnetosphere that under certain conditions couples the stored energy in the magnetic lobes to the inner magnetosphere. This coupling is especially noticeable during geomagnetic substorms, when lobe magnetic energy is converted to kinetic and thermal energy in the plasma sheet. The energy released during substorms can Corresponding author. Tel.: +1-617-353-7406; fax: +1617-353-6463. E-mail address: [email protected] (T. Guild).
enhance the dynamics and energetics of the plasma in the near-Earth region, causing near-Earth space technological disruptions known as space weather. Despite the importance of the plasma sheet to energy coupling, our relatively limited understanding of the region is largely based on two types of analysis, each of which yields differing pictures of the plasma sheet. Previous studies of the plasma sheet have largely used two analysis methods: individual event analysis and long baseline time averages. The former method enables studies of localized plasma sheet dynamics (cf Baumjohann et al., 1990; Angelopoulos et al., 1992, 1994), while the latter provides a global, statistical picture of the
1364-6826/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2004.03.021
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plasma sheet (cf Baumjohann et al., 1989; Angelopoulos et al., 1993; Huang and Frank, 1994; Kaufmann et al., 2002). Wing and Newell (1998) inferred plasma sheet properties from high time resolution ionospheric observations, achieving global coverage with a shorter time baseline than the previously mentioned studies. Long baseline temporal and spatial averaging leaves only trends and obscures dynamics. Those trends, however, can illuminate underlying magnetospheric physics, which are often masked by the time-dependent dynamics. For example, studies have shown that slow, steady magnetospheric convection exists globally, but localized, bursty high-speed flows dominate net transport (Angelopoulos et al., 1992). Meteorological analogies between terrestrial and space ‘climate’ and ‘weather’ can provide an ideological structure within which to frame our study. This study examines the global ‘climatology’ of the Earth’s plasma sheet, because having only a handful of spacecraft available for the study limits us to a time-averaged depiction of it. Global magnetohydrodynamic (MHD) simulations can augment sparse data coverage. In principle, they can provide a theoretical framework to fill in the coverage gaps and present a global picture of an event. Prior to applying the simulations in this manner, they must be ‘‘validated’’ in a climatological sense. Similar statistical features in the observations and simulations provide a necessary but not sufficient condition for model validation. In this study, we collect a large statistical sample of plasma sheet measurements from Geotail and simulation points from the Lyon–Fedder–Mobarry (LFM) MHD model, bin all parameters in the equatorial plane, and compare the resultant maps. Thus, we attempt to validate the LFM model in a climatological sense and to identify potential model improvements.
2. Observations We use observations from the Low Energy Particle (LEP) (Mukai et al., 1994) and Magnetic Fields (MGF) (Kokubun et al., 1994) Experiments aboard the Geotail spacecraft. We analyzed data from January 1995 to April 1998 while Geotail was in a 10 by 30RE equatorial orbit and use these data to obtain statistical properties of the near-Earth plasma sheet. We linearly interpolate the 12-s ion plasma moments (LEP) and the 3-s magnetic field (MGF) data to a common 12-s resolution time base. The measured plasma properties determine the plasma sheet encounters, in a similar fashion to previous studies (cf Baumjohann et al., 1989; Huang and Frank, 1994). We define a plasma sheet sample as a measurement where the local plasma b40:5, ðb ¼ PTH =PMAG Þ and the ion temperature T i 41 keV. We further require that Geotail was located tailward of X GSM ¼ 10RE .
To limit potential orbital biasing of our dataset in the Z direction, we further restrict our plasma sheet data points to be within 3RE of the position of the neutral sheet, ZNS , as defined by the empirical model of Hammond et al. (1994). The Hammond et al. (1994) neutral sheet model is based on a functional fit to a large dataset of average magnetic field measurements, and is parameterized by the solar wind dynamic pressure. For each measured plasma sheet point, we calculate the Z distance between Geotail and the model neutral sheet. Fig. 1 shows the data set coverage, projected into the XY , XZ NS , and YZ NS planes (in Figs. 1a–c, respectively), where Z NS ¼ ZACTUAL ZNS;MODEL . The figure shows all measured points where the three plasma sheet criteria are satisfied. We include the jZ NS jo3RE cutoffs (shown as gray lines) in the XZ NS and YZ NS planes. We obtain the solar wind inputs to the magnetosphere during the measured plasma sheet passes from the Solar Wind Experiment (SWE) (Ogilvie et al., 1995) and Magnetic Fields Investigation (MFI) (Lepping et al., 1995) instruments on the WIND spacecraft. We linearly interpolate the WIND data to the Geotail time resolution, smooth with a 20-min boxcar average filter, and ballistically propagate the data to the position of the Earth. The X GSM position and velocity of each averaged time series point determines its propagation time. We resample the resultant solar wind time series, averaging any parameters that arrive in the same time bin. We then select only those propagated solar wind points corresponding in time with Geotail plasma sheet measurements for the solar wind dataset. Our Geotail dataset consists of 797,830 points.
3. Simulations The corresponding statistical MHD study uses simulation results from the LFM global MHD model (Lyon et al., 2004). The LFM model solves the 3D timedependent single fluid MHD equations in a modified spherical simulation domain roughly stretching from þ304X SM 4 300RE , and from approximately þ100 to 100RE in the Y SM and Z SM directions. The fixed computational grid places the highest resolution in regions of a priori interest to the solar wind/magnetosphere system. The magnetospheric MHD simulation takes solar wind input as the upstream boundary condition and couples to a simple 2D height-integrated ionospheric model below the two RE magnetospheric inner boundary condition. Lyon et al. (2004), Fedder et al. (1995) and Wiltberger (1998) contain detailed information about the computational method of the LFM model. We analyze 10 continuous days when the simulation was driven by the real solar wind inputs of 11 September 1999 through 21 September 1999 with a time cadence of
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Fig. 1. Spatial coverage of the Geotail plasma sheet dataset. We plot projections of all Geotail measurements where the plasma sheet criteria are satisfied in the XY ; XZNS , and YZNS projections. The ZNS coordinate is defined as ZNS ¼ ZACTUAL Z NS;MODEL . The jZ NS jo3RE limits (gray lines) are included in parts (b) and (c) which exclude measurements far from the model neutral sheet.
of the LFM study, where the translucent surface bounds the volume of the MHD-identified plasma sheet according to the three aforementioned criteria. We take only those points within 3RE of the Hammond et al. (1994) neutral sheet model position, collapse this volume to the XY plane, and the cumulative set of all MHDplasma sheet points at all time steps over the 10-day interval comprise the MHD plasma sheet study. Even though it includes only 10 days, our MHD study consists of 15,744,526 points, approximately 20 times more than are included in the Geotail study.
4. Analysis Fig. 2. View from dusk of the noon–midnight plane of a representative time step in the LFM simulation, showing the gray plasma sheet boundary in the MHD domain. The background color scale is in logðnÞ, where n denotes the plasma density, the top upstream vector shows the IMF direction, and the lower upstream vector shows the solar wind direction. The color scale ranges from 0.01 (blue) to 10 (red) particles per cubic centimeter, and three (white) GSM axes are shown with tick marks every 10RE .
1:5 min. We identify the plasma sheet in the simulation domain with the same criteria as with the Geotail dataset, yielding a volume of points at each time step in the simulation. Fig. 2 shows one representative time step
4.1. Methodology Gross plasma sheet dynamics are closely related to solar wind energy input into the magnetosphere (cf Bargatze et al., 1985). Accordingly, meaningful statistical comparisons between the Geotail observations and the LFM model results require that the solar wind input to both datasets be similar. Ideally, comparisons should be of exactly the same time and positions with identical solar wind drivers. Unfortunately, Geotail achieves sufficient statistical coverage only after many years of operations, and it is impractical to simulate these same 3:5 years for direct comparison. Because we are constrained by computing resources, we select a shorter interval of simulation results for comparison. By doing
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so, we assume that the range of conditions experienced by Geotail in 3 years is approximated by conditions in the 10-day interval. Fig. 3 shows histograms of the solar wind parameters measured by WIND during Geotail plasma sheet encounters (solid line), and the solar wind inputs to the simulation (dashed line). It shows input distributions of the geoeffective quantities logðPRAM Þ, logðnÞ, jV SW j; BY ; BZ , and also DST . With the exception of n and jV SW j, all parameters show similar histogram shapes for both the Geotail and LFM studies, and both peak histogram values for each parameter correlate to within 8% of that parameter’s distribution range. The MHD solar wind dataset is characterized by higher speeds and proportionally smaller density than the Geotail dataset, which includes a greater balance of high- versus low-speed streams. Figs. 3e and f reveal that the simulated magnetosphere encounters larger BZ southward IMF values more often, and those input drivers (large-BZ and large V X ) yield larger negative DST values more often. These BZ and DST distributions show that the simulated magnetosphere is more greatly driven when compared to the statistical Geotail magnetosphere. However, neither set exhibits evidence for strong persistent storm conditions. 4.2. General features of the Geotail results For the Geotail study, we generate maps of the plasma parameters and fields as 2D functions of position
within the equatorial plasma sheet. Figs. 4a–c show maps of the median thermal pressure, magnetic pressure, and perpendicular flow velocity (flow perpendicular to the instantaneous magnetic field) in each 3 3RE cell. A vector length of 5RE corresponds to 100 km/s flow. We find that the thermal and magnetic pressures fall off with radial distance from the Earth, and the median flow is consistently Earthward, but the cross-tail flow is asymmetrically divided in the dawn–dusk direction. Our dataset shows stronger flows on the duskside of the plasma sheet. The results shown in Fig. 4 qualitatively agree with similar studies previously published. Spence et al. (1989), Kistler et al. (1992), and Huang and Frank (1994) investigated statistical properties of the central plasma sheet as a function of downtail distance, and found a plasma pressure fall-off with distance similar to the Geotail thermal pressure curve of our Fig. 5. Angelopoulos et al. (1993) examined plasma sheet flow patterns in the equatorial plane, and found that preferentially duskward ion flows were consistent with particle drift velocities. Hori et al. (2000) extended the investigation of Angelopoulos et al. (1993) by deriving the plasma drifts from observations. Our average flow pattern has such a dawn–dusk asymmetry. Wing and Newell (1998) mapped ionospheric plasma observations out to the plasma sheet using an assumption of isotropy, and found equatorial distributions of pressure, density, and temperature that are qualitatively similar to those results of our dataset. Our Geotail thermal pressure
Fig. 3. Solar wind parameter distributions during the Geotail plasma sheet passes (solid lines) and in the simulation interval (dashed lines). We show histograms of the logðnÞ; logðPRAM Þ; jV j; BY ; BZ , and DST . The Y -axes of each plot are independently scaled, and the peak of the Geotail (LFM) histograms typically have 105 ð 103 Þ samples.
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Fig. 4. Comparison of the median value of Geotail (top row) and LFM (bottom row) plasma sheet samples of thermal pressure (first column), magnetic pressure (middle column), and perpendicular flows (last column). Note that the LFM thermal pressure (d) falls off much steeper than the data (a). In addition, the Geotail magnetic pressure shows a dawn–dusk asymmetry (b), and the LFM (f) median perpendicular flow magnitudes are much ð 5xÞ higher than those in the Geotail data (c).
distribution exhibits an overall peak close to the inner boundary, but a detailed analysis (not shown) indicates that a peak at the midnight meridian is evident at all distances down the tail. This result is consistent with previous studies by Angelopoulos (1996) and Wing and Newell (1998), and has been interpreted as a statistical manifestation of bursty bulk flows. Additionally, the variances of our Geotail measurements within each bin are larger than or equal to the median value in that bin, consistent with the velocity measurements and variances of Angelopoulos et al. (1993). Overall, the pressures and flows determined from our dataset are generally consistent with those from the aforementioned studies, even though they used different satellites, methods, and differing criteria to identify plasma sheet samples. 4.3. Geotail-LFM comparisons Assuming that the Geotail study is representative of the average state of the plasma sheet, we now repeat the same analysis using the LFM MHD model for comparison. The statistical maps derived from the LFM simulation are shown in Figs. 4d–f. The Geotail (top row) and LFM (bottom row) color scales are the same for each parameter, and each 5RE flow vector corresponds to 100 km/s flow. Comparisons of the
thermal and magnetic pressures from both studies (Figs. 4a, d are the thermal and b, e are the magnetic pressure comparisons) show that both peak at local midnight nearest the Earth, and at nearly the same pressures ( 0:3 nP thermal, 0:18 nP magnetic). The LFM model exhibits a much steeper radial thermal pressure gradient than the Geotail results. There is also a dawn–dusk asymmetric magnetic pressure distribution seen in the Geotail data that is not present in the simulation results. Fig. 5 explores the pressure distributions of Fig. 4 in more detail. We plot profiles of thermal and magnetic pressures for the observations and the model along the X GSM -axis. The median thermal pressure at a given distance downtail always exceeds the corresponding magnetic pressure, as would be expected in a high-b plasma sheet and according to our plasma sheet selection criterion. Both data and model thermal pressures agree in magnitude at the earthward edge of the grid, but the LFM thermal pressure falls off much more steeply with downtail distance. At X GSM ¼ 30RE , the model underestimates the observed thermal pressure by a factor of approximately four. In contrast, the magnetic pressure distributions of both studies remain similar throughout the range of downtail distances.
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that E SW differences may partially reconcile the relative flow amplitude differences. We normalize the model and data flow vectors and plot both on the same grid in Fig. 6 to better illustrate direction discrepancies. We plot the Geotail (LFM) flows in red (blue), on the same equatorial 3 3RE grid. The normalized vector fields have a peak velocity of 50 km/s (displayed as a vector with a length of 2:5RE ). Large (Dy 50 1) equatorial flow direction discrepancies occur in the pre-midnight sector of the near earth plasma sheet, and along the tailward edge of the plasma sheet region. A trend for larger values of Dy with increasing Y GSM is apparent. Generally, the MHD flows are strongly earthward directed, more so than observed flows. Some caution is warranted though. Flow speed and flow direction may well be correlated. Weak average flows indicate smaller average cross-tail electric fields, meaning that gradient-curvature drifts (generally
Fig. 5. Thermal and magnetic pressure profiles along the X GSM -axis extracted from the median equatorial plots of the Geotail and LFM plasma sheet studies (Fig. 4). The thermal pressures of the model and data are similar near the earth ðX GSM ¼ 12RE Þ, but diverge as they are compared further down the tail. By X GSM ¼ 30RE , the model underestimates the thermal pressure of the data by a factor of approximately four.
Fig. 4b suggests that the distribution of median magnetic pressure measured by Geotail is not dawn–dusk symmetric. The magnetic pressure falls more rapidly with distance in the pre-midnight sector than the post-midnight sector. This feature is not present in the LFM results. Note that the thermal pressure distribution (Fig. 4a) shows no such spatial asymmetry in the opposite sense, as would be required in a statistical, pressure-balanced configuration. We explore and explain this apparent discrepancy in Section 5. Figs. 4c and f display the median perpendicular flow velocity of the Geotail measurements and the LFM plasma sheet samples. A 5RE flow vector corresponds to 100 km/s flow in both figures. The magnitudes of flow vectors in each study differ significantly. The median flow speed in the equatorial plane is 11 km=s ð 54 km=sÞ for the Geotail (LFM) study. A larger energy input to the LFM magnetosphere could cause this difference, as alluded to in Section 4.1. According to Figs. 3e and c, the simulation encounters larger BZ southward and substantially faster solar wind more often. Consequently, the net solar wind electric field energizing the simulation systematically exceeds that during the Geotail intervals. We do not attempt to relate the magnetospheric energy input to the median flow magnitudes in the plasma sheet, other than to argue
Fig. 6. Comparison of the perpendicular flow directions only, where the magnitude of the vectors are normalized to the peak flow in each study. Geotail (LFM) median flow vectors are plotted in red (blue). Aside from the far flanks (where the MHD plasma sheet samples magnetosheath plasma directed antisunward), large (50 1) direction discrepancies occur in the premidnight sector and along the tailward-most edge of the plasma sheet considered ðX GSM ¼ 30RE Þ.
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east–west) are accentuated, at least on the duskside. Energy dependent gradient-curvature drift effects are not present in the LFM solution to the ideal MHD equations, and the directions of the flows in the model presumably correspond to flows around a magnetized obstacle.
5. Discussion Our study finds similar statistical plasma pressures, magnetic pressures, and perpendicular flows in Geotail measurements, and the LFM MHD regions of the plasma sheet. We can crudely estimate the reproducibility in these quantities by sorting the same plasma sheet datasets according to the IMF BY observed upstream. We assume that the upstream IMF BY polarity does not have a drastic effect on the plasma sheet pressure or flow morphology. The resultant equatorial maps of thermal pressure, magnetic pressure, and perpendicular flows for IMF BY 40 and BY o0 are qualitatively similar (not shown). Median flow directions, though not magnitudes, are also qualitatively similar if we divide our Geotail and LFM studies according to DST 4 15 nT and DST o 15 nT (not shown). This and other such sorting demonstrates that the average features of these maps are robust and not dominated by one or a few data points. General features of both studies also exhibit peculiar differences. One curiosity is the presence of a statistical dawn–dusk total pressure gradient. This interest prompts us to look closer at our method and datasets. Previous studies have interpreted statistical dawn-todusk plasma sheet flow asymmetries as the effects of plasma drifts (E B, corotation, and diamagnetic) in the near-Earth plasma sheet (Angelopoulos et al., 1993; Spence and Kivelson 1993; Wing and Newell, 1998; Hori et al., 2000; Wang et al., 2001). Our Geotail observations also reveal statistical dawn–dusk asymmetries in the perpendicular flows as well as in equatorial maps of magnetic pressure. However, before drawing physical conclusions based on these asymmetries, we more carefully explore the possibility of orbital bias in our Geotail data set. Fig. 1c shows the distribution of Geotail plasma sheet measurements in the YZ NS plane. To minimize orbital bias, we included only those points within 3RE of the Hammond et al. neutral sheet model (within the gray lines in Figs. 1b and c) in the statistical analysis presented thus far. Despite this attempt to remove bias, note the incomplete coverage on the dusk side of the YZ NS plot within 3RE . Narrowing the Z NS limits would exclude too much Geotail data from our study, and our statistical coverage would suffer. This dawn–dusk data coverage bias could cause some of the
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asymmetries found in the plasma parameters and flows in the previous section. 5.1. Tsyganenko comparison reveals sampling bias In order to determine if the spatial distribution of Geotail measurements leads to a corresponding asymmetry in measured parameters, we compute the magnetic field from the Tsyganenko (1996) magnetic field model (Tsyganenko and Stern, 1996) at each point Geotail measured the plasma sheet in our study. The upstream solar wind values of PRAM ; BY ; BZ , along with the DST index parameterize the Tsyganenko (1996) model field. We selected these solar wind inputs from WIND observations ballistically propagated to the Earth when each Geotail measurement was taken in the plasma sheet, and the DST value concurrently with each Geotail measurement. The Tsyganenko (1996) model does not include a partial ring current, and thus is dawn–dusk symmetric in the equatorial plane (Tsyganenko, 2002). Plotting the median Tsyganenko input parameters (PRAM ; BY ; BZ , and DST ) as functions of position within the plasma sheet reveal no dawn–dusk asymmetry in the model inputs (not shown). Therefore, a map of the field values of a completely symmetric model sampled equally across the plasma sheet should show no dawn–dusk asymmetry. Fig. 7 shows the sampling of the Tsyganenko (1996) model at the Geotail positions. It displays the median BX component of the magnetic field as measured by Geotail (a) and as computed from the Tsyganenko model (b). We use the BX component, as it is a sensitive tracer of distance from the neutral sheet. Both data and model exhibit similar patterns of median BX values, especially on the dusk side. There are more positive BX values on the duskside than on the dawnside of both the data and model maps. The similarity of these distributions suggests that a portion of the observed dawn–dusk asymmetry could be due to orbital biases. 5.2. Unfolding the sampling bias The perpendicular flow distribution also exhibits a strong dawn–dusk asymmetry in the equatorial plane, with the observed duskside flows being stronger. As Figs. 1c and 7 suggest, our Geotail dataset samples positions within the plasma sheet at different latitudes and magnetic topologies as a function of cross-tail location. Geotail most often measures the duskside plasma sheet at high latitudes, but measures the dawnside plasma sheet more probably near its center. Maps of field components indicate, on average, that the largest component is BX on the duskside (Fig. 7), but BZ dominates on the dawnside (not shown). Because convective flow amplitudes likely depend on distance from the plasma sheet center owing to the variation of
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Fig. 7. Comparison between the median BX magnetic field components as measured by Geotail (a) and as computed from the Tsyganenko 96 model (b). Consistently, more positive BX values are apparent on the dusk side of the plasma sheet in both plots. This suggests that a portion of the observed dawn–dusk asymmetry could be due to orbital biases.
jBj along a flux tube, an orbital bias in latitude introduces an apparent gradient in flow speed. However, if we assume that magnetic field lines are equipotentials, then equatorial maps of jEj ¼ jv Bj will normalize high- and low-latitude flow magnitudes sampled at different distances from the center of the plasma sheet. Other studies have shown the value of exploring the electric field in addition to the velocity field (e.g. Schoedel et al., 2001). Fig. 8 compares equatorial plots of the median jEj calculated from the measured VGEOTAIL and BGEOTAIL (Fig. 8a), and the jEj computed from the LFM model (Fig. 8b). Note the scale of jEj calculated from the LFM model exceeds that calculated from Geotail measurements by a factor of two. Contrary to expectations, this amplitude factor is significantly less than the previously shown median flow amplitude ratio (see Fig. 4) that was closer to five. If the electric field normalizes flows at various distances from the neutral sheet, we would expect large flows measured at high-latitude to map to even larger flows near the neutral sheet. The jEj comparison in Fig. 8 shows that both distributions are asymmetric, with higher median values in the pre-midnight region. This is consistent with Fig. 4c, but now is a map of flux-tube averaged flow vectors in the equatorial plane, with the Geotail orbital bias effectively removed. Note that both electric field maps retain their dawn–dusk asymmetry, with the duskside jEj fields larger, consistent with our earlier conclusion of measuring stronger flows on the duskside of the plasma sheet. The origin of the higher jEj field in the on the
duskside of the LFM has not yet been explored, though one possible source of asymmetry, energy dependent plasma drifts, are not included in the single fluid ideal MHD equations and can be ruled out. Another possible source arises from ionospheric Hall conductance asymmetries mapping into the magnetosphere, demonstrated by Wolf (1970), and included in the LFM model. In addition, the LFM model result has the largest field values along the X GSM axis, indicative of fast, reconnection-induced flows originating on average between 20 and 25RE in the tail. Inspection of time-series visualizations of the LFM simulation corroborates this interpretation. The Geotail map exhibits a similar, suggestive large-field feature at X GSM ¼ 20RE , but further analysis is necessary to determine the robustness of the result.
6. Conclusions We performed a statistical study of flows and plasma properties in the near-Earth plasma sheet as measured by the Geotail spacecraft, and in the near-Earth simulation domain of the LFM global MHD model. While gross climatological similarities exist between the two, some differences require further analysis and explanation. We find a dawn–dusk asymmetry in the magnitude of the Geotail and LFM plasma flows, and a consistent difference in their flow directions, with stronger flows on the duskside. The model predicts a steeper thermal pressure gradient in the equatorial plane
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Fig. 8. Comparison between the median electric field magnitudes calculated from the measured v and B (a), and calculated from the LFM model (b). Note the LFM color scale maximum exceeds the Geotail color scale maximum by a factor of two, significantly less than the factor of approximately five difference in velocity magnitudes of Fig. 4. Both plots are dawn–dusk asymmetric, with larger jEj values predominantly on the duskside. The highest LFM jEj fields are associated with reconnection-induced flows along the X GSM axis.
than is observed, and the Geotail observations indicate a dawn–dusk magnetic pressure asymmetry. Previous studies interpreted the dawn–dusk asymmetry of the flow as the cumulative effect of plasma drifts in the nearEarth plasma sheet (Angelopoulos et al., 1993; Spence and Kivelson, 1993; Wing and Newell, 1998; Hori et al., 2000; Wang et al., 2001). Our results show a dawn–dusk sampling bias of the plasma sheet points used in the study, but normalizing all flows to the equatorial plane by considering jEj ¼ jv Bj still yields a small but persistent dawn–dusk asymmetry. This asymmetry is seen in the LFM simulation results. We suggest that flow magnitude differences may partially result from differing degrees of driving; the LFM data set was produced by stronger solar wind electric fields than were present during the Geotail observations. We anticipate that future work with more similar statistical MHD plasma sheet sampling will resolve this question. Finally, coupling to the Rice Convection Model (RCM, Harel et al., 1981) in the inner magnetosphere should serve to improve data/model comparisons of the magnitude and direction of plasma flows, particularly in the near-Earth magnetotail.
Acknowledgements We would like to thank H. Petschek, M.-C. Fok, T. Hori and A. Clark for useful discussions and suggestions. We would also like to express our gratitude to T.
Mukai for the LEP data, S. Kokubun for the MGF data, and the ISAS sponsored DARTS system for maintaining and delivering the Geotail data used in this study. We would also like to thank K. Ogilvie and R. Lepping for the plasma and magnetic field data from the WIND satellite. This material is based upon work supported by the National Science Foundation under Grant No. DGE-0221680, and in part by CISM, which is funded by the STC Program of the National Science Foundation under Agreement Number ATM-0120950.
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