1. High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO 80307, U.S.A.
2. Center for Space Science and Applied Research, Academia Sinica, Beijing 100080, P. R. C.
3. RMA Aerospace Inc., Mountain View, CA 94043, U. S. A.
4. Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024, U. S. A.
However, it is the nature of the plasma and magnetic field of the magnetosheath downstream of the bow shock that directly influences the magnetopause. Since the upstream variations in the solar wind plasma can be significantly modified upon traversing the bow shock and magnetosheath (Yan and Lee, 1994), the magnetosheath is an important region that any realistic space weather forecast model cannot ignore.
Several theoretical models have been developed to understand the plasma and magnetic field properties in the transition region from the bow shock to the magnetopause. These models differ in the role that magnetic forces play in them. (Spreiter et al., 1966) proposed a gasdynamic model in which ordinary sound waves determine the properties of plasma flow and field draping around the magnetopause and magnetic forces play no role. Lees (1964) and Zwan and Wolf (1976) invoked slow mode processes inherent to magnetized fluids and found a depletion effect of the magnetosheath plasma. Wu (1992) investigated the formation of a depletion layer close to the magnetopause with a 3-D MHD calculation.
Song et al. (1990, 1992) studied processes in the magnetosheath using data from ISEE-1 and 2 and discovered a region of plasma density enhancements and field depression near the magnetopause having a relatively large spatial scale. They also inferred that in some cases this slow-mode structure was locally generated in the magnetosheath as part of the interaction of the magnetosheath with the magnetosphere and was not one carried into the magnetosheath by the solar wind. Moreover the plasma depletion layer just outside the magnetopause often appears to be associated with a decline in density beginning at the slow-mode structure. Hammond et al. (1995) have recently reported a similar structure in the Jovian magnetosheath. Using a two-dimensional MHD simulation, Lee et al. (1991) showed that such a structure can be formed close to the stagnation region. Southwood and Kivelson (1992) suggested that slow-mode structures or slow wave fronts can be formed by sources of disturbances at the magnetopause. The structure may play an important role in establishing the flow and field pattern near the magnetopause (Song et al., 1992).
Omidi and Winske (1995) pointed out that the slow-mode wave front may originate at the magnetopause and that upstream mirror mode waves may play some roles. On the other hand,Yan and Lee (1994) drew attention to the possibility that slow-mode structures can be formed through the interaction between interplanetary rotational discontinuities and the bow shock, and hence some slow-mode magnetosheath variations may have their sources in the solar wind. Therefore, in order to understand the properties of the slow-mode structure and other processes in the magnetosheath, it is important to identify the sources of the variations observed in the magnetosheath. This work will examine in addition the validity and limitations of the gasdynamic convected field model.
The magnetosheath data are from the ISEE-2 magnetometer (Russell 1978) and Fast Plasma Experiment (FPE) (Bame et al., 1978a). The solar wind data are obtained by the magnetometer (Frandsen et al., 1978) and solar wind analyzer (Bame et al., 1978b) on ISEE-3. In this letter, we present three crossings in detail. The first case involved strong variations in both the solar wind plasma density and IMF. The second involved significant changes only in the IMF, but not in the solar wind plasma properties. The third occurred during relatively steady solar wind and IMF conditions.
|Figure 1. An outbound magnetosheath crossing by ISEE-2 (solid lines) and corresponding GDCFM prediction (dashed lines). The positions of the magnetopause and the bow shock are indicated by arrows. The solar wind Mach number M=6.0, Alfven Mach number M=7.5 and =1.44|
Several strong plasma density enhancements with large time scales are observed in the magnetosheath. The enhancement between 2145 and 2217 UT is well predicted by the model. Furthermore, the model predicts that ISEE-2 is very close to the bow shock during this time as evidenced by a pair of predicted but not observed bow shock crossings. The density prediction in general is good near the bow shock but higher than observed near the magnetopause. The difference is as large as 60o . There is a prediction of multiple magnetopause crossings, which are not actually recorded by ISEE-2. The actual slowdown of the magnetosheath flow as evidenced in the V component is significantly less than the prediction. Since the FPE was not designed to measure the solar wind and has widely separated energy channels [Bame et al., 1978a], its velocity in the solar wind is different in magnitude from that of ISEE-3. The V component of the observed velocity is positive from 2145 UT to the bow shock while the y component of ISEE-2 position is negative. The difference in sign is due to the aberration effect that is properly included in the forecast model. Prediction of the three components and magnitude of magnetic field is in good agreement with the observation except for some small regions principally from the magnetopause to 2145 UT. Because the model is a single fluid model, the temperature is considered to be the sum of the proton and electron temperatures. The predicted temperature is about 50% lower than the observation, and the difference becomes somewhat greater corresponding to the slow mode structures.
An outbound crossing of the magnetosheath on September 17, 1978 by ISEE-2 is shown in Figure 2 (in the same format as in Figure 1). This case has been previously studied by Song et al. . ISEE-2 was at (9.0, -2.4, 4.1)R GSE at 1500 UT and (12.5, -1.4, 5.2) R GSE at 1800UT. ISEE-3 was located at (211, -80, 17)R GSE. The timeshift between ISEE-3 and ISEE-2 observations is approximately 57 min. The solar wind was relatively steady, while the IMF rotated about 130o near 1510-1540UT and about 54o near 1550-1610UT.
|Figure 2. An outbound magnetosheath crossing in the same format as Figure 1. The solar wind Mach number M=5.0, Alfven Mach number M=9.0 and 3.2|
The magnetic field prediction agrees very well with the observations throughout the magnetosheath except for a thin region near the magnetopause. ISEE-2 detected plasma density enhancements from 1533 UT to 1610 UT with the peaks more than double the background value. The model predictions of density during this time show no indication of this structure. Again, the magnitude of V is significantly larger than the perdiction. The V is reasonably well predicted, but the observation shows a significant additional deflection within the large-scale slow mode structure. There is little fluctuation in observed and predicted temperatures, but the prediction again is approximately 50% lower than the observation. Within the large-scale slow mode structure, the correlation with the solar wind is good for the direction of the magnetic field but the predicted plasma density shows little correlation with the observed density variations.
Figure 3 presents an inbound magnetosheath pass on September 5, 1978 by ISEE-2 (in the same format to Figure 1). ISEE-2 was at (8.6, 10.0, 2.0 )RGSE at 0200 UT and (7.6, 9.5,1.7) R GSE at 0500UT. ISEE-3 was located at (195.6, -48.2, 18.3)R GSE. The timeshift fom ISEE-3 to ISEE-2 is about 51 min. A major difference between this case and previous two is that this pass occurred at a much greater solar zenith angle, about 50o from the stagnation streamline.
An inbound magnetosheath crossing in a format similar to Figure 1,
but with plasma the ratio of the thermal pressure
to the magnetic pressure shown in the bottom panel. The solar wind
Mach number M=5.5, Alfven Mach number|
M=9.0 and =3.0
Again, the model predictions for this pass are in good agreement with the observations in the magnetosheath except for a small region near the magnetopause. The changes of the plasma density and the magnetic field predicted by the model are very small for this pass because of the steady upstream condition. The slow mode structure with a plasma density enhancement and field decrease occurs from 0410 UT to 0440 UT and is not predicted by the model. The predictions of velocity components are much better than the other two cases and the aberration effect may become unimportant because the satellite was far from the stagnation streamline (nearly 10R). The plasma is a good indicator of slow mode processes because the thermal and magnetic pressures change out of phase. The predicted and observed s are about the same in the magnetosheath other than within the slow mode structure. There is no correlation between plasma density and magnetic field variations in the slow mode structure with those in the solar wind (after having examined the corresponding conditions in the solar wind).
For all these cases studied, there is an overestimate of the density prediction near the magnetopause. In some cases, the difference can be as large as 60%. Of the 60%, less than 10% may be accounted for by the compression included in the GDCFM. The remaining more than 50\% is most likely due to the plasma depletion effect. We note that the depletion effect appears to occur over the entire magnetosheath and not only in the small region near the magnetopause. We will further investigate this phenomenon statistically. Another interesting phenomenon is that the flow often slows down much less in the magnetosheath than predicted.
Determination of the timeshift has been a crucial issue when correlating the variations in the solar wind with those in the magnetosheath, and then with subsequent variations on the magnetopause, in the magnetosphere and ionosphere and on the ground. In the past several methods have been used: (1) dividing the distance in the x direction between the two spacecraft by the measured solar wind velocity; (2) determining the propagation delay when the solar wind monitor is not on the Sun-Earth line, assuming that the surface of constant IMF and solar wind contain both ecliptic pole and the path spiral direction; (3) similar to (2) but determining the normal to the surface of constant solar wind conditions by some technique such as minimum variance at the upstream monitor; and (4) shifting the time in order to maximize the correlation between the clock angle of the IMF and that of the sheath field [Song et al., 1992]. There are large uncertainties in the time delay using each of methods (1),(2) and (3). While method (4) is significantly better, only one timeshift is provided and it cannot account for the changes in the time shift when the solar wind velocity changes. Our method is similar to method (1) but with the advantage that the variation of velocity along the streamline with magnetosheath is properly accounted for prediction.
From the three presented cases, we have found that the thickness of magnetosheath is well predicted by the model, i.e., one may change either the magnetopause or the bow shock crossing time to improve its timing prediction, but it will worsen the other. Furthermore, the time shifts we used determine well the time of those field changes in the sheath whose origin was in the wind. Practically, one has no freedom in shifting the time. The bulk velocity, magnetic field and plasma density are in general well predicted by the model in the outer and middle magnetosheath while the predictions may become significantly different from the observations in the region near the magnetopause. As a whole, we find that the forecast model can provide a relatively accurate time shift with an uncertainty of less than 10 min., provide good reference locations of the bow shock and the magnetopause, and predict the magnitudes of the parameters reasonably well in the outer and middle magnetosheath. This justifies the use of the model predictions as a baseline to correlate the variations in the magnetosheath with those in the solar wind. The differences near the magnetopause and within the slow mode structure are due to the MHD effects not included in the model.
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Last Modified: July 22, 1996