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Spatial distribution of the magnetosheath ion flux
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Adv. Space Res. Vol. 30, No. 12, pp. 2751-2756, 2002 © 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-1177/02 $22.00 + 0.00 PII: S0273-1177(02)00779-2
S P A T I A L D I S T R I B U T I O N OF T H E M A G N E T O S H E A T H ION FLUX Z. N~me~ek1, J. ~afr~nkovel1, G. N. Zastenker2, P. Pigoft 1, and K. I. Paularena3
1 Charles University, Faculty of Mathematics and Physics, V Hole~ovi6kdch P, 180 O0 Prague 8, Czech Republic 2Space Research Institute, Moscow, Russia 3Center for Space Research, MIT, Cambridge, USA ABSTRACT The magnetosheath plays a crucial role in solar wind-magnetosphere interaction because it is the magnetosheath magnetic field and plasma that interact with the magnetopanse and magnetosphere, not the unshocked solar wind. We are presenting ion flux measurement statistics at both the dawn and dusk flanks of the magnetosheath and their comparison with a gasdynamic magnetosheath model. The study is based on three years of INTERBALL-1 measurements supported by simultaneous WIND solar wind and magnetic field observations. Statistical processing has shown (1) the limitations of the gasdynamic model, (2) the conditions favorable for the creation of a plasma depletion layer adjacent to the flank magnetopause, (3) strong dawn-dusk asymmetry of the ion fluxes, and (4) an evidence for the presence of a slow mode front adjacent to the magnetopause. © 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.
INTRODUCTION Many researchers still rely upon the gasdynamic model for magnetosheath plasma and magnetic field parameters presented by Spreiter et al. (1966). The model predicts that velocities decrease from the bow shock to the magnetopause, whereas densities increase near the stagnation streamline. Slightly sunward of the dusk/dawn meridian, the density and velocity decrease along radial profiles from the bow shock to the magnetopause. Along the flanks, minimum velocities occur in the middle magnet~sheath. Zwan and Wolf (1976) found that close to the dayside magnetopanse, the magnetosheath region experiences a depletion of plasma density and magnetic field enhancement as particles are "squeezed out" near the nose along field lines due to increasing magnetic pressure. The MHD model by Southwood and Kivelson (1992) predicted the formation of an upstream compressional slow mode front standing near the magnetopanse which was observed earlier by Song et al. (1990); (1992). Both mentioned models assumed the magnetic field being perpendicular to the solar wind flow but Southwood and Kivelson (1992) suggest that the distance between the front and the magnetopause would depend on the orientation of the interplanetary magnetic field (IMF). Later, Southwood and Kivelson (1995) reconciled aforementioned results and they have shown that although the squeezing effect suggested by Zwan and Wolf (1976) cannot exist under conditions discussed in their paper, the formation of the slow mode front would result in the formation of a depleted region just outside the magnetopause. The models do not include any interaction of the magnetospheric and magnetosheath magnetic fields and thus their validity is limited to northward oriented IMF. Nemecek et al. (2000) presented a complex statistical study of ion fluxes in the dusk magnetosheath and showed the dependence of the magnetosheath radial profile on upstream parameters. The authors compared experimental INTERBALL results with gasdynamic predictions by Spreiter et al. (1966). From their statistical results it follows that the averaged ion flux is equal or smaller in all points of the magnetosheath than that predicted, and that starting from the middle of the magnetosheath, the averaged ion flux exhibits a saturation, whereas the Spreiter et al. (1966) model predicts its further rise toward the bow shock. The difference between the averaged radial profile and its gasdynamic prediction decreases with increasing ion 2751
2752
Z. Ni!me~eket al.
plasma beta and/or Alfv4nic Mach number. In this paper, we continue these investigations but we concentrate on the difference between the dawn and dusk magnetosheath. Similar topics are treated in Paularena et al. (2000). They compared the IMP-8 magnetosheath densities normalized to the ISEE-3 and WIND solar wind densities with the predictions of the gasdynamic magnetosheath model of Spreiter and Stahara (1980). The authors found significant dawn-dusk asymmetry in the Earth's magnetosheath, with larger values of densities on the dawn than dusk side. According to their investigations, the observed density asymmetry does not depend on the in-ecliptic IMF orientation, apparently ruling out both foreshock effects and different compression by parallel and perpendicular shocks as causes. The authors note that the asymmetry is strongest when the upstream magnetic field is within 22.5 ° of the ecliptic plane. Because the gasdynamic model assumes axisymmetry, it could not reveal features resulting from the magnetic field configuration, in particular the dawn-dusk asymmetry which may arise from the average orientation of the IMF along the Parker spiral. For this reason, the authors compared MHD model predictions with the sheath observations. Their MHD simulations show that a clear asymmetry is present in the width of the magnetosheath region with the dusk sheath roughly 15% thicker than the dawn sheath, and this fact is consistent with their experimental magnetosheath observations. DATA PROCESSING The main differences between this present study and Paularena et al. (2000) is that we investigate the region - 1 5 < XGSE < 5 RE, whereas their data cover a more tailward region from XGSE = --10 to XGSE = --25. Moreover, our study deals with more averaged data to avoid a possible influence of magnetosheath waves. We used the magnetosheath ion flux derived from INTERBALL-1 observations. This spacecraft was launched into a highly elongated polar orbit and passed through the magnetosheath twice per orbit, which lasted four days. The data processing method is described fully in Nemecek et al. (2000); we only briefly repeat basic steps. One minute averages of the magnetosheath ion flux have been complemented with WIND solar wind and IMF data (lagged on propagation time) and predicted values of the magnetosheath density and velocity from Spreiter et al. (1966). We have used the model results for MA = 8 but as we have shown in Nemecek et al. (2000), the dependence of the magnetosheath flux on MA is very weak for MA _> 8 and a great majority of our measurements fulfill this condition. We defined model positions of the magnetopause (Shue et al., 1997) and bow shock (Spreiter et al., 1966) and estimated the magnetosheath thickness. Then, we calculated 30-minute averages of all parameters. The results are presented as plots of FCCm (measured flux compression coefficient defined as ion mass density times the bulk flow speed downstream of the bow shock divided by the same parameter upstream of the bow shock) versus the distance from the magnetopanse given in units of the magnetosheath thickness (Delta MSH [%]). For this purpose, the data were grouped into bins, each of them 10% of magnetosheath thickness wide. For a particular task, the data in a bin were sorted in accordance with other parameter(s). It would be noted that all data were measured in the magnetosheath but, due to a well known inaccuracy of the bow shock and magnetopause models, a part of our measurements lay either below the predicted magnetopanse or upstream of the predicted bow shock. We have processed these data in the same way as the rest of the set. In this case, as a predicted value of FCCm, we have used the Spreiter et al. (1966) results for the magnetopause or bow shock where appropriate.
E X P E R I M E N T A L RESULTS The magnetosheath is well known as a highly disturbed region. In order to depress a possible influence of magnetosheath waves on a magnetosheath profile, we have based our study on 30-minute averages. These averages represent a quasisteady state of the magnetosheath because, taking into account a typical magnetosheath speed, the whole magnetosheath is filled by a new plasma population within 30 minutes. Our study is limited to the region 5 > X > - 1 5 RE where INTERBALL-1 spent ~ 2500 hours during three years; from September 1995 to March 1998. Due to an evolution of the orbit, INTERBALL-1 scanned the dusk magnetosheath during spring and the dawn magnetosheath during fall. We have processed each of these two data sets separately. Figures la and lb show the comparison of the experimentally determined radial profiles of the normalized magnetosheath ion fluxes with that estimated from the gasdynamic model of Spreiter et al. (1966). The
Spatial Distribution of the Magnetosheath Ion Flux
2753
normalized ion flux (FCCm) exhibits a saturation; it never exceeds a value of 1.8, whereas the gasdynamic prediction yields a value of ,~ 2.7 near the bow shock. This feature is common for both flanks. We would like to note that the difference between predicted dawn and dusk profiles near the bow shock is partly a product of the data coverage. The prediction was computed for each measuring point and a mean value is presented in Figure 1. This mean value is thus weighted by the locations of measuring points along the XGSE axis and these locations have different distributions in both flanks. Taking into account this peculiarity, we can conclude that normalized ion fluxes are quite similar in the bow shock region but the ion fluxes near the maguetopause differ s!~nificantly being higher than the gasdynamic prediction on the dawn flank and lower on the dusk flank. However, this conclusion refers to an average magnetosheath profile (each point in Figure 1 represents ~ 100 hours of observations) because the spread of initial values is very large. We have quantified this spread computing the relative standard deviations (RSD) of the data in each bin and plotted them in Figure 1. The RSD values reach ~ 0.3 near the dawn magnetopause and ~ 0.2 near the dusk magnetopause and thus it is clear that our conclusions cannot be applied to any instantaneous profile of the magnetosheath ion flux.
INTERBALL & WIND, Sep-Oct 1995,1996, 1997 3
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Fig. 1. A comparison of the normalized experimental (FCCm)and predicted (FCC~r)ion fluxes and values of the relative standard deviation (RSD) across the dawn (a) and dusk (b) magnetosheath. The data presented in Figure 1 are averaged in space and they represent a mean radial profile from -15 to +5 RE of the XGSE coordinate. For this reason, we have divided each of the two data sets shown in Figure 1 into two subsets. The breakpoint is XGSE = --2 RE, which represents a compromise; it leaves enough data in all subsets and reasonably reflects the fact that dayside and nightside magnetosheath profiles would be different. The results of this division are plotted in Figure 2. One can note that "nightside" parts of both dawn and dusk plots are qualitatively similar. Both start at ~, 0.9 and more or less continuously rise reaching a saturated value at about 50% of the maguetosheath thickness. A more detailed analysis shows that the rise of the dawn profile is a little steeper but that it saturates at a lower level. O n ' t h e other hand, the difference between dawn and dusk "dayside" magnetosheath profiles is striking. Whereas the principal rise of the ion flux in the dawn magnetosheath is gradual and occurs from 25% to 75% of the magnetosheath thickness, the dusk profile exhibits two nearly equal steps, at the maguetopause and at -~ 50% of the thickness. The above comparison suggests that the gasdynamic approximation can be used for qualitative predictions in the nightside magnetosheath. MHD effects seem to be more important on the dayside and thus we analyze this region in detail. A natural cause of the observed dawn-dusk asymmetry of the ion flux profile would be the spiral IMF orientation, which biases the data. We describe the IMF direction by an angle ~a = a r c t a n ( B x / B r ) and plot the dayside radial profiles for positive and negative ~o separately in Figure 3. It should be noted that the orientation along the Parker spiral corresponds to ~a ,~ - 4 5 °. Generally, if ~o is negative, the dawn sector of the magnetosheath lies behind the quasiparallel and the dusk sector, behind
2754
Z. NSrae~eket al. I N T E R B A L L & WIND, 8 e p - O c t 1995, 1996, 1997 2.0 . . . . .
I N T E R B A L L & WIND, Jan-Mar 1996, 1997, 1998
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Fig. 2. A comparison of the normalized ion flux profiles in the "dayside" (XGsE > --2RE) and "nightside" (XGsE < -2Rz~) magnetosheath. Panels (a) and (b) show the dawn and dusk magnetosheath profiles, respectively.
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Fig. 3. Profiles of the normalized ion fluxes in the "dayside" magnetosheath plotted separately for the nominal bow shock type upstream. Panels (a) and (b) show the dawn and dusk magnetosheath, respectively.
the quasiperpendicular shocks and vice versa. The curves in Figure 3 are denominated as parallel and perpendicular in agreement with this note. As can be seen from Figure 3, the IMF orientation strongly influences the dayside magnetosheath radial profile but not in the way that one would expect. First, the sign of 9 influences more the region adjacent to the magnetopanse, whereas the changes are negligible at the bow shock region. This probably excludes foreshock effects as a possible cause of the asymmetry. Second, the profiles on both flanks exhibit enhanced ion fluxes near the magnetopause for the orthospiral IMF orientation. This enhancement is more pronounced at the dusk magnetosheath, where the compression in front of the magnetopause is even higher than that just behind the bow shock. We should note that these results should be considered with care because the number of measurements is rather low and the standard deviation of depicted mean values varies from 0.1 to 0.4. The magnetosheath profile near the magnetopause would be influenced by the magnetopause processes as reconnection, magnetic field pile-up or leakage of magnetospheric particles. All these processes are sensitive to the orientation of the IMF B z component. Our analysis shows (Figure 4a) that the orientation of IMF B z exhibits only a minor influence on the dawn magnetosheath profile. A slight plasma depletion
Spatial Distribution of the M a g n e t o s h e a t h Ion Flux
INTERBALL & WIND, Sep-Oct 1995, 1996, 1997 2.0
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Fig. 4. Influence of the IMF Bz orientation on the normalized ion flux profiles measured across the dawn (a) and dusk (b) magnetosheath. seen in the magnetopause region for negative Bz can hardly be interpreted as a plasma depletion layer. Another depletion at --~ 20% of the magnetosheath thickness is observed for both B z orientations and can be consistent with an MHD prediction of a cdmpressional (slow mode) front at the magnetopause (Southwood and Kivelson, 1995). This effect is clearly seen for negative Bz but the profile is very smooth for the opposite Bz orientation. The dusk magnetosheath seems to be more sensitive to the Bz direction, as we demonstrate in Figure 4b. During intervals of negative Bz, the ion flux is enhanced near the magnetopause as well as in the bow shock region. These enhancements are separated by a depletion at ,-~ 40% of the magnetosheath thickness. The profile for positive Bz starts at the magnetopause with a lower value of the ion flux and exhibits a continuous rise toward the bow shock up to ,,~ 40% of the magnetosheath thickness. A small depletion at 50% of the thickness bounds this region from the region of the saturated ion flux in the outer magnetosheath. The spatial oscillations of the ion flux at the outer magnetosheath can be caused by insufficient statistics and we will not discuss them. DISCUSSION AND CONCLUSION We have carried out a statistical study of the magnetosheath radial profile for different directions of IMF. In general, the magnetosheath profile in the region under study (XGsE = --15 < X < 5 RE) does not correspond to the gasdynamic prediction of Spreiter et al. (1966) because the real averaged profile is constant in the outer magnetosheath, whereas the model predicts a steep rise. This is true for both dawn and dusk magnetosheath flanks. By contrast, a clear dawn-dusk asymmetry is seen in the inner magnetosheath, the dawn flux is significantly larger (20%) than the dusk flux. We have been trying to find a source of the previously mentioned asymmetry by dividing our original data set into different subsets. A detailed examination of Figure 2 shows that the highest difference between dawn and dusk in the nightside parts of our data sets occurs at about ~ 30% of the magnetosheath thickness, where the dawn flux is on ,-~ 15% higher than dusk one. This is generally consistent with findings of Paularena et al. (2000). When we are moving sunward, the asymmetry increases and moves toward the magnetopause. Surprisingly, this asymmetry is connected but not caused by the prevailing IMF orientation. Since there is no similarity between the dawn and dusk profiles when they lie behind quasiparallel (quasiperpendicular) shocks, this mearts that the asymmetry would be caused by more factors and a multifactorial analysis is required. An interesting feature is the increase of the ion flux in the inner magnetosheath during periods of ortho-spiral orientation of the IMF. This effect is clearly seen in both flanks and thus it cannot be caused by the IMF orientation only. An answer could bring a study of other solar wind parameters during periods of this unusual IMF direction. The dependence of the whole magnetosheath profile on the IMF Bz orientation suggests that MHD and
2756
Z. Nilmei~ek et al.
kinetic processes are equally important in the magnetosheath. The presence of a depletion layer at the magnetopause has been found in the dusk flank only being more pronounced for positive Bz consistently with the MHD prediction of Southwood and Kivelson (1995). Evidence for the presence of a compressional front near the magnetopause has been found in both flanks. This region of a slightly enhanced ion flux is narrower at the dawn and broader at the dusk magnetosheath. The thickness of this front seems to increase with decreasing IMF Bz in the dusk flank. The presence and dimension of this front is more influenced by the in-ecliptic IMF coordinates because they are present during ortho-spiral orientation and vanish when the IMF turns to the standard orientation (Figure 3). We can conclude that our study brings more questions than answers. An averaged magnetosheath profile and its changes with the distance from the nose have been found but the interpretation of the results in terms of particular interactions or processes is still unclear. ACKNOWLEDGEMENTS The present work was supported by the Czech Grant Agency under Contract No. 205/00/1686 and by the Charles University Grant Agency under Contracts No. 163/2000 and 181/1999. Authors are grateful to A. Lazarus and R. Lepping for the WIND plasma and magnetic field data and to L. Frank for the GEOTAIL plasma data. The authors thanks Paul Song and another referee for their assistance in evaluating this paper. REFERENCES N~me~ek, Z., J. ~afr~nkov~, G. N. Zastenker, P. Pi~oft, K. I. I. Paularena, et al., Observations of the radial magnetosheath profile and a comparison with gasdynamic model predictions, Geophys. Res. Lett., 27, 2801, 2000. Paularena K. I., J. D. Richardson, M. A. Kolpak, C. R. Jackson, and G. L. Siscoe, A puzzling dawn-dusk density asymmetry in Earth's magnetosheath, J. Geophys. Res., 2000, in press. Shue, J.-A., J. K. Chao, H. C. Fu, C. T. Russell, P. Song, et al., A new functional form to study the solar wind control of the magnetopause size and shape, J. Geophys. Res., 102, 9497, 1997. Song, P., C. T. Russell, J. T. Gosling, M. F. Thomsen, and R. C. Elphic, Observations of the density profile in the magnetosheath near the stagnation streamline, Geophys. Res. Lett., 17, 2035, 1990. Song, P., C. T. Russell, and M. F. Thomsen, Slow mode transition in the frontside magnetosheath, J. Geophys. Res., 97, 8295, 1992. Southwood, B. U. O. and M. G. Kivelson, On the form of the flow in the magnetosheath, J. Geophys. Res., 97, 2873, 1992. Southwood, B. U. O. and M. G. Kivelson, Magnetosheath flow near the magnetopause: Zwan-Wolf and Southwood-Kivelson theories reconciled, Geophys. Res. Lett., 22, 3275, 1995. Spreiter, J. R., A. L. Summers, and A. Y. Alksne, Hydromagnetic flow around the magnetosphere, Planet. Space Sci., 14, 223, 1966. Spreiter, J. R. and S. S. Stahara, A new predictive model for determing solar wind-terrestrial planet interactions, J. Geophys. Res., 85, 6769, 1980. Zwan, B. J. and R. A. Wolf, Depletion of the solar wind plasma near a planetary boundary, J. Geophys. Res., 81, 1636, 1976.
Adv. Space Res. Vol. 30, No. 12, pp. 2751-2756, 2002 © 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-1177/02 $22.00 + 0.00 PII: S0273-1177(02)00779-2
S P A T I A L D I S T R I B U T I O N OF T H E M A G N E T O S H E A T H ION FLUX Z. N~me~ek1, J. ~afr~nkovel1, G. N. Zastenker2, P. Pigoft 1, and K. I. Paularena3
1 Charles University, Faculty of Mathematics and Physics, V Hole~ovi6kdch P, 180 O0 Prague 8, Czech Republic 2Space Research Institute, Moscow, Russia 3Center for Space Research, MIT, Cambridge, USA ABSTRACT The magnetosheath plays a crucial role in solar wind-magnetosphere interaction because it is the magnetosheath magnetic field and plasma that interact with the magnetopanse and magnetosphere, not the unshocked solar wind. We are presenting ion flux measurement statistics at both the dawn and dusk flanks of the magnetosheath and their comparison with a gasdynamic magnetosheath model. The study is based on three years of INTERBALL-1 measurements supported by simultaneous WIND solar wind and magnetic field observations. Statistical processing has shown (1) the limitations of the gasdynamic model, (2) the conditions favorable for the creation of a plasma depletion layer adjacent to the flank magnetopause, (3) strong dawn-dusk asymmetry of the ion fluxes, and (4) an evidence for the presence of a slow mode front adjacent to the magnetopause. © 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.
INTRODUCTION Many researchers still rely upon the gasdynamic model for magnetosheath plasma and magnetic field parameters presented by Spreiter et al. (1966). The model predicts that velocities decrease from the bow shock to the magnetopause, whereas densities increase near the stagnation streamline. Slightly sunward of the dusk/dawn meridian, the density and velocity decrease along radial profiles from the bow shock to the magnetopause. Along the flanks, minimum velocities occur in the middle magnet~sheath. Zwan and Wolf (1976) found that close to the dayside magnetopanse, the magnetosheath region experiences a depletion of plasma density and magnetic field enhancement as particles are "squeezed out" near the nose along field lines due to increasing magnetic pressure. The MHD model by Southwood and Kivelson (1992) predicted the formation of an upstream compressional slow mode front standing near the magnetopanse which was observed earlier by Song et al. (1990); (1992). Both mentioned models assumed the magnetic field being perpendicular to the solar wind flow but Southwood and Kivelson (1992) suggest that the distance between the front and the magnetopause would depend on the orientation of the interplanetary magnetic field (IMF). Later, Southwood and Kivelson (1995) reconciled aforementioned results and they have shown that although the squeezing effect suggested by Zwan and Wolf (1976) cannot exist under conditions discussed in their paper, the formation of the slow mode front would result in the formation of a depleted region just outside the magnetopause. The models do not include any interaction of the magnetospheric and magnetosheath magnetic fields and thus their validity is limited to northward oriented IMF. Nemecek et al. (2000) presented a complex statistical study of ion fluxes in the dusk magnetosheath and showed the dependence of the magnetosheath radial profile on upstream parameters. The authors compared experimental INTERBALL results with gasdynamic predictions by Spreiter et al. (1966). From their statistical results it follows that the averaged ion flux is equal or smaller in all points of the magnetosheath than that predicted, and that starting from the middle of the magnetosheath, the averaged ion flux exhibits a saturation, whereas the Spreiter et al. (1966) model predicts its further rise toward the bow shock. The difference between the averaged radial profile and its gasdynamic prediction decreases with increasing ion 2751
2752
Z. Ni!me~eket al.
plasma beta and/or Alfv4nic Mach number. In this paper, we continue these investigations but we concentrate on the difference between the dawn and dusk magnetosheath. Similar topics are treated in Paularena et al. (2000). They compared the IMP-8 magnetosheath densities normalized to the ISEE-3 and WIND solar wind densities with the predictions of the gasdynamic magnetosheath model of Spreiter and Stahara (1980). The authors found significant dawn-dusk asymmetry in the Earth's magnetosheath, with larger values of densities on the dawn than dusk side. According to their investigations, the observed density asymmetry does not depend on the in-ecliptic IMF orientation, apparently ruling out both foreshock effects and different compression by parallel and perpendicular shocks as causes. The authors note that the asymmetry is strongest when the upstream magnetic field is within 22.5 ° of the ecliptic plane. Because the gasdynamic model assumes axisymmetry, it could not reveal features resulting from the magnetic field configuration, in particular the dawn-dusk asymmetry which may arise from the average orientation of the IMF along the Parker spiral. For this reason, the authors compared MHD model predictions with the sheath observations. Their MHD simulations show that a clear asymmetry is present in the width of the magnetosheath region with the dusk sheath roughly 15% thicker than the dawn sheath, and this fact is consistent with their experimental magnetosheath observations. DATA PROCESSING The main differences between this present study and Paularena et al. (2000) is that we investigate the region - 1 5 < XGSE < 5 RE, whereas their data cover a more tailward region from XGSE = --10 to XGSE = --25. Moreover, our study deals with more averaged data to avoid a possible influence of magnetosheath waves. We used the magnetosheath ion flux derived from INTERBALL-1 observations. This spacecraft was launched into a highly elongated polar orbit and passed through the magnetosheath twice per orbit, which lasted four days. The data processing method is described fully in Nemecek et al. (2000); we only briefly repeat basic steps. One minute averages of the magnetosheath ion flux have been complemented with WIND solar wind and IMF data (lagged on propagation time) and predicted values of the magnetosheath density and velocity from Spreiter et al. (1966). We have used the model results for MA = 8 but as we have shown in Nemecek et al. (2000), the dependence of the magnetosheath flux on MA is very weak for MA _> 8 and a great majority of our measurements fulfill this condition. We defined model positions of the magnetopause (Shue et al., 1997) and bow shock (Spreiter et al., 1966) and estimated the magnetosheath thickness. Then, we calculated 30-minute averages of all parameters. The results are presented as plots of FCCm (measured flux compression coefficient defined as ion mass density times the bulk flow speed downstream of the bow shock divided by the same parameter upstream of the bow shock) versus the distance from the magnetopanse given in units of the magnetosheath thickness (Delta MSH [%]). For this purpose, the data were grouped into bins, each of them 10% of magnetosheath thickness wide. For a particular task, the data in a bin were sorted in accordance with other parameter(s). It would be noted that all data were measured in the magnetosheath but, due to a well known inaccuracy of the bow shock and magnetopause models, a part of our measurements lay either below the predicted magnetopanse or upstream of the predicted bow shock. We have processed these data in the same way as the rest of the set. In this case, as a predicted value of FCCm, we have used the Spreiter et al. (1966) results for the magnetopause or bow shock where appropriate.
E X P E R I M E N T A L RESULTS The magnetosheath is well known as a highly disturbed region. In order to depress a possible influence of magnetosheath waves on a magnetosheath profile, we have based our study on 30-minute averages. These averages represent a quasisteady state of the magnetosheath because, taking into account a typical magnetosheath speed, the whole magnetosheath is filled by a new plasma population within 30 minutes. Our study is limited to the region 5 > X > - 1 5 RE where INTERBALL-1 spent ~ 2500 hours during three years; from September 1995 to March 1998. Due to an evolution of the orbit, INTERBALL-1 scanned the dusk magnetosheath during spring and the dawn magnetosheath during fall. We have processed each of these two data sets separately. Figures la and lb show the comparison of the experimentally determined radial profiles of the normalized magnetosheath ion fluxes with that estimated from the gasdynamic model of Spreiter et al. (1966). The
Spatial Distribution of the Magnetosheath Ion Flux
2753
normalized ion flux (FCCm) exhibits a saturation; it never exceeds a value of 1.8, whereas the gasdynamic prediction yields a value of ,~ 2.7 near the bow shock. This feature is common for both flanks. We would like to note that the difference between predicted dawn and dusk profiles near the bow shock is partly a product of the data coverage. The prediction was computed for each measuring point and a mean value is presented in Figure 1. This mean value is thus weighted by the locations of measuring points along the XGSE axis and these locations have different distributions in both flanks. Taking into account this peculiarity, we can conclude that normalized ion fluxes are quite similar in the bow shock region but the ion fluxes near the maguetopause differ s!~nificantly being higher than the gasdynamic prediction on the dawn flank and lower on the dusk flank. However, this conclusion refers to an average magnetosheath profile (each point in Figure 1 represents ~ 100 hours of observations) because the spread of initial values is very large. We have quantified this spread computing the relative standard deviations (RSD) of the data in each bin and plotted them in Figure 1. The RSD values reach ~ 0.3 near the dawn magnetopause and ~ 0.2 near the dusk magnetopause and thus it is clear that our conclusions cannot be applied to any instantaneous profile of the magnetosheath ion flux.
INTERBALL & WIND, Sep-Oct 1995,1996, 1997 3
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Fig. 1. A comparison of the normalized experimental (FCCm)and predicted (FCC~r)ion fluxes and values of the relative standard deviation (RSD) across the dawn (a) and dusk (b) magnetosheath. The data presented in Figure 1 are averaged in space and they represent a mean radial profile from -15 to +5 RE of the XGSE coordinate. For this reason, we have divided each of the two data sets shown in Figure 1 into two subsets. The breakpoint is XGSE = --2 RE, which represents a compromise; it leaves enough data in all subsets and reasonably reflects the fact that dayside and nightside magnetosheath profiles would be different. The results of this division are plotted in Figure 2. One can note that "nightside" parts of both dawn and dusk plots are qualitatively similar. Both start at ~, 0.9 and more or less continuously rise reaching a saturated value at about 50% of the maguetosheath thickness. A more detailed analysis shows that the rise of the dawn profile is a little steeper but that it saturates at a lower level. O n ' t h e other hand, the difference between dawn and dusk "dayside" magnetosheath profiles is striking. Whereas the principal rise of the ion flux in the dawn magnetosheath is gradual and occurs from 25% to 75% of the magnetosheath thickness, the dusk profile exhibits two nearly equal steps, at the maguetopause and at -~ 50% of the thickness. The above comparison suggests that the gasdynamic approximation can be used for qualitative predictions in the nightside magnetosheath. MHD effects seem to be more important on the dayside and thus we analyze this region in detail. A natural cause of the observed dawn-dusk asymmetry of the ion flux profile would be the spiral IMF orientation, which biases the data. We describe the IMF direction by an angle ~a = a r c t a n ( B x / B r ) and plot the dayside radial profiles for positive and negative ~o separately in Figure 3. It should be noted that the orientation along the Parker spiral corresponds to ~a ,~ - 4 5 °. Generally, if ~o is negative, the dawn sector of the magnetosheath lies behind the quasiparallel and the dusk sector, behind
2754
Z. NSrae~eket al. I N T E R B A L L & WIND, 8 e p - O c t 1995, 1996, 1997 2.0 . . . . .
I N T E R B A L L & WIND, Jan-Mar 1996, 1997, 1998
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Fig. 2. A comparison of the normalized ion flux profiles in the "dayside" (XGsE > --2RE) and "nightside" (XGsE < -2Rz~) magnetosheath. Panels (a) and (b) show the dawn and dusk magnetosheath profiles, respectively.
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the quasiperpendicular shocks and vice versa. The curves in Figure 3 are denominated as parallel and perpendicular in agreement with this note. As can be seen from Figure 3, the IMF orientation strongly influences the dayside magnetosheath radial profile but not in the way that one would expect. First, the sign of 9 influences more the region adjacent to the magnetopanse, whereas the changes are negligible at the bow shock region. This probably excludes foreshock effects as a possible cause of the asymmetry. Second, the profiles on both flanks exhibit enhanced ion fluxes near the magnetopause for the orthospiral IMF orientation. This enhancement is more pronounced at the dusk magnetosheath, where the compression in front of the magnetopause is even higher than that just behind the bow shock. We should note that these results should be considered with care because the number of measurements is rather low and the standard deviation of depicted mean values varies from 0.1 to 0.4. The magnetosheath profile near the magnetopause would be influenced by the magnetopause processes as reconnection, magnetic field pile-up or leakage of magnetospheric particles. All these processes are sensitive to the orientation of the IMF B z component. Our analysis shows (Figure 4a) that the orientation of IMF B z exhibits only a minor influence on the dawn magnetosheath profile. A slight plasma depletion
Spatial Distribution of the M a g n e t o s h e a t h Ion Flux
INTERBALL & WIND, Sep-Oct 1995, 1996, 1997 2.0
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Fig. 4. Influence of the IMF Bz orientation on the normalized ion flux profiles measured across the dawn (a) and dusk (b) magnetosheath. seen in the magnetopause region for negative Bz can hardly be interpreted as a plasma depletion layer. Another depletion at --~ 20% of the magnetosheath thickness is observed for both B z orientations and can be consistent with an MHD prediction of a cdmpressional (slow mode) front at the magnetopause (Southwood and Kivelson, 1995). This effect is clearly seen for negative Bz but the profile is very smooth for the opposite Bz orientation. The dusk magnetosheath seems to be more sensitive to the Bz direction, as we demonstrate in Figure 4b. During intervals of negative Bz, the ion flux is enhanced near the magnetopause as well as in the bow shock region. These enhancements are separated by a depletion at ,-~ 40% of the magnetosheath thickness. The profile for positive Bz starts at the magnetopause with a lower value of the ion flux and exhibits a continuous rise toward the bow shock up to ,,~ 40% of the magnetosheath thickness. A small depletion at 50% of the thickness bounds this region from the region of the saturated ion flux in the outer magnetosheath. The spatial oscillations of the ion flux at the outer magnetosheath can be caused by insufficient statistics and we will not discuss them. DISCUSSION AND CONCLUSION We have carried out a statistical study of the magnetosheath radial profile for different directions of IMF. In general, the magnetosheath profile in the region under study (XGsE = --15 < X < 5 RE) does not correspond to the gasdynamic prediction of Spreiter et al. (1966) because the real averaged profile is constant in the outer magnetosheath, whereas the model predicts a steep rise. This is true for both dawn and dusk magnetosheath flanks. By contrast, a clear dawn-dusk asymmetry is seen in the inner magnetosheath, the dawn flux is significantly larger (20%) than the dusk flux. We have been trying to find a source of the previously mentioned asymmetry by dividing our original data set into different subsets. A detailed examination of Figure 2 shows that the highest difference between dawn and dusk in the nightside parts of our data sets occurs at about ~ 30% of the magnetosheath thickness, where the dawn flux is on ,-~ 15% higher than dusk one. This is generally consistent with findings of Paularena et al. (2000). When we are moving sunward, the asymmetry increases and moves toward the magnetopause. Surprisingly, this asymmetry is connected but not caused by the prevailing IMF orientation. Since there is no similarity between the dawn and dusk profiles when they lie behind quasiparallel (quasiperpendicular) shocks, this mearts that the asymmetry would be caused by more factors and a multifactorial analysis is required. An interesting feature is the increase of the ion flux in the inner magnetosheath during periods of ortho-spiral orientation of the IMF. This effect is clearly seen in both flanks and thus it cannot be caused by the IMF orientation only. An answer could bring a study of other solar wind parameters during periods of this unusual IMF direction. The dependence of the whole magnetosheath profile on the IMF Bz orientation suggests that MHD and
2756
Z. Nilmei~ek et al.
kinetic processes are equally important in the magnetosheath. The presence of a depletion layer at the magnetopause has been found in the dusk flank only being more pronounced for positive Bz consistently with the MHD prediction of Southwood and Kivelson (1995). Evidence for the presence of a compressional front near the magnetopause has been found in both flanks. This region of a slightly enhanced ion flux is narrower at the dawn and broader at the dusk magnetosheath. The thickness of this front seems to increase with decreasing IMF Bz in the dusk flank. The presence and dimension of this front is more influenced by the in-ecliptic IMF coordinates because they are present during ortho-spiral orientation and vanish when the IMF turns to the standard orientation (Figure 3). We can conclude that our study brings more questions than answers. An averaged magnetosheath profile and its changes with the distance from the nose have been found but the interpretation of the results in terms of particular interactions or processes is still unclear. ACKNOWLEDGEMENTS The present work was supported by the Czech Grant Agency under Contract No. 205/00/1686 and by the Charles University Grant Agency under Contracts No. 163/2000 and 181/1999. Authors are grateful to A. Lazarus and R. Lepping for the WIND plasma and magnetic field data and to L. Frank for the GEOTAIL plasma data. The authors thanks Paul Song and another referee for their assistance in evaluating this paper. REFERENCES N~me~ek, Z., J. ~afr~nkov~, G. N. Zastenker, P. Pi~oft, K. I. I. Paularena, et al., Observations of the radial magnetosheath profile and a comparison with gasdynamic model predictions, Geophys. Res. Lett., 27, 2801, 2000. Paularena K. I., J. D. Richardson, M. A. Kolpak, C. R. Jackson, and G. L. Siscoe, A puzzling dawn-dusk density asymmetry in Earth's magnetosheath, J. Geophys. Res., 2000, in press. Shue, J.-A., J. K. Chao, H. C. Fu, C. T. Russell, P. Song, et al., A new functional form to study the solar wind control of the magnetopause size and shape, J. Geophys. Res., 102, 9497, 1997. Song, P., C. T. Russell, J. T. Gosling, M. F. Thomsen, and R. C. Elphic, Observations of the density profile in the magnetosheath near the stagnation streamline, Geophys. Res. Lett., 17, 2035, 1990. Song, P., C. T. Russell, and M. F. Thomsen, Slow mode transition in the frontside magnetosheath, J. Geophys. Res., 97, 8295, 1992. Southwood, B. U. O. and M. G. Kivelson, On the form of the flow in the magnetosheath, J. Geophys. Res., 97, 2873, 1992. Southwood, B. U. O. and M. G. Kivelson, Magnetosheath flow near the magnetopause: Zwan-Wolf and Southwood-Kivelson theories reconciled, Geophys. Res. Lett., 22, 3275, 1995. Spreiter, J. R., A. L. Summers, and A. Y. Alksne, Hydromagnetic flow around the magnetosphere, Planet. Space Sci., 14, 223, 1966. Spreiter, J. R. and S. S. Stahara, A new predictive model for determing solar wind-terrestrial planet interactions, J. Geophys. Res., 85, 6769, 1980. Zwan, B. J. and R. A. Wolf, Depletion of the solar wind plasma near a planetary boundary, J. Geophys. Res., 81, 1636, 1976.