[1] Peredo et al. (1995) derived a frequently used three-dimensional bow shock model parameterized by the upstream Alfvénic Mach number from the set of approximately 550 bow shock crossings provided by 17 distinct spacecraft over the period of 1963-1980. However, several studies reported some systematic biases in the bow shock model predictions. Therefore we have attempted to improve upon the bow shock model of Peredo et al. (1995) using their original data set and methodology in an effort to better understand these effects. We have performed three-dimensional best fits to the bow shock crossings binned by the upstream Mach numbers M A , M S , and M MS and found that the best fitting surfaces were best ordered with the M A . In agreement with predictions from the magnetohydrodynamic theory, the results show that the bow shock surface expands when the M A decreases. The found dawn-dusk asymmetry in the bow wave is consistent with previous studies only in the Geocentric Plasma Ecliptic System (GPE) coordinates but not in the Geocentric Interplanetary Medium (GIPM) coordinates which suggests that the employed data set is not comprehensive enough for resolving this asymmetry. Nor is the Mach cone asymmetry resolved in our data set (not even in the GIPM frame). We have derived two models predicting the statistical position and shape of the bow shock in the GPE or GIPM coordinates. Error analysis shows that the GPE-based model is more accurate and applicable for M A = 3-20 except the nose region where the model underestimates the bow shock position for M A < 5. A direct comparison of the model predictions with 5870 IMP 8 bow shock crossings demonstrated high accuracy of predictions and, for the GPEbased model, an exceptional stability of predictions even under extreme upstream conditions. Indeed, the new GPE-based bow shock model is more accurate and equally or more stable than the Formisano (1979), Němeček and Š afránková (1991), Farris and Russell (1994)

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[1] We present results from a new three-dimensional empirical magnetopause model based on 15,089 magnetopause crossings from 23 spacecraft. To construct the model, we introduce a Support Vector Regression Machine (SVRM) technique with a systematic approach that balances model smoothness with fitting accuracy to produce a model that reveals the manner in which the size and shape of the magnetopause depend upon various control parameters without any assumptions concerning the analytical shape of the magnetopause. The new model fits the data used in the modeling very accurately, and can guarantee a similar accuracy when predicting unseen observations within the applicable range of control parameters. We introduce a new error analysis technique based upon the SVRM that enables us to obtain model errors appropriate to different locations and control parameters. We find significant east-west elongations in the magnetopause shape for many combinations of control parameters. Variations in the Earth's dipole tilt can cause significant magnetopause north/south asymmetries and deviation of the magnetopause nose from the Sun-Earth line nonlinearly by as much as 5 Re. Subsolar magnetopause erosion effect under southward IMF is seen which is strongly affected by solar wind dynamic pressure. Further, we find significant shrinking of high-latitude magnetopause with decreased magnetopause flaring angle during northward IMF.

[1] On 5 May 1996 the Interball-1 and IMP 8 spacecraft crossed the bow shock boundary. The upstream conditions were special in two factors: (1) the interplanetary magnetic field was anti-parallel to the solar wind flow within 15°and (2) the conditions were stable for a prolonged period ($9 hours). At the nose of the magnetosphere, the Interball-1 data revealed that the magnetopause was farther outward by $2 R E than model predictions and the subsolar magnetosheath was unusually thin, at most 10% of the magnetopause standoff distance. Both results stand in contrast to predictions of existing magnetopause/bow shock models. Assuming a hyperboloidal (paraboloidal) shock wave, the calculated shock's standoff distance was 13.7 (13.6) R E , and the focus was located on the x axis at 4.5 (4.2) R E . On the basis of the IMP 8 observation, the bow shock flares significantly less than MHD simulations predict for a field-aligned bow shock at the magnetospheric flanks. This study discusses differences between the observations and existing MHD bow shock simulations for field-aligned upstream flow. Furthermore, it is suggested that the flowaligned IMF orientation causes a significant change of the magnetopause shape into a bullet-like obstacle.

[1] Over 12 years of IMP 8, data was searched for observed bow shock crossings. Out of the total 4562 crossings found, we used the 2293 unambiguous bow shocks for which upstream interplanetary magnetic field and solar wind parameters were available to study selected bow shock models under normal and unusual solar wind conditions. The chosen models were F79, NS91, FR94, FR94c, CL95, and P95 [Formisano, 1979; Němeček and Šafránková, 1991;Farris and Russell, 1994;Cairns and Lyon, 1995;Peredo et al., 1995]. This statistical study investigates these models' reliability not only for average solar wind plasma and interplanetary magnetic field (IMF) conditions but also for unusual conditions and as a result points out some deficiencies of these models. Statistically, the predictions of F79 and the phenomenological and MHD models FR94, FR94c, and CL95 are the most accurate, with F79 giving a slightly better result. The P95 model predicts standoff distances which are too large by $20%. For large values of the IMF and its components, all models except NS91 underestimate the bow shock distance. Furthermore, the models underestimate the bow shock distance when the upstream Mach numbers are low (]5). The models also do not properly reflect changes in the relative orientation of the IMF and solar wind velocity vectors. An independent evaluation of the dawn and dusk sectors suggests an asymmetry in the bow shock shape and/or a different reaction of the flanks to solar wind deviations from a radial flow. Taking the upstream parameters from a distant solar wind monitor (the Wind spacecraft) resulted in the models predicting the shock farther away from the Earth, which is likely a result of the spacecraft separation perpendicular to the solar wind flow, or of calibrational differences of the plasma density measurements by the spacecraft.

Abstract. The width of the cusp region is an indicator of the strength of the merging process and the degree of opening of the magnetosphere. During three years, the Magion-4 satellite, as part of the Interball project, has collected a unique data set of cusp-like plasma observations in middle and high altitudes. For a comparison of high-and low-altitude cusp determination, we map our observations of cusp-like plasma along the magnetic field lines down to the Earth's surface. We use the Tsyganenko and Stern 1996 model of the magnetospheric magnetic field for the mapping, taking actual solar wind and IMF parameters from the Wind observations. The footprint positions show substantial latitudinal dependence on the dipole tilt angle. We fit this dependence with a linear function and subtract this function from observed cusp position. This process allows us to study both statistical width and location of the inspected region as a function of the solar wind and IMF parameters.Our processing of the Magion-4 measurements shows that high-altitude regions occupied by the cusp-like plasma (cusp and cleft) are projected onto a much broader area (in magnetic local time as well as in a latitude) than that determined in low altitudes. The trends of the shift of the cusp position with changes in the IMF direction established by low-altitude observations have been confirmed.

We develop a model for the strahl population in the solar wind -a narrow, low-density and high-energy electron beam centered on the magnetic field direction. Our model is based on the solution of the electron drift-kinetic equation at heliospheric distances where the plasma density, temperature, and the magnetic field strength decline as power-laws of the distance along a magnetic flux tube. Our solution for the strahl depends on a number of parameters that, in the absence of the analytic solution for the full electron velocity distribution function (eVDF), cannot be derived from the theory. We however demonstrate that these parameters can be efficiently found from matching our solution with observations of the eVDF made by the Wind satellite's SWE strahl detector. The model is successful at predicting the angular width (FWHM) of the strahl for the Wind data at 1 AU, in particular by predicting how this width scales with particle energy and background density. We find the strahl distribution is largely determined by the local temperature Knudsen number γ ∼ |T dT /dx|/n, which parametrizes solar wind collisionality. We compute averaged strahl distributions for typical Knudsen numbers observed in the solar wind, and fit our model to these data. The model can be matched quite closely to the eVDFs at 1 AU; however, it then overestimates the strahl amplitude at larger heliocentric distances. This indicates that our model may be improved through the inclusion of additional physics, possibly through the introduction of "anomalous diffusion" of the strahl electrons.

[1] The database of IMP 8 bow shock crossings was used to investigate properties of the bow shock's cross section between 10 and 15 R E tailward of Earth in response to selected upstream and magnetospheric parameters. Best-fitted ellipses were derived for each parameter subset and analyzed. We have found that for average solar wind conditions, the shock's cross section moves in the north-south directions by 3.8 R E when the dipole tilt changes from sunward to antisunward orientations. Comparisons with results provided by global three-dimensional MHD simulations of the magnetosphere have shown that the tilt angle effect is likely to be also important for the estimation of the dayside shock wave's position. We have found the orientation of the IMF with respect to the solar wind flow, expressed by the angle q Bv , to influence the size and stability of the shock shape/position. The observed Mach number dependence agreed with previous studies and no other significant IMF-induced asymmetries were found.