American Geophysical Union (AGU)

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.

Measurements of the magnetic field at the four Cluster spacecraft, typically separated by ∼600 km, during bow shock crossings allow the orientation and motion of this structure to be estimated. Results from 48 clean and steady quasiperpendicular crossings during 2000 and 2001, covering local times from 0600 to 1700, reveal the bow shock normal to be remarkably stable, under a wide range of steady upstream conditions. Nearly 80% of normals lay within 10° of those of two bow shock models, suggesting that the timing method is accurate to around 10°, and possibly better, and therefore that four spacecraft timings are a useful estimator of the orientation and motion of quasiperpendicular bow shocks. These results show that models provide a good approximation to the bow shock surface and can therefore be used when four spacecraft data are not available. In contrast, only 19% of magnetic coplanarity vectors were within 10° of the model normal. The mean deviation of the coplanarity vector from the timing‐derived normal for shocks with θ_BN < 70° was 22 ± 4°. Typical shock velocities were ∼35 km s⁻¹, although the fastest measured shock was traveling outbound at nearly 150 km s⁻¹.

We explore the factors that determine the bow shock standoff distance. These factors include the parameters of the solar wind, such as the magnetosonic Mach number, plasma beta, and magnetic field orientation, as well as the size and shape of the obstacle. In this report we develop a semiempirical Mach number relation for the bow shock standoff distance in order to take into account the shock's behavior at low Mach numbers. This is done by determining which properties of the shock are most important in controlling the standoff distance and using this knowledge to modify the current Mach number relation. While the present relation has proven useful at higher Mach numbers, it has lacked effectiveness at the low Mach number limit. We also analyze the bow shock dependence upon the size and shape of the obstacle, noting that it is most appropriate to compare the standoff distance of the bow shock to the radius of curvature of the obstacle, as opposed to the distance from the focus of the object to the nose. Last, we focus our attention on the use of bow shock models in determining the standoff distance. We note that the physical behavior of the shock must correctly be taken into account, specifically the behavior as a function of solar wind dynamic pressure; otherwise, erroneous results can be obtained for the bow shock standoff distance.

The bow shock is created in front of an obstacle immersed into a supersonic flow and its location depends on the size and shape of the obstacle. It was found that the obstacle (magnetopause) is scaled with the solar wind dynamic pressure and changes its dimensions and shape with the dipole tilt angle and interplanetary magnetic field orientation. Similar functional dependencies would be expected for the bow shock position, however, none of the bow shock models considers the parametrization of bow shock properties with the tilt angle. The present study employs a set of bow shock crossings registered during 1994–2002 by different spacecraft and demonstrates the tilt angle influence on the bow shock location. The study is based on a comparison of a recent bow shock model with observations and shows that the night–side bow shock moves in the direction of the positive Z_GSM axis for positive tilt angles. The magnitude of the displacement can reach ≈3 R_E. The analysis reveals that the high–latitude bow shock surface is significantly distorted near the dawn–dusk meridian. This effect was identified as a counterpart of the magnetopause indentation in the cusp region.

We examine seven periods during which IMP 8 made multiple crossings of Earth's bow shock during times when IMP 7 data were available to monitor external solar wind conditions. The positions of the bow shock encounters are consistent with reference shock shape models normalized to the solar wind conditions. We find that multiple crossings can usually be interpreted as being due to changes in the external solar wind parameters. We also find that inward motion of the shock is accompanied by large magnetosheath densities just before the shock sweeps across the spacecraft. We perform a chi‐square minimization analysis using a limited set of Rankine‐Hugoniot conditions across the bow shocks in order to determine their speeds and normals; we find that the shock velocities are generally consistent with the postulated inward and outward bow shock motions. Whether the crossings are observed on the dawnside or the duskside, most of the bow shock structures are quasi‐perpendicular due to changes in the external field orientation just upstream of the shock. The orientations of the normals are consistent with a model in which effects of changes in external conditions propagate as shock shape deformations which move downstream from the nose to the flanks.

The present study examines the interaction of solar wind discontinuities with the Earth's bow shock, using multipoint observations in the magnetosheath by Time History of Events and Macroscale Interactions During Substorms (THEMIS), Cluster, and Double Star TC1. We focus on the deformation and evolution of two discontinuities observed on 21 June 2007, one of which involves a density increase and a magnetic field decrease, while the other is accompanied by a density decrease and a magnetic field increase. In the magnetosheath, the discontinuities are deformed into a concave shape; that is, the normal is inclined toward dusk (dawn) on the dawnside (duskside). The density‐increase (‐decrease) discontinuity is being compressed (expanded) as it propagates in the magnetosheath. We conclude that the compression (expansion) is due to antisunward (sunward) motion of the bow shock which is initiated or enhanced by the impact of the discontinuity on the bow shock. The steepening of B_z reversal followed by an overshoot of the total magnetic field, which appears at the trailing edge of the density‐decrease discontinuity, is also discussed.

Shortly after 0600 UT on 7 April 2000 a tangential discontinuity (TD) in the solar wind passed the Advanced Composition Explorer satellite (ACE). It was characterized by a rotation of the interplanetary magnetic field (IMF) by ∼145° and more than a factor‐of‐2 decrease in the plasma density. About 50 min later, Polar encountered more complex manifestations of the discontinuity near noon in the magnetosheath outside the Northern Hemisphere cusp. On the basis of Polar observations, theoretical modeling, and MHD simulations we interpret the event as demonstrating that (1) a fast mode rarefaction wave was generated during the TD‐bow shock interaction, (2) the fast wave carried a significant fraction of the density change to the magnetopause while the remainder stayed with the transmitted discontinuity, and (3) magnetic merging occurred between IMF field lines within the magnetosheath on opposite sides of the discontinuity's surface as it approached the magnetopause. Before the discontinuity passed the spacecraft, Polar detected ions accelerated antiparallel to B in the fast wave and perpendicular to B in a weak slow mode structure located adjacent to and just downstream of the fast wave. The antiparallel accelerated ions in the fast wave had no measurable ion‐velocity dispersion signature, placing their source a few R_E equatorward of Polar. Simulation results, a Walén test, detections of wave Poynting flux parallel to B, bidirectional electron heat flux, and ion velocity enhancements all indicate that the three ion bursts associated with the passage of the discontinuity were signatures of time‐dependent, magnetic merging events within the magnetosheath.

Global, three‐dimensional, ideal MHD simulations of Earth's bow shock are reported for low Alfven Mach numbers M_A and quasi‐perpendicular magnetic field orientations. The simulations use a hard, infinitely conducting magnetopause obstacle, with axisymmetric three‐dimensional location given by a scaled standard model, to directly address previous gasdynamic (GD) and field‐aligned MHD (FA‐MHD) work. Tests of the simulated shocks’ density jumps X for 1.4 ≲ M_A ≲ 10 and the high M_A shock location, and reproduction of the GD relation between magnetosheath thickness and X for quasi‐gasdynamic MHD runs with M_A ≫ M_S, confirm that the MHD code is working correctly. The MHD simulations show the standoff distance a_s increasing monotonically with decreasing M_A. Significantly larger a_s are found at low M_A than predicted by GD and phenomenological MHD models and FA‐MHD simulations, as required qualitatively by observations. The GD and FA‐MHD predictions err qualitatively, predicting either constant or decreasing a_s with decreasing M_A. This qualitative difference between quasi‐perpendicular MHD and FA‐MHD simulations is direct evidence for a_s depending on the magnetic field orientation θ. The enhancement factor over the phenomenological MHD predictions at M_A ∼ 2.4 agrees quantitatively with one observational estimate. A linear relationship is found between the magnetosheath thickness and X, modified both quantitatively and intrinsically by MHD effects from the GD result. The MHD and GD results agree in the high M_A limit. An MHD theory is developed for a_s, restricted to sufficiently perpendicular θ and high sonic Mach numbers M_S. It explains the simulation results with excellent accuracy. Observational and further simulation testing of this MHD theory, and of its predicted M_A, θ, and M_S effects, is desirable.