Three‐dimensional position and shape of the bow shock and their variation with Alfvénic, sonic and magnetosonic Mach numbers and interplanetary magnetic field orientation

Abstract

A large set of bow shock crossings (i.e., 1392) observed by 17 spacecraft has been used to explore the three-dimensional shape and location of the Earth's bow shock and its dependence on solar wind and interplanetary magnetic field (IMF) conditions. This study investigates deviations from gas dynamic flow models associated with the magnetic terms in the magnetohydrodynamic (MHD) equations. Empirical models predicting the statistical position and shape of the bow shock for arbitrary values of the solar wind pressure, IMF, and Alfv6nic Mach number (MA) have been derived. Individual crossings have been rotated into aberrated GSE coordinates to remove asymmetries associated with the earth's orbital •r•otion. Variations due to changes in solar wind dynamic pressure have been taken into consideration by normalizing the observed crossings to the average value (p) = 3.1 nPa. The resulting data set has been used to fit three-dimensional bow shock surfaces and to explore the variations in these surfaces with sonic (Ms), Alfv6nic (MA) and magnetosonic (MMS) Mach numbers. Analysis reveals that among the three Mach numbers, MA provides the best ordering of the least square bow shock curves. The subsolar shock is observed to move Earthward while the flanks flare outward in response to decreasing MA; the net change represents a 6-10% effect. Variations due to changes in the IMF orientation were investigated by rotating the crossings into geocentric interplanetary medium coordinates. Past studies have suggested that the north-south extent of the bow shock surface exceeds the east-west dimension due to asymmetries in the fast mode Mach cone. This study confirms such a north-south versus east-west asymmetry and quantifies its variation with M S, M A, MMS, and IMF orientation. A 2-7% effect is measured, with the asymmetry being more pronounced at low Mach numbers. Combining the bow shock models with the magnetopause model of Roelof and Sibeck (1993), variations in the magnetosheath thickness at different local times are explored. The ratio of the bow shock size to the magnetopause size at the subsolar point is found to be 1. 46; at dawn and dusk, the ratios are found to be 1.89 and 1.93, respectively. The subsolar magnetosheath thickness is used to derive the polytropic index y according to the empirical relation of Spreiter et al. (1966). The resulting y = 2.3 suggests the empirical formula is inadequate to describe the MHD interaction between the solar wind and the magnetosphere. Greenstadt, et al., 1990]. An essential point revealed by many of the previous investigations is that the bow shock formed upstream of the Earth is a highly dynamic boundary, controlled by steady and transient variations in solar wind characteristics. To date, Fairfield's [1971] model enjoys perhaps the widest use as representative of the average shape and position of the bow shock. Fairfield's model, however, is based only on observations made near the ecliptic plane; thus the model is two-dimensional in that it assumes axial symmetry about the solar wi...

Response of neutral atom emissions in the low‐latitude and high‐latitude magnetosheath direction to the magnetopause motion under extreme solar wind conditions

“…The latter dimension is in line with results from Peredo et al [1995]. The shape between these two points is approximated with a second-order polynomial function.…”

Bow shock specularly reflected ions in the presence of low-frequency electromagnetic waves: a case study

“…They found that the Earth's bow shock shape is well represented by an eccentric conic when taking into account the variations of the solar wind dynamical pressure. A more extensive study using data from 17 different spacecraft was reported by Peredo et al (1995). This uses a 3-D bow shock shape, and includes the effects of solar wind variations parameterized by the sonic M S , Alfvènic M A and magnetosonic M MS Mach Numbers, as well as the orientation of the IMF direction.…”

“…For comparison purposes, we use the Farris et al (1991), Cairns et al (1995), and Slavin and Holzer (1981) models. We do not use the recent Peredo et al (1995) model because it has been shown to overestimate the bow shock stand-off position by as much as 20% (Merka et al, 2003). Table 2 lists the distance from the bow shock along the magnetic field direction and θ Bn0 as obtained from the three bow shock models mentioned above.…”

Impact of solar wind depression on the dayside magnetosphere under northward interplanetary magnetic field

“…The plasma parameter is β ∼ 0.35 with a critical Mach number ∼2.3 (Edmiston and Kennel, 1984). For this set of plasma parameters, the Earth's bow shock positions along the OX and OY axis are expected from observations at ∼(14.8 R E , 29 R E ) respectively (Peredo et al, 1995). The magnetopause is expected around ∼10.6 R E along the nose direction (Peredo, 1995;Merka, 2005).…”