3-DIMENSIONAL POSITION AND SHAPE OF THE BOW SHOCK AND THEIR VARIATIONWITH ALFVENIC, SONIC AND MAGNETOSONIC MACH NUMBERS AND INTERPLANETARYMAGNETIC-FIELD ORIENTATION

A large set of bow shock crossings (i.e., 1392) observed by 17 spacecr aft has been used to explore the three-dimensional shape and location of the Earth's bow shock and its dependence on solar wind and interpla netary magnetic field (IMF) conditions. This study: investigates devia tions from gas dynamic flow models associated with the magnetic terms in the magnetohydrodynamic (MHD) equations. Empirical models predictin g the statistical position and shape of the bow shock for arbitrary va lues of the solar wind pressure, IMF, and Alfvenic Mach number (M(A)) have been derived. Individual crossings have been rotated into aberrat ed GSE coordinates to remove asymmetries associated with the earth's o rbital motion. Variations due to changes in solar wind dynamic pressur e have been taken into consideration by normalizing the observed cross ings to the average value [p] = 3.1 nPa. The resulting data set has be en used to fit three-dimensional bow shock surfaces and to explore the variations in these surfaces with sonic (M(S)), Alfvenic (M(A)) and m agnetosonic (M(MS)) Mach numbers. Analysis reveals that among the thre e Mach numbers, M(A) provides the best ordering of the least square bo w shock curves. The subsolar shock is observed to move Earthward while the flanks flare outward in response to decreasing M(A); the net chan ge represents a 6-10% effect. Variations due to changes in the IMF ori entation were investigated by rotating the crossings into geocentric i nterplanetary medium coordinates. Past studies have suggested that the north-south extent of the bow shock surface exceeds the east-west dim ension due to asymmetries in the fast mode Mach cone. This study confi rms such a north-south versus east-west asymmetry and quantifies its v ariation with M(S), M(A), M(MS), and IMF orientation. A 2-7% effect is measured, with the asymmetry being more pronounced at low Mach number s. Combining the bow shock models with the magnetopause model of Roelo f and Sibeck (1993), variations in the magnetosheath thickness at diff erent 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 inde x gamma according to the empirical relation of Spreiter et al. (1966). The resulting gamma = 2.3 suggests the empirical formula is inadequat e to describe the MHD interaction between the solar wind and the magne tosphere.