MHD simulations of Earth's bow shock: Interplanetary magnetic field orientation effects on shape and position

Abstract

[1] The location and geometry of Earth's bow shock vary considerably with the solar wind conditions. More specifically, Earth's bow shock is formed by the steepening of fast mode waves, whose speed v ms depends upon the angle q bn between the local shock normal n and the magnetic field vector B IMF , as well as the Alfvén and sound speeds (v A and c S ). Since v ms is a minimum for q bn = 0°and low Alfvén Mach number M A , and maximum for q bn = 90°and high M A , this implies that as q IMF (the angle between B IMF and v sw ) varies, the magnitude of v ms should vary also across the shock, leading to changes in shape. This paper presents 3-D MHD simulation data which illustrate the changes in shock location and geometry in response to changes in q IMF and M A , for 1.4 M A 9.7 and 0° q IMF 90°. Specifically, for oblique IMF the shock's geometry is shown to become skewed in planes containing B IMF (e.g., the x À z plane). This is also emphasized in the terminator plane data, where the shock is best represented by ellipses, with centers translated along the z axis. For the q IMF = 90°simulations the shock is symmetric about the x axis in both the x À y and x À z planes. Simulations for fieldaligned flow (q IMF = 0°) show a dimpling of the nose of the shock as M A ! 1. The simulations also illustrate the general movement of the shock in response to changes in M A ; high M A shocks are found closer to Earth than low M A shocks. Farris et al. 's [1991] magnetopause model is used in the simulations, and we discuss the limitations of this, as well as the expected results using a self-consistent model.

The dipole tilt angle dependence of the bow shock for southward IMF: MHD results

“…The Earth's bow shock is created by interaction of the supersonic and superalfvenic solar wind with the magnetospheric obstacle; its location and shape depend on the properties of the upstream solar wind, as well as the size and shape of the downstream magnetopause (e.g., Spreiter et al, 1966;Fairfield, 1971;Slavin and Holzer, 1981;Slavin et al, 1996;Němeček and Šáfranková, 1991;Farris and Russell, 1994;Cairns et al, 1995;Cairns and Lyon, 1996;Peredo et al, 1995;Petrinec and Russell, 1997;Verigin et al, 2003;Dmitriev et al, 2003;Chapman et al, 2004;Jelínek et al, 2008Jelínek et al, , 2012. As many studies indicate that the solar wind dynamic pressure (P d ) and interplanetary magnetic field (IMF) are the two main parameters defining the global structure of the magnetopause (e.g., Martyn, 1951;Ferraro, 1960;Fairfield, 1971;Coroniti and Kennel, 1972;Roelof and Sibeck, 1993;Shue et al, 1997Shue et al, , 1998Lu et al, 2010;Jelínek et al, 2012;Wang et al, 2014), the position and the shape of the Earth's bow shock are primarily controlled by solar wind dynamic pressure (P d ), upstream Mach number(s), and the orientation of the interplanetary magnetic field (IMF) (e.g., Chao et al, 2002;Chapman and Cairns, 2003;.…”

“…The upstream solar wind Mach number dependencies of the bow shock have been analyzed extensively, demonstrating that the bow shock approaches the Earth in response to an increase in the magnetosonic Mach number (M MS ) in most models (e.g., Farris and Russell, 1994;Verigin et al, 2001a;Chao et al, 2002). The interplanetary magnetic field (IMF) and its orientation is another parameter commonly used in bow shock models (e.g., Spreiter and Rizzi, 1974;Slavin et al, 1984Slavin et al, , 1996de Sterck et al, 1998;Kabin, 2001;Chao et al, 2002;Verigin et al, 2003;Chapman et al, 2004;Merka et al, 2003 the M MS has a small value and the shock should be farther from the Earth; while B IMF is parallel to the shock wave normal direction, the M MS is larger and a more Earthward shock can be observed. On the other hand, the interplanetary magnetic field can affect the bow shock by influencing the magnetopause obstacle.…”

Modeling of Earth's bow shock: Applications

“…For the Interball crossings the spacecraft was at the rotated coordinates (19.2, 14.6, 0.0) R E and (16.2, −4.3, 1.5) R E at hours 24.9 and 62.3, with M A = 2.9 and 4.0 and θ IMF = 27 and 94, respectively. The first Interball crossing is predicted early at hour 22, not inconsistent with the simulations showing smaller a s for smaller θ IMF [ Chapman et al , 2004]. The second crossing is predicted within 1 R E by all models.…”

“…To test the models against observed bow shock crossings, the spacecraft positions are rotated into a coordinate system in which the new x axis lies along the solar wind vector and the new z axis is defined so that B IMF lies in the x ‐ z plane. This system is defined using the observed solar wind conditions and IMF vectors and is identical to the coordinate system in the simulations of Cairns and Lyon [1995] and Chapman et al [2004], as well as in the CC2003 models presented in section 2.…”

“…An additional result is that the shock's symmetry axis tilts away from the nominal direction (along v sw ) for θ IMF = 45° but not for θ IMF = 90°, with these effects becoming increasingly prevalent as M A → 1. More recently, additional simulations were performed for several IMF orientations in the ranges 20° ≤ θ IMF ≤ 60° and 1.4 ≤ M A ≤ 9.7 [ Chapman et al , 2004]. They showed that strong skewing effects were larger for lower M A , with the shock becoming increasingly asymmetric.…”