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Astron. Astrophys. 343, 641-649 (1999)

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1. Introduction

Shock phenomena are abundant in space physics plasmas. Large-scale flows involving shocks are often modeled as `continuous fluids' and described by the equations of hydrodynamics and magnetohydrodynamics (MHD) (e.g. Petrinec & Russell 1997). Bow shocks are formed when the solar wind encounters comets (e.g. Gombosi et al. 1994, 1996) and planets (e.g. Wu 1992, Tanaka 1993, Song & Russell 1997). Shocks play an important role in the magnetic topology of the heliosphere which interacts with the interstellar wind (e.g. Pogorelov 1995, Pogorelov & Semenov 1997, Linde et al. 1998, Ratkiewicz et al. 1998). Helios 1 spacecraft observations have detected interplanetary shocks which are well correlated with fast solar coronal mass ejections (CMEs) observed by the Solwind coronagraph (Sheeley et al. 1985), and some bright features present in SMM coronagraph images have been interpreted as signatures of shocks induced by fast CMEs (Steinolfson & Hundhausen 1990a, 1990c, Hundhausen 1998).

Hydrodynamic bow shocks around a cylindrical object have the classical form and topology of Fig. 1a, with a single shock front which is concave-inward (to the object). Most MHD bow shocks described in the space physics literature have the same simple shape and topology, but recent numerical simulation results have revealed a MHD bow shock flow which exhibits a more complex shape and topology, for the case of a low inflow plasma [FORMULA] and an inflow Alfvénic Mach number [FORMULA] which corresponds to moderately super-Alfvénic flow. De Sterck et al. (1998b) study the steady state planar ([FORMULA] and [FORMULA]) field-aligned bow shock flow with top-bottom symmetry around a perfectly conducting cylinder for one set of parameters in this parameter domain. They describe a steady state bow shock flow which exhibits a complex multiple-front shape and topology. The bow shock solution is shown in Fig. 2, and the topology of the flow is sketched in Fig. 1b. The leading shock front contains a concave-outward `dimple', and is followed by several other discontinuities. The `dimpling' of shock fronts in a low-[FORMULA] plasma had been observed earlier in time-dependent numerical simulations of CMEs moving faster than the Alfvén speed, and dimpled bright features in coronagraph images have been related to dimpled shock fronts preceding super-Alfvénic CMEs (Steinolfson & Hundhausen 1990a, 1990c, Hundhausen 1998). These effects have to be clearly separated from the observed concave-outward shapes of some slow (sub-Alfvénic) CME fronts, which have been related to the geometrical properties of slow MHD shocks (Steinolfson & Hundhausen 1990b). In this paper we discuss the geometrical shapes of fast (super-Alfvénic) MHD bow shocks.

[FIGURE] Fig. 1a and b. Possible bow shock topologies for a 2D uniform flow (streamlines have arrows) falling in on a cylinder from the left. Shock normals are shown as thin dashed lines. a  Traditional single-front bow shock topology. b  Complex multiple-front bow shock topology which appears for the field-aligned MHD bow shock flow of Fig. 2 with parameters in the switch-on domain.

[FIGURE] Fig. 2. Part of the steady bow shock solution for one set of inflow parameters in the switch-on domain obtained in De Sterck et al. (1998b) (inflow Mach number [FORMULA] and inflow plasma [FORMULA], 120 [FORMULA] 120 grid). We show density contours (piling up in the shocks) and magnetic field lines (coming in horizontally on the left). The flow comes in from the left. The cylinder is situated on the right (thick solid). The leading shock front is slightly dimpled. In the central part of the flow, a second front has separated and is trailing the leading front. Additional discontinuities can be seen in the central interaction region. The topology of the flow is sketched in Fig. 1b. The shocks are fast, hydrodynamic, and intermediate, as discussed in Sect. 2.1.

Theoretical reasoning based on symmetry considerations has proposed the possible occurrence of fast switch-on shocks in a parameter regime which is called the switch-on regime, as an explanation for the occurrence of multiple-front MHD bow shocks and the dimpling of the leading shock front of fast CMEs (Steinolfson & Hundhausen 1990a, 1990c, Hundhausen 1998, De Sterck et al. 1998b). This line of thought will be clarified in Sect. 2.1. This reasoning predicts complex bow shock topologies for all bow shock flows with parameters in the switch-on regime. In the present paper we will verify this prediction.

In the present paper we extend the numerical results of De Sterck et al. (1998b) on MHD bow shock topology in the switch-on regime in two ways. In Sect. 3 we carry out a detailed parameter study of symmetrical planar ([FORMULA] and [FORMULA]) field-aligned bow shock flows around a cylinder. We study how the shape and topology of the bow shock solution which was obtained by De Sterck et al. (1998b) for one particular set of parameters within the switch-on domain, changes when parameters are varied within the switch-on domain and when parameters are taken outside the switch-on domain. In Sect. 4 we present results for the axi-symmetrical field-aligned bow shock flow over a perfectly conducting sphere for a set of parameters in the switch-on domain. The presentation of these results is preceded by a short discussion in Sect. 2 of the properties of MHD shocks and the switch-on regime, and a discussion of the numerical solution technique. Finally, our conclusions are formulated and discussed in Sect. 5.

These extended results on MHD bow shock flows in the switch-on regime, together with the detailed discussion of one example of a complex bow shock flow in De Sterck et al. (1998b), form an extension of the general theory and phenomenology of MHD bow shock flows, with possible applications in space physics (Petrinec & Russell 1997).

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Online publication: March 1, 1999