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

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5. Conclusion

In this paper we have shown how symmetrical field-aligned bow shock flows around a perfectly conducting cylinder and over a perfectly conducting sphere exhibit a complex flow topology in a parameter regime which corresponds closely to the parameter regime for which switch-on shocks are possible. This proves that the complex bow shock topology is indeed closely related to the possible occurrence of switch-on shocks. The topology of the bow shock solution obtained in De Sterck et al. (1998b) and sketched in Fig. 1b is encountered for all the cylinder bow shock flows with parameters in the switch-on domain, and this topology is thus more generally valid than only for the single set of parameters considered in De Sterck et al. (1998b). The shapes, sizes and shock strengths of the shock parts present in the topology of Fig. 1b, vary when [FORMULA] and [FORMULA] are varied in the switch-on regime. The dimple effect is more pronounced for low values of [FORMULA] and [FORMULA].

The parameter study of the cylinder flow and the result for the axi-symmetrical flow over a sphere are extensions of the result presented in De Sterck et al. (1998b). The results on MHD bow shock flows in the switch-on regime of the present paper, together with the detailed discussion of one example of a complex bow shock flow in De Sterck et al. (1998b), form an important extension of the general theory and phenomenology of MHD bow shock flows, with possible applications in space physics (Petrinec & Russell 1997). Fast coronal mass ejections moving away from the sun in the low-[FORMULA] inner corona may induce preceding shock fronts with upstream parameters in the switch-on domain. The solar wind is normally high-[FORMULA], but planetary and cometary bow shocks may have upstream parameters in the switch-on domain when the impinging solar wind occasionally becomes low-[FORMULA] (Steinolfson & Cable 1993). The effects described by our simulations may be important for phenomena in the Earth's magnetosheath (Petrinec & Russell 1997, Song & Russell 1997).

The current 2D results, however, do not complete the theory of MHD bow shocks in the switch-on regime. If we want to relax the condition on field-aligned flow by allowing for a finite angle between the incoming velocity and magnetic field, we have to consider the 3D ideal MHD problem of a stationary flow around a sphere, because in a 2D flow the magnetic flux can not be carried around a cylinder without reconnection when the flow is not field-aligned. In this case the flow will lose some of its symmetries and the stationary solution may be different. It will be interesting to see how the intermediate shocks present in our 2D planar simulation results, would survive in a 3D context which allows for non-planar perturbations. Preliminary results show that also in the 3D case the leading shock front is dimpled and is followed by a second intermediate shock front. This remains subject of further study.

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999