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Context. Shocks are frequently detected by spacecraft in the interplanetary space. However, the in situ data of a shock do not provide direct information on its overall properties even when a following interplanetary coronal mass ejection (ICME) is detected. Aims. The main aim of this study is to constrain the general shape of ICME shocks with a statistical study of shock orientations. Methods. We first associated a set of shocks detected near Earth over 10 years with a sample of ICMEs over the same period. We then analyzed the correlations between shock and ICME parameters and studied the statistical distributions of the local shock normal orientation. Supposing that shocks are uniformly detected all over their surface projected on the 1 AU sphere, we compared the shock normal distribution with synthetic distributions derived from an analytical shock shape model. Inversely, we derived a direct method to compute the typical general shape of ICME shocks by integrating observed distributions of the shock normal. Results. We found very similar properties between shocks with and without an in situ detected ICME, so that most of the shocks detected at 1 AU are ICME-driven even when no ICME is detected. The statistical orientation of shock normals is compatible with a mean shape having a rotation symmetry around the Sun-apex line. The analytically modeled shape captures the main characteristics of the observed shock normal distribution. Next, by directly integrating the observed distribution, we derived the mean shock shape, which is found to be comparable for shocks with and without a detected ICME and weakly a ected by the limited statistics of the observed distribution. We finally found a close correspondence between this statistical result and the leading edge of the ICME sheath that is observed with STEREO imagers. Conclusions. We have derived a mean shock shape that only depends on one free parameter. This mean shape can be used in various contexts, such as studies for high-energy particles or space weather forecasts.

Mean shape of interplanetary shocks deduced from in situ observations and its relation with interplanetary CMEs