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Aims: Bow shock waves are a common feature of groups and clusters of galaxiessince they are generated as a result of supersonic motion of galaxies throughthe intergalactic medium. The goal of this work is to present an analyticalsolution technique for such astrophysical hypersonic blunt body problems.Methods: A method, developed by Schneider (1968, JFM, 31, 397) in the contextof aeronautics, allows calculation of the galaxy's shape as long as the shapeof the bow shock wave is known (so-called inverse method). In contrast to otheranalytical models, the solution is valid in the whole flow region (from thestagnation point up to the bow shock wings) and in particular takes intoaccount velocity gradients along the streamlines. We compare our analyticalresults with two-dimensional hydrodynamical simulations carried out with anextended version of the VH-1 hydrocode which is based on the piecewiseparabolic method with a Lagrangian remap. Results: It is shown that the appliedmethod accurately predicts the galaxy's shape and the fluid variables in thepost-shock flow, thus saving a tremendous amount of computing time for futureinterpretations of similar objects. We also find that the method can be appliedto arbitrary angles between the direction of the incoming flow and the axis ofsymmetry of the body. We emphasize that it is general enough to be applied toother astrophysical bow shocks, such as those on stellar and galactic scales.

Astrophysical bow shocks: An analytical solution for the hypersonic blunt body problem in the intergalactic medium