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

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