  The existence of dark matter can be proved in an astrophysical context by the
discovery of a system in which the observed baryons and the inferred dark
matter are spatially segregated, such as the bullet cluster (1E0657-558). The
full descriptions of the dark matter halo and X-ray gas substructure motions
are necessary to forecast the location of the dark halo from X-ray maps, which
can be confirmed by the detection of a galaxy concentration or by gravitational
lensing. We present an analytical hydrodynamic model to determine the distance
between the X-ray and dark-matter components and the Mach number of the merger
shock. An approximate solution is given for the problem of the substructure
propagation in merging clusters. A new method to predict the position of a dark
matter halo in clusters, where there is a separation between the X-ray gas and
the dark halo, is proposed and applied to the clusters 1E0657-558 and Abell
1763.
