We demonstrate that all properties of the hot X-ray emitting gas in galaxy clusters are completely determined by the underlying dark matter (DM) structure. Apart from the standard conditions of spherical symmetry and hydrostatic equilibrium for the gas, our proof is based on the Jeans equation for the DM and two simple relations which have recently emerged from numerical simulations: the equality of the gas and DM temperatures, and the almost linear relation between the DM velocity anisotropy profile and its density slope. For DM distributions described by the NFW or the Sersic profiles, the resulting gas density profile, the gas-to-total-mass ratio profile, and the entropy profile are all in good agreement with X-ray observations. All these profiles are derived using zero free parameters. Our result allows us to predict the X-ray luminosity profile of a cluster in terms of its DM content alone. As a consequence, a new strategy becomes available to constrain the DM morphology in galaxy clusters from X-ray observations. Our results can also be used as a practical tool for creating initial conditions for realistic cosmological structures to be used in numerical simulations.
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