We investigate the formation of spherical cosmological structures following both dark matter and gas components .
We focus on the dynamical aspect of the collapse assuming an adiabatic , \gamma = 5 / 3 , fully ionized primordial plasma .
We use for that purpose a fully Lagrangian hydrodynamical code designed to describe highly compressible flows in spherical geometry .
We investigate also a “ fluid approach ” to describe the mean physical quantities of the dark matter flow .
We test its validity for a wide range of initial density contrast .
We show that an homogeneous isentropic core forms in the gas distribution , surrounded by a self-similar hydrostatic halo , with much higher entropy generated by shock dissipation .
We derive analytical expressions for the size , density and temperature of the core , as well as for the surrounding halo .
We show that , unless very efficient heating processes occur in the intergalactic medium , we are unable to reproduce within adiabatic models the typical core sizes in X-ray clusters .
We also show that , for dynamical reasons only , the gas distribution is naturally antibiased relative to the total mass distribution , without invoking any reheating processes .
This could explain why the gas fraction increases with radius in very large X-ray clusters .
As a preparation for the next study devoted to the thermodynamical aspect of the collapse , we investigate the initial entropy level required to solve the core problem in X-ray clusters .