Equilibration processes in the warm-hot intergalactic medium

The Warm-Hot Intergalactic Medium (WHIM) is thought to contribute about 40-50% to the baryonic budget at the present evolution stage of the universe. The observed large scale structure is likely to be due to gravitational growth of density fluctuations in the post-inflation era. The evolving cosmic web is governed by non-linear gravitational growth of the initially weak density fluctuations in the dark energy dominated cosmology. Non-linear structure formation, accretion and merging processes, star forming and AGN activity produce gas shocks in the WHIM. Shock waves are converting a fraction of the gravitation power to thermal and non-thermal emission of baryonic/leptonic matter. They provide the most likely way to power the luminous matter in the WHIM. The plasma shocks in the WHIM are expected to be collisionless. Collisionless shocks produce a highly non-equilibrium state with anisotropic temperatures and a large differences in ion and electron temperatures. We discuss the ion and electron heating by the collisionless shocks and then review the plasma processes responsible for the Coulomb equilibration and collisional ionisation equilibrium of oxygen ions in the WHIM. MHD-turbulence produced by the strong collisionless shocks could provide a sizeable non-thermal contribution to the observed Doppler parameter of the UV line spectra of the WHIM.