A two-temperature model of the intracluster medium

We investigate evolution of the intracluster medium (ICM), considering the relaxation process between the ions and electrons. According to the standar d scenario of structure formation, the ICM is heated by the shock in the ac cretion flow to the gravitational potential well of the dark halo. The shoc k primarily heats the ions because the kinetic energy of an ion entering th e shock is larger than that of an electron by the ratio of masses. Then the electrons and ions exchange the energy through Coulomb collisions and reac h equilibrium. From simple order estimation we find that the region where t he electron temperature is considerably lower than the ion temperature spre ads out on a megaparsec scale. We then calculate the ion and electron tempe rature profiles by combining the adiabatic model of a two-temperature plasm a by Fox & Loeb with spherically symmetric N-body and hydrodynamic simulati ons based on three different cosmological models. It is found that the elec tron temperature is about half the mean temperature at radii similar to 1 M pc. This could lead to about a 50% underestimation in the total mass contai ned within similar to 1 Mpc when the electron temperature profiles are used . The polytropic indices of the electron temperature profiles are similar o r equal to 1.5, whereas those of mean temperature are similar or equal to 1 .3 for r greater than or equal to 1 Mpc. This result is consistent both wit h the X-ray observations on electron temperature profiles and with some the oretical and numerical predictions about mean temperature profiles.