We present the results of two-temperature magnetohydrodynamic simulations of the propagation of sub-relativistic jets of active galactic nuclei. The dependence of the electron and ion temperature distributions on the fraction of electron heating fe at the shock front is studied for fe=0, 0.05, and 0.2. Numerical results indicate that in sub-relativistic, rarefied jets, the jet plasma crossing the terminal shock forms a hot, two-temperature plasma in which the ion temperature is higher than the electron temperature. The two-temperature plasma expands and forms a backflow referred to as a cocoon, in which the ion temperature remains higher than the electron temperature for longer than 100 Myr. Electrons in the cocoon are continuously heated by ions through Coulomb collisions, and the electron temperature thus remains at Te > 10^9 K in the cocoon. X-ray emissions from the cocoon are weak because the electron number density is low. Meanwhile, soft X-rays are emitted from the shocked intracluster medium surrounding the cocoon. Mixing of the jet plasma and the shocked intracluster medium through the Kelvin--Helmholtz instability at the interface enhances X-ray emissions around the contact discontinuity between the cocoon and shocked intracluster medium.
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