Intergalactic medium: X-ray background and compton parameter

A model of intergalactic medium heated by QSOs and cooled by the expansion of the universe and Compton cooling is studied in the framework of a Friedmann-Robertson-Walker universe. Cosmological evolution functions of the comoving density of QSO's as well as the case of no evolution are considered. The theoretical X-ray background spectrum (through thermal bremsstrahlung) and Comptony parameter are calculated including relativistic corrections in the electron-electron, electron-proton and electron-photon interactions. The observed X-ray background and the upper limit of the Compton parametery cobe given by the COBE satellite are used to adjust, for each value of reheating redshiftsz _c ranging from 0.1 to 5.0, the present values of the temperatureT ₀ and densityn ₀ of the intergalactic gas. Forz _c > 0.25, when the theoretical X-ray spectrum fits the observed one, the adjusted values ofT ₀ andn ₀ imply iny >y cobe. On the other hand, whenT ₀ andn ₀ are consistent withy cobe, the calculated X-ray spectrum is lower than the observed one. Unless 100% of the observed X-ray background is due to discrete sources and if the intergalactic medium contributes more than 2.5% to such background we come to the interesting result that the medium must have been heated atz _c < 1. In this case we shall have to explain the high energy rates necessary to heat the intergalactic medium. Forz _c 0.25, it is possible to find values ofT ₀ andn ₀ such that both the calculated X-ray background and the y parameter simultaneously reproduce the corresponding observed values. However, in this case, unless it could be shown to be otherwise by future observations or theoretical studies, it seems that the model of hot intergalactic medium is not plausible because of the high energies required to heat the intergalactic gas.