Ion-supported tori: A thermal bremsstrahlung model for the X-ray background

We discuss the possibility that a significant contribution to the hard X-ray background is the result of the integrated emission from a population of galaxies undergoing advection-dominated accretion in their nuclei. Owing to poor coupling between ions and electrons and to efficient radiative cooling of the electrons, the accreting plasma is two-temperature, with the ions being generally much hotter than the electrons and forming an ion-supported torus. We show that the electron temperature then saturates at approximate to 100 keV, independent of model parameters. At this temperature the hard X-ray emission can be dominated by bremsstrahlung radiation. A bremsstrahlung model with that temperature gives an excellent fit to the spectrum of the XRB in the 3-60 keV range, provided that there is some evolution associated with the spectral emissivity, which must peak at a redshift similar to 2. The average luminosity of objects implied by such a contribution is high for the model sources, requiring high black hole masses and accretion rates. These constraints are relaxed if the gas is clumped, which is plausible when the accretion rate is close to the critical rate for the formation of an advection-dominated flow. We speculate that the X-ray background is due to an advection-dominated accretion phase which follows the quasar phase for massive black holes.