A model for the origin of the cosmic X-ray background (hereafter XRB) is presented. The component of the background left after subtraction of the known classes of sources is explained by emission from a population of black hole sources at the redshift of z ~ 4-5. The model is presented in more detail elsewhere (Zdziarski 1988). Here, we summarize its most important results. The cosmic X-ray background after subtraction of the estimated contributions of Seyfert galaxies and quasars yields a

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... ual spectrum in the 3-50 keV range, dF -<xE-°*exp(-E/E 0 ), with 23 keV < E 0 < 30 keV and \a x \ £ 0.2 (Leiter and Boldt 1982; Setti 1985) . We study here a hypothesis in which the spectrum (1) is due to the contribution from a population of presently unresolved discrete sources (e.g., Leiter and Boldt 1982). The existence of such a population is suggested by Hamilton and Helfand (1987) , who found that the quasar spatial density is too small to account for the low amplitude fluctuations in the X-ray counts of the Einstein Deep Survey. The spectrum of an individual source contributing to the residual XRB should follow eq. (1) with E 0 = (23-30)(l + z) keV in the rest frame of the source. In the model, the emission of an individual source is due to a turbulent spherical accretion flow (Meszaros 1975) . The gravitational energy is used to heat thermal electrons in the flow and to generate magnetic fields in equipartition with the flow energy density. The emitted spectrum, which is self-consistently solved for, is due to Compton upscattering by the thermal electrons of cyclo-synchrotron photons emitted by the same electrons and partially self-absorbed. The X-ray spectrum is found to have an approximately constant spectral index, a x ~ 0, in the wide range of the dimensionless mass accretion rate of 0.5 i£ m <; 20. Here m = Mc 2 /LE, M is the mass accretion rate, and Xg is the Eddington luminosity. The spectra are cut off above ~ 2kT ~ const ~ 150 keV in the range of m specified above. Such spectra closely resemble that of the residual cosmic XRB if z ~ 4. This stability of the spectral parameters with the changing accretion rate is critical for our model. The approximate constancy of kT ~ 10 2 keV is explained in part by the thermostatic effect of thermal e + e~ pair production (e.g., Leiter and Boldt 1982; Svensson 1984) . The spectral index of ~ 0 is characteristic of saturated Comptonization. The Comptonization process is saturated because of the relative deficiency of the self-absorbed thermal cyclo-synchrotron photons. The model requires that the sources no longer radiate the a x ~ 0 spectrum at z ^ 4. This change of the character of the sources can be associated, for example, with the accretion (1) https://www.cambridge.org/core/terms. https://doi.