Several models for the hard X-ray Background ( XRB ) suggest that it is due to the emission from heavily obscured AGN .
Recent studies have revealed the presence of a new population of hard X-ray sources which must contribute significantly to the XRB .
However , whether the majority of these sources are obscured AGN or some other type of object at present remains unclear .
Here , we further examine the possibility that a significant fraction of the XRB comes from a population of galaxies undergoing advection-dominated accretion in the high– \dot { m } regime and thus produce intrinsically hard spectra .
When the accretion rate is close to \dot { m } _ { crit } , above which an advection–dominated accretion flow ( ADAF ) no longer exists , the major contribution to X-ray emission is due to inverse Compton scattering of the soft seed photons produced by cyclo–synchrotron radiation .
In this regime , the resulting ADAF spectra are relatively hard with a fairly constant X-ray spectral index \alpha \sim 0.2 - 0.4 and a spectral cut-off at \sim 200 { \thinspace keV } .
We show that the integrated emission from such sources can provide a good fit to the hard ( > 2 { \thinspace keV } ) X-ray background , provided that the spectrum is dominated by the contribution from objects located at redshifts z \sim 2 - 3 .
The model requires most of the contribution to the XRB to be due to objects accreting at \hbox { $ \dot { m } $ } _ { crit } .