We have carried out a fluctuation analysis in four bands ( R4 , R5 , R6 and R7 corresponding to 0.44-1.01 keV , 0.56-1.21 keV , 0.73-1.56 keV and to 1.05-2.04 keV respectively ) of two very deep ROSAT PSPC observations in directions where the galactic H I column is minimal .
This has enabled us to study the average spectrum of the sources contributing to 0.5-2 keV fluxes \sim 10 ^ { -15 } erg { cm } ^ { -2 } { s } ^ { -1 } .
The best fit spectral energy index for the average faint source spectrum , \alpha = 0.95 ^ { +0.10 } _ { -0.15 } , is still steeper than the one measured for the extragalactic XRB at these energies \alpha \sim 0.4 - 0.7 , but flatter than the typical AGN spectral index \alpha \sim 1 - 1.5 .
This result has allowed us to constrain the existence of a population of sources harder than the AGNs contributing to the source counts at these fluxes .
We find that a population of X-ray sources with energy spectral index \alpha \sim 0.4 - 0.6 would contribute ( 30 \pm 20 ) per cent to the source counts at these fluxes if the rest of them are AGNs with energy spectral index \alpha \sim 1.2 .