The deepest extragalactic X-ray observation , the 2 Ms Chandra Deep Field North ( CDF-N ) , resolves \sim 80 % of the total extragalactic cosmic X-ray background ( CXB ) in the 1–2 keV band .
Recent work has shown that 70 % of the remaining CXB flux is associated with sources detected by the Hubble Space Telescope ( HST ) .
This paper uses the existing CDF-N data to constrain the X-ray flux distribution of these X-ray-undetected HST sources by comparing the number of 0.5–2 keV X-ray counts at the HST positions to those expected for model flux distributions .
In the simple case where all the undetected HST X-ray sources have the same 0.5–2 keV flux , the data are best fit by 1.5–3 counts per source in 2 Ms , compared to a detection limit ( at 10 % completeness ) of 9 counts .
Assuming a more realistic power-law \log { N } - \log { S } distribution [ N ( > S ) \propto S ^ { - \alpha } ] , the data favor a relatively steep flux distribution , with \alpha = 1.1 ^ { +0.5 } _ { -0.3 } ( limits are 99 % confidence ) .
This slope is very similar to that previously found for faint normal and starburst galaxies in the CDF-N .
These results suggest deeper Chandra observations will detect a new population of faint X-ray sources , but extremely deep exposures are needed to resolve the remainder of the soft CXB .
In the most optimistic scenario , when the HST sources have the flattest allowed flux distribution and all the sources without HST counterparts are detected , observations 5 times more sensitive than the existing ones would resolve at most \sim 60 % of the remaining soft CXB .