As one of the first ROSAT surveys, Shanks et al.  have carried out a program of optical spectroscopy of sources detected in a 30 ks PSPC verification phase observation in one of the AAT deep optical QSO fields and could quickly identify an impressive fraction of faint X-ray sources as classical broad-line AGNs (mainly QSOs). Using data from medium-deep ROSAT fields combined with the Einstein medium sensitivity survey, Boyle et al.  could significantly improve on the derivation of the AGN XLF and its cosmological evolution. Their data was consistent with pure luminosity evolution proportional to (1 + z)21 up to a redshift zmax ~ 1.5, similar to what was found previously in the optical range. This result has been confirmed and improved later on by more extensive or deeper studies of the AGN XLF, e.g., the RIXOS project  or the UK deep survey project .
All these studies agree that at most half of the faint X-ray source counts and, correspondingly, half of the soft X-ray background can be explained by classical broad-line AGN based on the luminosity evolution models. There was, indeed, mounting evidence that a new class of sources might start to contribute to the XRB at faint X-ray fluxes. The faintest X-ray sources in ROSAT deep surveys on average show a harder spectrum than the identified QSOs [2, 31]. In medium-deep pointings a number of optically "innocent" narrow-emission line galaxies (NELGs) at moderate redshifts (z < 0.4) were identified as X-ray sources, which was in excess of those expected from spurious identifications with field galaxies . Roche et al.  have found a significant correlation of X-ray fluctuations with optically faint galaxies. Finally, in an attempt to push optical identifications to the so far faintest X-ray fluxes, McHardy et al.  claimed that broad-line AGN practically cease to exist at fluxes below 5 x 10~15 erg cm~2 s~\ while the NELG number counts still keep increasing, so that they would dominate below a flux of 10~15 erg cm~2 s^1.
While this is obviously an interesting possibility, it is useful to remind that these results were only statistical in nature. All these findings were based on identifications near the limit of deep PSPC surveys, at fluxes where our simulations suggested that the PSPC data start to be severely confused. Because moderate-redshift field galaxies almost all show emission lines , there is the possibility to either misidentify a field galaxy as the counterpart of an X-ray source, which in reality is associated to a different optical object (e.g., a fainter AGN) or to misclassify an intrinsically faint AGN hidden in a NELG-type spectrum as a new class of X-ray sources. (Later Chandra observations confirmed, that both problems indeed existed.) On the contrary, the X-ray positions in the ultradeep Lockman Hole survey were largely determined by the HRI raster scan and ultradeep pointing. Instead of confused PSPC error boxes of (realistically) 15-20 arcsec radius, they therefore had error box radii of 2-5 arcsec.
Using optical spectroscopy from the Keck telescopes, the optical identifications in the Lockman Hole could be completed down to a flux limit of 1 . 2 x 10-15 ergcm~2 s^1 in 0.5-2.0keV energy band [44,73]. Nearly complete spectroscopic identifications (90%) of the sample of 94 X-ray sources were presented based on low-resolution Keck spectra. In this survey, which has one of the highest rates of optical identifications among existing deep X-ray surveys and has a high degree of reliability, no evidence for the emergence of a new non-AGN source population at low X-ray fluxes was found. However, the identified type-II AGN provided the first glimpse of the missing source population to explain the hard X-ray background spectrum. Using a set of ROSAT surveys with a large range of flux limit and solid angle coverage, Miyaji et al.  have determined a state of the art X-ray luminosity function and its cosmological evolution.
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