A deep ROSAT survey XV. the average QSO spectrum and its evolution
  Using a sample of 165 X-ray selected QSOs from seven deep ROSAT fields we investigate the X-ray spectral properties of an ``average''radio-quiet broad line QSO as a function of redshift. The QSO stacked spectra, in the observers 0.1-2 keV band, in five redshift bins over the range 0.1<z<3.2 apparently harden from an equivalent photon index of 2.6 at z=0.4 to ~2.1 at z=2.4 as seen in other QSO samples. In contrast, the spectra in the 0.5-2 keV band show no significant variation in spectral index with redshift. This suggests the presence of a spectral upturn at low energies (<0.5 keV). Indeed, while at high redshifts (z>1.0) the single power-law model gives an acceptable fit to the data over the full energy band, at lower redshifts the spectra need a second component at low energies, a `soft excess'. Inclusion of a simple model for the soft excess, i.e. a black-body component (kT~100 eV), results in a significant improvement to the model fit, and yields power-law slopes of 1.8-1.9, for all redshift bins. This power-law is not inconsistent, within the error bars, with those of nearby AGN in the 2-10 keV band, suggesting that the same intrinsic power-law slope may continue from 10 keV down to below 0.5 keV. We caution that there is a possibility that the spectral upturn observed may not represent a real physical component but could be due to co-adding spectra with a large dispersion in spectral indices. Regardless of the origin of the soft excess, the average QSO spectrum has important consequences for the origin of the X-ray background: the average spectra of the typical, faint, high redshift QSO are significantly steeper than the spectrum of the X-ray background extending the spectral paradox into the soft 0.1-2 keV X-ray band. 
A.J. Blair, G.C. Stewart, I. Georgantopoulos, B.J. Boyle, R.E.   Griffiths, T. Shanks, O. Almaini