2007MNRAS.377.1113T

We critically examine the dependence of spectral index on luminosity in optically selected AGN samples. An analysis of optically selected high-z quasars showed an anticorrelation of α_OX, the spectral index between the rest-frame 2500 Å and 2 keV, with optical luminosity. We examine this relationship by means of Monte Carlo simulations and conclude that a constant α_OX independent of optical luminosity is still consistent with this high-z sample. We further find that contributions of large dispersions and narrow range of optical luminosity are most important for the apparent, yet artificial, α_OX-l_o correlation reported. We also examine another, but more complete, low-z optical selected AGN sub-sample from Steffen et al., and our analysis shows that a constant α_OX independent of optical luminosity is also consistent with the data. By comparing X-ray and optical luminosity functions, we find that a luminosity-independent α_OX is in fact more preferred than the luminosity-dependent α_OXmodel. We also discuss the selection effects caused by flux limits, which might systematically bias the l_X-l_o relation and cause discrepancy in optically selected and X-ray selected AGN samples. To correctly establish a dependence of α_OX of AGNs on their luminosity, a larger and more complete sample is needed and consequences of luminosity dispersions and selection effects in flux-limited samples must be taken into account properly.