Is the dependence of spectral index on luminosity real in optically selected AGN samples?

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 OX model. 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.