Optical spectral index-luminosity relation for the 17 mapped Palomar-Green quasars

In this paper, the optical spectra index-luminosity relationship is checked for the well-known 17 individually mapped quasi-stellar objects (QSOs), in order to give one more clearer conclusion on the so far conflicting dependence of the spectral index on the luminosity for an active galactic nucleus (AGN). Unlike the global relationships based on the colour difference (photometry parameters) for samples of AGNs, a more reliable relationship is determined for the multi-epoch observed individually mapped QSOs with no contamination from the host galaxies, the line variabilities and the very different central properties. The final confirmed results are as follows. (i) No strong dependence of the optical spectral index on the continuum luminosity can be found for all 17 QSOs, besides two objects (PG 0026 and PG 1613) that have some weak trends (with 3 Sigma confidence level) for the relationship. In other words, the common expectation that 'AGNs get bluer when they get brighter' is not so common. (ii) There are very different damped intrinsic variability time-scales for the variability modes of the optical spectral index and the continuum emission, through the well-applied damped random walk method for the AGN variability. In other words, there are some different intrinsic mechanisms controlling the variabilities of the optical spectral index and the power-law AGN continuum emission. Therefore, the much weaker dependence of the optical spectral index on the continuum luminosity can be further confirmed.