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 individual mapped QSOs, in order to give one more clearer
conclusion on the so far conflicting dependence of the spectral index on the
luminosity for AGN. Different from the global relationships based on the color
difference (photometry parameters) for samples of AGN, the more reliable
relationship is determined for the multi-epoch observed individual mapped QSOs
with no contamination from the host galaxies, the line variabilities and the
much different central properties. The final confirmed results are as follows.
(1): No strong dependence of the optical spectral index on the continuum
luminosity can be found for all the 17 QSOs, besides two objects (PG 0026 and
PG 1613) having some weak trends (with $3\sigma$ confidence level) for the
relationship. In other words, the common sense 'AGNs get bluer when they get
brighter' is not so common. (2): There are much 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 weak dependence of the
optical spectral index on the continuum luminosity can be further confirmed.
