Spectral Classification of Quasars in the Sloan Digital Sky Survey: Eigenspectra, Redshift, and Luminosity Effects

We study 16,707 quasar spectra from the SDSS using the Karhunen-Lo\`eve (KL)transform (or Principal Component Analysis, PCA). The quasar eigenspectra ofthe full catalog reveal the following: 1st order - the mean spectrum; 2nd order- a host-galaxy component; 3rd order - the UV-optical continuum slope; 4thorder - the correlations of Balmer emission lines. We find that the spectralclassification of quasars is redshift and luminosity dependent, as such theredoes not exist a compact set (< 10 modes) of eigenspectra (covering 900 to 8000angstrom) which can describe most variations (> 95%) of the entire catalog. Wetherefore construct several sets of eigenspectra in different redshift andluminosity bins. From these eigenspectra we find that quasar spectra can beclassified (by the first two eigenspectra) into a sequence that is defined by asimple progression in the steepness of the slope of the continuum. We also finda dependence on redshift and luminosity in the eigencoefficients. The dominantredshift effect is a result of the evolution of the blended FeII emission(optical) and the Balmer continuum (the ``small bump''). A luminositydependence is also present in the eigencoefficients and is related to theBaldwin effect. The eigenspectra constructed from the wavelength-selected SDSSspectra are found to agree with the principal components by Francis et al.(1992) and the well-known ``Eigenvector-1'' (Boroson and Green 1992).(Abridged)Comment: AJ accepted. 65 pages, 27 figures, 9 tables. Resolutions of some figures are lowere