Recent III] emission,and Hb line asymmetry. Principal component

Recent studies have derived black hole masses for normaland active galactic nuclei (AGNs) and have attempted torelate them to observable properties. Perhaps the moststriking of these relations is the discovery that the nuclearblack hole mass in normal galaxies is tightly correlated withpn, where p is the velocity dispersion of the bulge of the hostgalaxy and n is in the range 3.75È4.8 (Gebhardt et al. 2000 ;Ferrarese & Merritt 2000). Although the distances to eventhe nearest QSOs preclude the spatially resolved spectros-copy that is the basis for determination of black hole massesfor normal galaxies, other techniques (e.g., reverberationmapping), as well as the presumed extension of the relationbetween black hole mass and host galaxy bulges, permit thecomparison of physical parameters with observable proper-ties for AGNs.Boroson and Green (1992, hereafter BG92) showed thatmost of the variance in the measured optical emission-lineproperties and a broad range of continuum properties(radio through X-ray) in a complete sample of low-redshiftQSOs was contained in two sets of correlations, eigen-vectors of the correlation matrix. Principal component 1(PC1) links the strength of Fe II emission, O III emission,and Hb line asymmetry. Principal component 2 (PC2) pro-jects most strongly on optical luminosity and the strengthof He II j4686 emission. Subsequent studies (see Sulentic etal. 2000 and references therein) have added observedproperties to the list and have, in general, conÐrmed thereality of the correlations.BG92 and others since have tried to understand therelationship between the principal components and thephysical parameters that govern the energy-producing andradiation-emitting processes. As the summary presentationin a conference titled “” Structure and Kinematics of QuasarBroad Line Regions,ÏÏ Gaskell (1999) polled the conferenceattendees on the question, “” What drives Boroson-GreenEigenvector 1 ? ÏÏ The overwhelming consensus was “” donÏtknow,ÏÏ which received 68% of the votes. Of course, the eigenvectors are merely a mathematicalconstruct to describe and to reduce the dimensionality ofthe object-to-object variations. They are orthogonal bydeÐnition, but their relationship to real physical propertiesmay be complex or nonexistent. It is tempting, however, touse them and to explore their relationship to physical pa-rameters because (a) by reducing the dimensionality theyallow models to be parameterized in simpler ways, (b) theylink together diverse properties and provide more robusttests of such models, and (c) they increase the signal-to-noise ratio by allowing the merging of multiple samples.By far the most popular interpretation has been that PC1is highly correlated with L /L , the Eddington ratio. ThisEdd basis for a picture in whichwas put forward by BG92 as thethe vertical structure of the accretion disk, governed by theEddington ratio, drives line strengths and continuum com-ponents through its illumination of broad-line clouds andan extended narrow-line region. Other factors that havebeen discussed as possibly playing a role in the propertiesthat PC1 comprises are black hole spin and orientation.In this paper, we explore the relation between the prin-cipal components that describe the observed properties anddeterminations of the physical properties. We begin byreviewing the observed correlations, including a simplevisualization of the PC1 and PC2 sequences in ° 2. In ° 3, weadopt from the literature methods for determining thephysical properties and attempt to understand PC1 andPC2 in terms of these. In ° 4, these relations are extended toinclude new samples of radio-loud objects, and it is demon-strated that a consistent picture of the relation betweenobservables and physical properties emerges. In ° 5, thispicture is further explored as a context for the classiÐcationof QSOs, including the expected e†ects of orientation. Con-clusions are summarized in ° 6.