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6.1. Line Profile Issues

Another means of investigating the BE and its underlying physics is to examine the luminosity dependence of emission as a function of velocity within the line profile. OPG examined difference spectra between high- and low-luminosity composites, and demonstrated that most of the variation in equivalent widths stems from changes in the strength of the line core. Another way of stating this result is that the variable component has a full-width at half maximum (FWHM) that is narrower than the overall profile. This finding bears an intriguing similarity to the results of the PCA analysis of FHFC, which found that most of the variance in quasar line strengths (as quantified in their first principal component) derived from modulations in the emission line cores (6) . The role of the core, or ``intermediate line region'' (ILR; Wills et al. 1993a) component in this regard is also suggested by significant negative correlations in QSO spectra between line velocity width and equivalent width (e.g., Francis et al. 1993; Wills et al. 1993a; Brotherton et al. 1994b). Detailed models of the ILR (Wills et al. 1993a; Brotherton et al. 1994a) predict only weak contributions to the Hbeta and lambda1400 features, consistent with the little evidence for a BE in these lines (Section 3.1).

Understanding the BE as purely a line-core phenomenon is not without complications, however. FHFC used their PCA eigenvectors to explore the relative contributions of line cores and wings to the BE, and found that the wings acted as an important contributor to the BE. Additional evidence for a BE in the line wings has been presented by Francis & Koratkar (1995), who argued that the red wing of C IV in particular displayed a luminosity dependence (see also Corbin & Boroson 1996). A common thread throughout these studies, however, is that the strength of the BE (i.e. fractional change in Wlambda) is greater for the line core than for the line wings, in general accord with the results from OPG.

If we take the link between line core variation and the BE at face value, this finding may have important theoretical consequences. If the BE is ultimately a consequence of the luminosity dependence of the continuum SED in QSOs (Section 3.2), it is perhaps surprising that the line core and wings do not show comparable response to continuum hardness variations. This result may point to rather specific distributions of cloud properties as a function of radius, if the velocity field of the BLR is Keplerian (e.g., Brotherton et al. 1994a). Korista et al. (1997a) have published a grid of BLR Wlambda predictions as a function of continuum SED and cloud properties, which might be explored for this purpose; our brief inspection of their figures did not lead to an obvious prescription for matching the observations, however. An alternative solution might entail anisotropic continuum emission such that different cloud components within the BLR see a different ionizing SED. While this represents a more complicated scenario, it would not be altogether surprising in light of analyses implying that the ionizing continuum incident on the BLR clouds is not the same as what we see (Korista et al. 1997b) - which opens up more general worries concerning the validity of invoking a luminosity-dependent SED, derived from measurements, for explaining the BE.

Finally, while the line core strength may be fundamental to defining the BE, it is important to recognize that there is considerable variation in the cores, and the overall line strengths, which is apparently unrelated to source luminosity. These variations thus appear as scatter in the Baldwin diagrams; physically this range of behavior may trace differences in orientation or structure of the BLR and continuum source. The extent to which core modulation and the BE are in fact distinct phenomena is suggested by the properties of the first eigenvector identified in the PCA analysis by FHFC. In comparison with the other eigenvectors, this component features strong, relatively narrow emission lines, described by a large Lyalpha / C IV ratio. As a result, when this component weakens, the line cores and overall equivalent widths diminish, which would be consistent with the trend with increasing luminosity seen in the BE; but the diminution of this component is accompanied by a decrease in the composite Lyalpha / C IV ratio, which runs counter to the observed correlation with L (Section 3.2). While the FHFC first eigenvector may capture much of the variance in QSO spectra, other parameters clearly come into play in establishing their luminosity-dependent behavior.

6 A PCA analysis of IUE spectra for variable Seyfert nuclei revealed a quite different behavior, with the line wings showing the strongest fluctuations (Türler & Courvoisier 1998). The contrasting behavior of the intrinsically variable sources can probably be attributed to the strong influence of light travel-time effects on the response across the line profile. Back.

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