4.2. Second Order Effects

While the BE is usually parametrized quantitatively by the slope of a straight line in the log W - log L diagram, there is considerable evidence suggesting that curvature exists within the Baldwin trends. The sense of this behavior is that the BE exhibits a steeper slope at higher luminosities (e.g., Véron-Cetty et al. 1983; Wu et al. 1983; KRK; OPG). The flattening at low luminosities has resulted in suggestions by some authors that Seyfert nuclei do not participate in the BE, but instead have equivalent widths independent of luminosity (e.g., Wampler et al. 1984). Discerning luminosity-dependent behavior within Seyfert ensembles is again complicated by substantial scatter about any underlying trend, with much of the dispersion stemming from intrinsic variability (e.g., KRK). What seems clear from existing studies, however, is that Seyferts connect smoothly with QSOs in the Baldwin diagrams; when all luminosities are considered together, the BE displays strong indications of curvature, although we note that quantitative measures of this curvature will depend at some level on the choice of cosmology (q₀, H₀) for calculation of quasar luminosities.

The causes of curvature in the BE remain uncertain. Wamsteker & Colina (1986) noted the similarity between curvature in the BE and a similar curvature (i.e. nonlinear response; Section 5.1) in the Baldwin diagrams for individual variable sources. They argued that both phenomena could be interpreted as the result of a transition of the BLR to a matter-bounded state for luminous sources. While matter-bounded nebular components may well contribute to curvature in the Baldwin diagrams, a global transition to a matter-bounded state generally predicts that the Ly / C IV and C III] / C IV ratios should decrease at higher luminosities (Shields et al. 1995), in conflict with the observed trends (Section 3.2). The relationship between the ensemble BE and phenomenology of variable sources is considered in more detail in the following section. An alternative explanation for curvature in the BE was advanced by Netzer et al. (1992), who generated a similar pattern theoretically, using thin accretion disks with random inclination and luminosity-dependent spectral energy distribution (SED). As noted earlier (Section 4.1), this model has been criticized on the basis of its predicted distribution of W (Francis 1993); the theoretical treatment of accretion disks (or other continuum sources) in AGNs is also the subject of continuing discussion and debate.