3.2. Slope as a Function of Ionization

For those lines that show a BE, the growth in observations now makes it possible to go beyond testing for correlations, by measuring and comparing the slopes of W versus L for different lines. Several studies have completed this exercise, and produced evidence that lines of relatively high ionization, such as C IV, exhibit systematically steeper slopes in the Baldwin diagram than lines of lower ionization, such as Mg II or Ly (e.g., Wu et al. 1983; Kinney et al. 1987; KRK; Baldwin et al. 1989; Zheng et al. 1997). This result is sometimes expressed in terms of the luminosity behavior of line ratios, such that, for example, Ly / C IV and C III] / C IV appear to increase systematically with increasing luminosity. The existence of this trend was confirmed at this meeting by Brian Espey, who reported results for the BE based on a very large sample of AGN spectra. Zheng, Kriss, & Davidsen (ZKD, 1995) found a particularly steep BE for the O VI line, consistent with its high ionization. ZKD's study benefited from inclusion of HUT spectra for low-redshift objects, which resulted in a wide baseline in luminosity for analysis. An apparently contradictory finding was reported by Paul Green (1996), however, who found no statistically significant BE in O VI for an overlapping sample drawn from the IUE archive; Green emphasized the importance of including upper limits in the Baldwin diagram when testing for correlations. Nonetheless, Green considered the ZKD result to be valid because of their detection of O VI in all their objects and because their sample covered a larger range in luminosity than his ⁽⁴⁾.

The fact that different lines show different slopes in the Baldwin diagram is important for understanding the BE theoretically. A simple luminosity dependence of broad-line-region (BLR) covering factor for the central continuum source should lead to similar variations in W for all lines. Likewise, simple models invoking inclination variations of accretion disks (which produce an anisotropic continuum radiation field) as the source of the BE do not predict different slopes for different lines. The trend of steeper slopes for lines of higher ionization is an important clue that must be accommodated by alternative explanations for the BE. Dust internal to the BLR could potentially introduce BE-like behavior if cloud properties conspire to produce more absorption for higher L (Shuder & Macalpine 1979), but is unlikely to produce the observed ordering, even if dust were able to survive in this inhospitable environment.

Several scenarios that take into account the ionization dependence of the BE have been advanced. Mushotzky & Ferland (1984) argued that this behavior was consistent with a luminosity dependence of the ionization parameter U (ratio of ionizing photon and particle densities) for the BLR clouds, such that U was less in more luminous sources. Since U provides an indicator of the degree of ionization for a photoionized cloud, this prescription takes explicit account of the BE ionization dependence, although the underlying cause of a L - U correlation is not obvious. This model does not predict a BE for Ly, however, and this line might actually be expected to increase in equivalent width as U diminishes (Shields & Ferland 1993); an additional luminosity dependence of covering factor may be required to fit the observations. Shields et al. (1995) recast this formulation as a luminosity dependence of coverage by high-U clouds; this scenario was motivated in part by reverberation-mapping evidence for matter-bounded clouds, coupled with a luminosity dependence in outflow (signaled by narrow blueshifted resonance absorption in Seyferts versus broad absorption lines in QSOs) that may affect the coverage of tenuous components of the BLR.

A final interpretation that is gaining considerable support views the ionization trend in the BE as the consequence of a luminosity-dependent continuum spectral energy distribution (e.g., Schulz 1992; Netzer et al. 1992; Zheng et al. 1992; Zheng & Malkan 1993; Green 1996, 1998; Wang et al. 1998; Korista et al. 1998). In this picture, more luminous AGNs feature softer ionizing continua; the reduction in ionizing photons at a given optical/UV luminosity leads to smaller equivalent widths, with the high-ionization lines responding most strongly, due to their greater sensitivity to the high-energy continuum. This explanation has several attractive features. First, some accretion disk models naturally predict a softer continuum for more luminous systems (e.g., Netzer et al. 1992). Second, observational evidence exists in direct support of the requisite continuum behavior. These data are often cast in terms of the luminosity dependence of _ox, the two-point spectral index connecting 2500 Å and 2 keV in the source rest-frame (e.g., Zamorani et al. 1981). The role of selection effects and photometric errors in defining these trends continues to be of concern, however (e.g., La Franca et al. 1995), and a recent paper by Yuan et al. (1998) on this subject provoked much discussion at this conference.