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.