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 H and
1400 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 W) 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 W 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
Ly / 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 Ly
/ 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.
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