5.2. The Intrinsic versus Ensemble BE
Detailed comparisons of the global and intrinsic BEs have drawn attention to the different slopes exhibited in Baldwin diagrams for the two trends, with the intrinsic effect systematically steeper in W versus L (e.g., KRK). As a quantitative example, AGN ensembles plotted in the W(C IV) versus continuum luminosity plane typically display a logarithmic slope of ~ -0.1 to -0.3 (Korista et al. 1998 and references therein), while variable sources display slopes of ~ -0.3 to -0.9 (KRK; Edelson et al. 1990). While this contrast may be ascribed in general terms to the differences between static and time-variable systems, some additional examination of this issue is potentially informative.
Quasars and Seyfert galaxies have quite similar spectra, to first order, which implies that their broad-line regions scale in some nearly uniform sense, in terms of covering factor, velocity field, density, ionization parameter, etc. The ensemble Baldwin Effect tells us that this scaling is not altogether homologous, although the luminosity dependence is weak - a factor of 10 variation in W(C IV) over 6 orders of magnitude in L. Quasars evidently undergo significant evolution in luminosity, and we can thus consider the behavior of line emission as a Seyfert evolves to a quasar, or vice versa. A variable Seyfert nucleus (e.g., Fairall 9, with a factor of 30 variation in luminosity; see Figure 5) arguably represents this process in miniature. That being the case, it is perhaps surprising that the intrinsic and global BEs are so different, i.e., Seyfert nuclei do not simply slide along the locus of the ensemble relation as they vary.
Some perspective on the intrinsic versus ensemble behavior can be derived from considering quasar luminosity evolution in conjunction with the locally optimally-emitting cloud (LOC) model for the BLR (Baldwin et al. 1995). The essential idea of the LOC model is that clouds emit with high efficiency in a given line only in a rather restricted portion of the parameter space of cloud density n and incident ionizing flux (or distance r from the continuum source) (5). If we consider an ensemble of clouds surrounding a continuum source, we can imagine correspondingly a zone in radius where clouds with the appropriate density will dominate the total emission in, say, C IV; clouds at smaller radii are either too dense or too highly ionized to emit strongly in this line, while clouds at larger radii will have little C+3 or lie outside the BLR. If we were to increase the luminosity of the central continuum source, the radius describing the region of efficient C IV emission would move outward. The effect on W(C IV) would then depend on cloud covering factor as a function of radius (see Figure 7).
If the covering factor fc of the clouds diminishes rapidly with radius, we would expect the line equivalent width to decrease as the source brightens (a Baldwin Effect); correspondingly, radial distributions should also exist that would yield an increase in equivalent width for higher L (an anti-Baldwin Effect). What radial distribution constitutes the intermediate case, corresponding to the homologous BLR? To obtain W independent of L, the fractional coverage fc represented by clouds with a given density, within an interval of incident flux , should be independent of L. The relevant differential covering factor is then
Note that r
sqrt(L / ), so that dr / d
L1/2 -3/2. If we express dfc / dr r, then
dfc / dr
L/2 -/2,
and
which is homologous and independent of L if = -1.
If the intrinsic Baldwin Effect ultimately stems from a steep fall-off
in circumnuclear covering factor ( < -1), then the luminosity
evolution of AGNs must be accompanied (perhaps unsurprisingly) by
substantial structural changes within the BLR, in terms of the distribution
of matter. A less violent adjustment is required for a homologous profile,
which in turn provides a natural basis for producing grossly similar
Seyfert and quasar spectra. The structure of fc(r)
thus contains
potentially significant information on the physical evolution of AGNs.
An important independent constraint on fc(r) is
available from global fits to quasar spectra.
Baldwin (1997)
has reviewed the LOC
model and its predictions for relative line strengths as a function of
fc(r), parametrized in terms of the differential
power-law index
. As can be seen
from his Figure 1, good agreement with the
average quasar spectrum is obtained with = -1, which may
imply that the BLR is indeed homologous. In this case the dominant
cause underlying the intrinsic BE is likely to be variability and
light travel-time effects, as discussed in the previous section.
Further comparisons of this type, perhaps including added constraints from
linewidth measurements, may provide stronger constraints on
and hence BLR structure, as well as the origins of the intrinsic BE.
5 Column density represents another free parameter
describing the clouds, and the distribution of column densities will
influence the proportions of ionization- and matter-bounded clouds.
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