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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 Wlambda versus L (e.g., KRK). As a quantitative example, AGN ensembles plotted in the Wlambda(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 Wlambda(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 Phi (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 Wlambda(C IV) would then depend on cloud covering factor as a function of radius (see Figure 7).

Figure 7

Figure 7. Effects of covering factor versus radius, for variable luminosity. If the lightly shaded clouds in this example are most efficient at emitting C IV, then Wlambda(C IV) will drop as the continuum source brightens (producing a BE), due to the rapid falloff in fractional coverage.

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 Wlambda independent of L, the fractional coverage Delta fc represented by clouds with a given density, within an interval of incident flux Delta Phi, should be independent of L. The relevant differential covering factor is then

Equation 1 (1)

Note that r propto sqrt(L / Phi), so that dr / d Phi propto L1/2 Phi-3/2. If we express dfc / dr propto rgamma, then dfc / dr propto Lgamma/2 Phi-gamma/2, and

Equation 2 (2)

which is homologous and independent of L if gamma = -1.

If the intrinsic Baldwin Effect ultimately stems from a steep fall-off in circumnuclear covering factor (gamma < -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 gamma. As can be seen from his Figure 1, good agreement with the average quasar spectrum is obtained with gamma = -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 gamma 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. Back.

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