5. VARIABLE LUMINOSITY

Variability is now recognized as a probable source of scatter in the ensemble BE, rather than its origin, and the observed (negative) correlation between luminosity and equivalent width in individual variable sources has become known as the ``intrinsic Baldwin Effect'' (Pogge & Peterson 1992). An intrinsic BE is commonly observed for most of the strong UV lines in Seyfert galaxies. Different lines exhibit different slopes, as in the ensemble case, and there are some indications that the higher ionization lines again show a systematically steeper relation. For variable objects, the trend is often expressed in terms of line versus continuum fluxes, rather than equivalent width versus luminosity; the intrinsic BE then appears as a nonlinear correlation in this plane (or a slope less than unity in a log-log plot; see Figure 5). The physics underlying the intrinsic BE may be quite different from that of the global trend, but the resemblance remains intriguing and the study of variable sources offers additional relevant information on broad-line region structure.

Figure 5. Line flux for C IV plotted as a function of 1338Å continuum flux for the variable Seyfert galaxy Fairall 9; measurements are taken from Clavel et al. (1989). Each point represents a different epoch of observation. No attempt has been made to remove time delay effects. The dashed line corresponds to a constant W = 100 Å.

Several explanations have been advanced to account for the intrinsic BE. One possibility, discussed previously for the ensemble BE (Section 3.2), is that the trend arises from a luminosity dependence of the ionizing continuum shape, such that the continuum becomes softer when it brightens. In this scenario, the optical/UV continuum luminosity varies with greater amplitude than does the far-UV/X-ray continuum; the line emission, responding to the high-energy radiation, thus varies less strongly than the observable continuum, resulting in a nonlinear relation between the two.

The luminosity dependence of continuum shape can be tested directly for variable sources via simultaneous monitoring at UV and X-ray energies. Assembling the requisite data sets with reasonable temporal coverage remains challenging, however, and at present only a handful of sources have received such scrutiny. The results are heterogeneous: Fairall 9 exhibited some degree of correlation in the expected sense, with variability amplitudes greater in the UV bandpass than in X-rays (Clavel et al. 1989); but in NGC 5548 the fluxes at 1350 Å and 2-10 keV scaled together by similar factors (Clavel et al. 1992), and an intensive monitoring campaign for NGC 4151 found a higher amplitude of variation at 1-2 keV than in the observable UV bandpass (Edelson et al. 1996). The lack of a clear signature is underscored by recent intensive monitoring of NGC 7469; the UV and X-ray fluxes for this source varied with comparable amplitude, and moreover exhibited only a weak degree of correlation (Nandra et al. 1998). Studies restricted to the optical/UV bandpass have also examined the luminosity dependence of continuum shape, and to the extent that any trend is present, the observable continuum appears to get harder with increasing luminosity in variable sources (e.g., Edelson et al. 1990).

A second potential cause of an intrinsic BE stems from ionization and temperature effects in broad-line region clouds subject to a changing radiation field. The most straightforward example is provided by matter-bounded (``optically thin'') clouds, which can undergo a global change in characteristic ionization state as the ionizing continuum fluctuates; this behavior contrasts with that of high column-density clouds, which retain a region contributing intermediate- and low-ionization emission for any continuum level. For thin clouds, the result can be a positive, null, or negative response in a given line to changes in the continuum (Figure 6), with reduced response contributing to an intrinsic BE.

Figure 6. Cloud emissivity in lines as a function of continuum luminosity state. The abscissa is expressed in terms of ionization parameter U, the dimensionless ratio of ionizing photon and particle densities at the irradiated cloud face. The density of hydrogen (with associated cosmic abundances) within the clouds is fixed at 1011 cm-3, appropriate for the BLR, and column density N = 1023 cm-2. The incident radiation field is described by a representative AGN continuum shape (see Shields et al. 1995 for details). Slopes less than unity translate into a decrease in line equivalent width W with increasing luminosity L - i.e., an intrinsic Baldwin Effect.

1. Evidence of negative line response for clouds in the inner BLR. Sparke (1993) examined light curve data for NGC 5548, and noted that the line autocorrelation function for prominent UV features was narrower in width than the autocorrelation function for the continuum, in conflict with expectations for photoionized clouds described by a positive line response.

2. The strength of high ionization emission features such as O VI 1034 and Ne VIII 774. The prominence of these features may require a distinct, highly ionized, and presumably optically thin component within the BLR (Netzer 1976; Davidson 1977; Hamann et al. 1998).

3. The luminosity dependence of the C IV / Ly line ratio. Photoionization calculations for thick clouds generally predict that this ratio will increase as the continuum brightens (e.g., Ferland & Persson 1989), while a number of Seyfert galaxies show the opposite trend. A very soft continuum can sometimes reproduce the observed behavior (Gondhalekar 1992), but often has difficulty in simultaneously matching the line equivalent widths. A mix of thick and thin clouds provides an alternative that can account for the observed line responses and strengths (Shields et al. 1995).

4. X-ray ``warm'' absorbers. These highly ionized components are now known to be present in a large fraction of Seyfert nuclei (e.g., Reynolds 1997; George et al. 1998). Variability and recombination timescale arguments have been used in a few cases to bound the absorber location to a scale comparable to the BLR (e.g., Otani et al. 1996). In these instances the absorber may represent the high-ionization extension of the BLR; the same material would be expected to emit efficiently in the Ne VIII line. Warm absorbers are unambiguously matter-bounded systems.

A further possible contributor to an intrinsic BE arises from radiative transfer effects within the broad-line clouds. Line photons with energy sufficient to ionize hydrogen from the n = 2 state can be destroyed via Balmer continuum absorption. Balmer continuum opacity is expected to scale in proportion to the ionizing flux incident on a cloud, so that the efficiency of line destruction increases in higher luminosity states (see Shields & Ferland 1993 for details). The result is a nonlinear response in the line. This effect is important for Lyman , as demonstrated by explicit calculations, and is also expected to be relevant to varying degrees for other lines. At present, no means appear to be available for isolating this behavior from other contributors to an intrinsic Baldwin Effect.

A final basis for generating an intrinsic BE originates in light travel-time effects in variable sources. In the observer's frame, line emission from circumnuclear clouds is expected to respond to continuum variations with a delay, resulting from the added path length for the continuum light to reach clouds outside our line of sight, plus path length variations for the emitted line radiation that depend on the geometrical distribution of clouds. Correlation analyses of Seyfert light curves provide abundant evidence for such delays, which form the basis for reverberation mapping studies of BLR structure. Pogge & Peterson (1992) have emphasized that the resulting phase offset between the continuum and line light curves is a source of scatter for the intrinsic BE; removal of a characteristic ``lag'' between the two light curves results in a tighter correlation between line and continuum flux.

A complication to this general picture arises because there is unlikely to be a single lag that is appropriate for all the emitting components in the BLR. The emission-line response to continuum variations is both time-shifted and smeared by light travel-time effects determined by the three-dimensional structure of the BLR. As a result, there will be a general tendency for some of the emission components to be referenced to an inappropriate continuum level, regardless of the choice of a lag. The resulting phase offsets will lead to larger W at low continuum states, and smaller W in high states, compared to the predictions for idealized clouds with no light travel-time delays. The general role of such delays in producing an intrinsic BE may be even stronger, however, if significant emitting gas is present at large distances from the continuum source, such that the light crossing time for the cloud distribution is considerably greater than the timescale of variability in the continuum. In this case the emitting aggregate of clouds may contribute a nearly constant line flux while the continuum undergoes substantial variation, leading to a strong BE. The existence of substantial emitting gas at large radius within the BLR can be difficult to exclude or constrain (e.g., Done & Krolik 1996).

To summarize this section, several causes may contribute to the intrinsic BE observed in variable AGNs. These include a luminosity-dependent continuum shape, the influence of matter-bounded clouds, luminosity-dependent optical depth effects, and time delays for light propagation across the BLR. Light travel-time effects are known to be operative at some level, while the importance of continuum shape for the intrinsic BE is less certain. The relevance of the other two factors, thin clouds and optical depth effects, will depend on the aggregate distribution of cloud properties in the BLR, since reduced emissivity in one subset of clouds may be overwhelmed by growth in emissivity elsewhere. We consider this point in more detail in the following section.