4.5. The Emergent Spectrum

4.5.1. Input parameters. A complete model for an isolated cloud requires that the following parameters be defined:

1. The frequency dependence of the incident continuum, L.
2. The gas density (or pressure) and column density, N_col.
3. The gas chemical composition.
4. The geometrical shape of the cloud.
5. The ionization parameter, U.

The incident continuum is known over a large range of frequencies. Unfortunately, the most important part, the Lyman continuum up to the soft X-ray energies, is not observed except in some high redshift quasars. This is a major drawback and indirect methods (chapter 10) must be used to estimate L in that gap. Another uncertainty is the high energy tail (h > 30 keV) which is not yet observed in many AGNs. This has important implications in models of large N_col. Finally, free-free absorption at low frequencies may be a significant heating source for the BLR, but it is not at all clear that the observed far infrared radiation originates in a small, point-like continuum source (see R. Blandford's contribution), If this radiation comes from an extended disk, or any other structure large in comparison with the BLR size, then its effect on the broad line gas, via free-free heating, is largely reduced.

Fig. 7 shows a typical continuum which is used in photoionization calculations and is consistent with our knowledge of many radio quiet AGNs. The characteristic features are the steep infrared (1 - 3µm) slope (a spectral index of about 1.5), the flattening at optical and ultraviolet wavelengths, sometimes referred to as "the big blue bump", the cutoff at about 3-10 Ryd (implied by the models but not directly observed) and the flat X-ray continuum. The drop at > 30µm is artificially introduced, because of the above mentioned uncertainty about the origin of this component.

Figure 7. A characteristic AGN continuum.

It is customary to fix either the density or the pressure at the illuminated face of the cloud, and proceed by assuming constant density, constant pressure, or some other assumption. This depends, of course, on conditions outside the cloud. For example, in the "two phase model" (chapter 9) the BLR clouds are embedded in a hot (~ 10⁸ K) intercloud gas that provides the external confining pressure. Constant pressure models are appropriate in this case. On the other hand, the cloud internal pressure, near a variable continuum source, varies in time following the changes in T_e, N_e and the line radiation pressure. Since the sound crossing time (chapter 9) of the BLR clouds is comparable to the variability time of the central radiation source, a stable pressure equilibrium may never be achieved. Constant density models may be more appropriate in this case. Finally, if AGN clouds are stellar atmospheres or the outer parts of accretion disks (chapter 9), then their the structure is controlled by the local gravity.

The lower limit on the column density of the BLR clouds is of the order of 10²² cm^-2. This is derived from the presence of strong low excitation lines of MgII and FeII. Some clouds of much larger N_col are likely to exist, as deduced from the frequently observed lines of CaII, but a general upper limit is difficult to establish. Obviously, N_col is not necessarily the same in all clouds and in all objects. The column density of typical NLR clouds is not well known but it is estimated to be smaller than the BLR column density.

The chemical composition of AGN clouds is difficult to measure because of the nonstellar continuum shape, which results in a mixing of several stages of ionizations in one zone. In the BLR it is possible to use some observed line ratios, that do not depend much on the temperature and the ionization parameter, to estimate the composition. An example is the NIV]1486 / CIV1549 ratio which is a good C/N abundance indicator. The abundances relative to hydrogen are ill determined because of the uncertainty in the calculated intensity of the hydrogen lines. There is a similar difficulty in the NLR, due to the difficulty in determining the electron density and temperature from optical forbidden lines. The hope is to use ultraviolet HST measurement of dielectronic recombination lines, and to combine them with collisionally excited lines, to determine the temperature. Thus the line pair (CII1335, CIII]1909), can be used to measure T_e in the C⁺⁺ zone. This temperature, combined with the measured intensity of NIII]1750 that comes from the same region, will enable us to directly measure the C/N abundance ratio.

The comparison of observations of many line ratios with the best model calculations suggest that the following cosmic abundances (Table 2) are within a factor 2 of the abundances in many AGNs.

The shape of the clouds is important because it determines the escape of line and continuum photons. The escape probability function in a sphere is different from that in a slab and there are "skin effects" to be considered. An infinite slab model has been adopted in many cases and will be used here. Later (chapter 5) we consider spherical BLR clouds but retain the slab escape probability function. This is well within the general limitation and uncertainty of using such transfer methods.

Finally, the value of the ionization parameter has to be determined (alternatively, the cloud distance and L at some frequency). This is often used as the variable parameter in the calculations.

4.5.2 Examples. Fig. 8 shows calculated line fluxes, as a function of the ionization parameter, for an isolated BLR cloud. The input continuum is the one shown in Fig.7, the density is constant at 10¹⁰ cm^-3, the column density is 10²³ cm^-2 and the composition is as in Table 2. The line intensities are given relative to H. Calculations for an isolated NLR cloud, with the same continuum source and abundances and N = 10⁴ cm^-3, are shown in Fig. 9. In this case the calculations stop at ₉₁₂ = 10^3.5.

Figure 8. Broad line ratios, relative to H, as a function of the ionization parameter.

Figure 9. Narrow line ratios, relative to H, as a function of the ionization parameter.

As evident from the diagrams, some line ratios are good ionization parameter indicators. In the BLR model, this is OVI1035 / CIV1549; in the NLR model [OII]3727 / [OIII]5007. The CIII]1909 / CIV1549 ratio, that was thought to be a good ionization parameter indicator for the BLR, is not so, because of the big changes in the ionization structure at large U that limit the extent of the C⁺⁺⁺ zone. The low excitation lines of MgII and FeII (not shown here) depend on U in a very complicated way and are not good ionization parameter indicators. They are further discussed in chapter 6.

The observed intensities of the broad high excitation lines (Table 1) suggest that the typical ionization parameter for the BLR is at least 0.1, if all lines are to be produced in the same population of clouds. There are, however, other ways to produce strong, high excitation lines, such as optically thin material. A typical ionization parameter for the NLR is about 0.01, but there is a large diversity in this value, as discussed in chapter 11. The observed strength of [FeX]6734 and other narrow [FeX] and [FeXI] lines presents a problem, since such lines are calculated to be too weak in clouds with the ionization parameter required to give the observed [OII]3727 / [OIII]5007 ratio. The origin of these lines may be some transition zone between the BLR and the NLR, or perhaps the interstellar matter of the host galaxy.

Regarding the broad hydrogen lines, the calculated change in L / H / H is mainly due to the increase of the Balmer optical depth with U. This is related to a well known problem of AGN study to be discussed in chapter 6. Finally, the diffuse bound-free and free-free continua, emitted by one of the broad line clouds considered here, are shown in Fig. 10.

Figure 10. Diffuse continua emitted by a broad line cloud with U = 0.3 and all other parameters as specified in the text.