5.2. Non-spherical Models
There are two classes of non-spherical models, having to do with the isotropy of the radiation field and the distribution of the line emitting gas.
5.2.1 Non-spherical gas distribution. The accretion of material with large angular momentum may lead to the formation of a flat rotating system. In particular, accretion disks are thought to play an important role in AGNs (chapter 10 and R. Blandford's contribution) and it is natural to surmise that the emission line region is an extension of the inner disk.
Some modifications of the spherical model are required in order to allow for the different geometry. The easiest way is to add an extra parameter, which is the latitude angle of the clouds. This would mean an angle dependent covering factor, which is easy to implement within the general integration scheme outlined above.
A more complex picture has been suggested in which part of the centrally emitted continuum radiation is reflected back by some scattering material above the disk surface. This class of models has been introduced to help explain the strong low ionization emission lines (chapter 6) and some line profiles (chapter 9). It assumes a very large accretion disk, up to 106 gravitational radii (RG = GM / c2). The lines are emitted from the outer parts of the disk, where they are excited by the back-scattered hard ionizing radiation. The high ionization lines, and most of the L flux, come from a more "normal", spherical system of clouds, that are ionized by the non-scattered ultraviolet radiation. A schematic illustration of the model is shown in Fig. 13.
Figure 13. A schematic two-component model for the BLR. The high ionization lines are emitted in a spherical system of clouds, and are excited by the direct ultraviolet radiation of the central source. The low ionization lines come mainly from the outer regions of the central disk, where most of the line excitation is due to back-scattered, hard ionizing photons. (After Collin-Souffrin, Perry and Dyson (1988), Collin-Souffrin (1986) and Dumont and Collin-Souffrin (1990)).
There are several important implications to the model, to do with the line profiles (chapter 9) and covering factor. A possible difficulty is the very large disk radii postulated to explain the line strength. As explained in chapter 10, and in R. Blandford's contribution, the structure of geometrically thin AGN disks is not well understood. Current models suggest that such disks are radiation pressure dominated, and their self gravity radius is of the order of 103 - 104 RG. Much of the postulated low ionization lines originate outside this radius, where the disk, if it exists, is probably fragmented. This is, perhaps, not a strong objection considering the large uncertainties in the disk model. Moreover, a fragmented disk is as likely location for such lines as a uniform, continuous disk.
5.2.2 Anisotropic radiation field. A spherical or a flat cloud system can be illuminated by radiation from an anisotropic central source. This can be caused by relativistic beaming or by the combined effects of inclination and limb darkening in an accretion disk. The anisotropic disk radiation can be supplemented by an isotropic X-ray source, or perhaps some other components. Several examples of this continuum are shown in chapter 10. The ionization and excitation of the gas depends, in this case, on both r and the latitude angle of the clouds. This must be included in a modified integration scheme for calculating the cumulative line emission. Currently, there are too few observational constraints to test these ideas.
Relatively little has been done on combining isolated cloud models in the way described here. Rees, Netzer and Ferland (1989) suggested the general scheme and calculated many models for different values of s. Some more examples are given in Netzer (1989). See also Viegas-Aldrovandi and Gruenvald (1984) for references on multi-cloud NLR models. The idea of low ionization disk emission lines is described in several papers by Collin-Souffrin and collaborators, see for example Dumont and Collin-Souffrin (1990) and references therein. Non-spherical models related to thin accretion disks are discussed in Netzer (1987).