3.2 The Standard BLR Model

Early photoionization BLR models were quite successful in terms of predicting line ratios in accordance with observed values. ⁸⁷ After some refinements, a standard model was developed, in which the BLR lines are emitted from cool, dense clouds or filaments, photoionized by the continuum. Clouds are preferred over a continuous matter distribution, since the observed emissivity indicates a ratio ~ 10^-6 between emitting and total volumes.

One initial suggestion to avoid rapid evaporation of the clouds was a hot (T ~ 10⁸ K) inter-cloud medium with some unspecified kinematical properties. ⁸⁸ However, even then the clouds apparently do not last long enough to emit the necessary amount of line radiation. This and other difficulties may have essentially ruled out this scenario. ⁸⁹ Another suggestion involves magnetic confinement, ⁹⁰ producing clouds with a filamentary structure along the field lines. The required magnetic field strength would be ~ 1 G, whose origin could lie in a relativistic wind from, e.g., an accretion disk. Still another possibility is a continuous creation of BLR clouds, so that no confinement becomes necessary. Some specific mechanisms for this include (a) winds due to mass loss from giant stars, ⁹¹ (b) orbiting clouds which during infall break up into fragments at about 1 pc from the central source, ⁹² (c) transient shocks ⁹³ and (d) thermal instabilities in the inter-cloud medium. ⁹⁴

Perhaps the most important parameter in photoionization models is the ionization parameter, one version being defined as

(7)

where Q is the ionizing photon flux, R the distance from the cloud to the continuum source and N the hydrogen number density at the illuminated side of the cloud. Apparently, U measures the degree of ionization in the cloud, dividing the photon flux by the gas density. A specific model for one cloud is defined by ⁸⁹

- the continuum shape,

- the density or pressure, and the column density,

- the chemical composition,

- the parameter U.

The generalization to many clouds involves a pressure and matter distribution over the BLR region. The clouds are assumed to be optically thick, from the presence of strong MgII and FeII lines. Broad forbidden lines are often absent, indicating a typical cloud density ~ 10⁸-10¹⁰ cm^-3. Chemical abundances are assumed to lie around the solar value (within a factor of 3). Using these values and U ~ 10^-2, the BLR size as deduced from Eq. (7) becomes ~ 0.1 and ~ 2 pc for Seyferts and bright QSOs, respectively.

The standard BLR model has recently encountered an increasing number of difficulties. Thus, the high ionization lines (such as NV1240) are stronger than predicted and the strong FeII lines in some objects are difficult to explain, and the correlation between obtained results (e.g., line ratios) and the shape of the continuum is rather small. ⁹⁵ The attempts to use photoionization codes for revealing accretion disks as the continuum source therefore seem futile. ⁹⁶ Furthermore, the standard U-value is significantly exceeded in some sources. ⁹⁷ Finally, the NGC 5548 campaigns may have ruled out the customary one-zone type of model.