Small Dense Broad-Line Regions in Active Nuclei

Recent observational studies indicate that the broad-line region (BLR) of active galactic nuclei (AGN) may be much smaller than previously thought. One consequence is that the flux of ionizing radiation is considerably larger and the clouds may be denser than assumed in "standard photoionization models" for these objects. This paper attempts to investigate such questions by exploring realistic cloud distributions over a range of radii and densities. We propose some simple pressure laws and integrate over the radial distribution of clouds to obtain the contribution to the line and continuum emission for all parts of the BLR. This requires photoionization calculations at very high densities, up to 10^13^ cm^-3^, and we discuss in detail the most important processes that are included and the improvements over previous calculations of this kind. In particular, hydrogen and helium are approximated as ~ 100 level systems, three-body recombination contribution to all elements is included, and we take full account of optical depth effects, including Stark broadening, in all lines. Finally, we predict line profiles, assuming that the cloud ensemble is in virial equilibrium. The main results are as follows: (1) Most pressure laws imply a rapid increase of the covering factor with radius so that the emission-line spectrum of the ensemble is weighted toward the outside of the BLR. As a result, the gas distribution must be truncated at N ~ 10^9^ cm^-3^ to prevent broad, strong O[III] lines. (2) Clouds of very high density are cooled mainly by free-free and recombination continua. The emergent spectrum of such clouds is very different from that observed in AGNs, having both strong ultraviolet lines, such as C III λ977, and Balmer and Paschen continuum. The fact that these are not observed sets a strong limit on the contribution of high-density material to the observed spectrum. (3) The observed C III λ1909 line still provides the best indication that much of the gas is characterized by densities N ~ 10^10^ cm^-3^, but there is a nonnegligible contribution to the 1909 A feature from Si III] λ1893. Si IV λ1397 is the dominant contribution to the 1400 A blend at high densities. (4) Some models produce significant line emission from very small radii. However, these models can be ruled out because the predicted line profiles for different lines do not agree to the extent required by observations. Models which do produce similar line profiles tend to have their emissivity strongly weighted to either inner or outer radii, and it is difficult to force the ensemble to conspire to produce similar line profiles over a wide range of radii and density. (5) The best estimate of the BLR size, deduced from the new models, is smaller than in previous calculations, but it is still larger than indicated by some line reverberation measurements. Our normalization of the ionization parameter, based on old photoionization calculations, may thus be wrong.