We have investigated the observational characteristics of a class of broad emission line region (BLR) geometries that connect the outer accretion disc with the inner edge of the dusty toroidal obscuring region (TOR). We suggest that the BLR consists of photoionized gas of densities which allow for efficient cooling by ultraviolet (UV)/optical emission lines and of incident continuum fluxes which discourage the formation of grains, and that such gas occupies the range of distance and scale height between the continuum-emitting accretion disc and the dusty TOR. As a first approximation, we assume a population of clouds illuminated by ionizing photons from the central source, with the scale height of the illuminated clouds growing with increasing radial distance, forming an effective surface of a ‘bowl’. Observer lines of sight which peer into the bowl lead to a Type 1 active galactic nuclei (AGN) spectrum. We assume that the gas dynamics are dominated by gravity, and we include in this model the effects of transverse Doppler shift (TDS), gravitational redshift (GR) and scale-height-dependent macroturbulence.
Our simple model reproduces many of the commonly observed phenomena associated with the central regions of AGN, including (i) the shorter than expected continuum–dust delays (geometry), (ii) the absence of response in the core of the optical recombination lines on short time-scales (geometry/photoionization), (iii) an enhanced redwing response on short time-scales (GR and TDS), (iv) the observed differences between the delays for high- and low-ionization lines (photoionization), (v) identifying one of the possible primary contributors to the observed line widths for near face-on systems even for purely transverse motion (GR and TDS), (vi) a mechanism responsible for producing Lorentzian profiles (especially in the Balmer and Mg ii emission lines) in low-inclination systems (turbulence), (vii) the absence of significant continuum–emission-line delays between the line wings and line core (turbulence; such time delays are weak for virialized motion, and turbulence serves to reduce any differences which may be present), (viii) associating the boundary between population A and population B sources as the cross-over between inclination-dependent (population A) and inclination-independent (population B) line profiles (GR+TDS), (ix) a partial explanation of the differences between the emission-line profiles, here explained in terms of their line formation radius (photoionization and/or turbulence) and (x) the unexpectedly high (but necessary) covering fractions (geometry).
A key motivation of this work was to reveal the physical underpinnings of the reported measurements of supermassive black hole (SMBH) masses and their uncertainties. We have driven our model with simulated continuum light curves in order to determine the virial scale factor f from measurements of the simulated continuum–emission-line delay, and the width (fwhm, σl) and shape (fwhm / σl) of the rms and mean line profiles for the energetically more important broad UV and optical recombination lines used in SMBH mass determinations. We thus attempt to illuminate the physical dependencies of the empirically determined value of f. We find that SMBH masses derived from measurements of the fwhm of the mean and rms profiles show the closest correspondence between the emission lines in a single object, even though the emission-line fwhm is a more biased mass indicator with respect to inclination. The predicted large discrepancies in the SMBH mass estimates between emission lines at low inclination, as derived using σl, we suggest may be used as a means of identifying near face-on systems. Our general results do not depend on specific choices in the simplifying assumptions, but are in fact generic properties of BLR geometries with axial symmetry that span a substantial range in radially increasing scale height supported by turbulence, which then merge into the inner dusty TOR.