Failed Radiatively Accelerated Dusty Outflow Model of the Broad Line Region in Active Galactic Nuclei. I. Analytical Solution

The physical origin of the broad line region in active galactic nuclei is still unclear despite many years of observational studies. The reason is that the region is unresolved, and the reverberation mapping results imply a complex velocity field. We adopt a theory-motivated approach to identify the principal mechanism responsible for this complex phenomenon. We consider the possibility that the role of dust is essential. We assume that the local radiation pressure acting on the dust in the accretion disk atmosphere launches the outflow of material, but higher above the disk the irradiation from the central parts causes dust evaporation and a subsequent fallback. This failed radiatively accelerated dusty outflow is expected to represent the material forming low ionization lines. In this paper we formulate simple analytical equations to describe the cloud motion, including the evaporation phase. The model is fully described just by the basic parameters of black hole mass, accretion rate, black hole spin, and viewing angle. We study how the spectral line generic profiles correspond to this dynamic. We show that the virial factor calculated from our model strongly depends on the black hole mass in the case of enhanced dust opacity, and thus it then correlates with the line width. This could explain why the virial factor measured in galaxies with pseudobulges differs from that obtained from objects with classical bulges, although the trend predicted by the current version of the model is opposite to the observed trend.