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 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
cause the dust evaporation and a subsequent fall back. This failed radiatively
accelerated dusty outflow (FRADO) is expected to represent the material forming
low ionization lines. In this paper we formulate simple analytical equations
describing the cloud motion, including the evaporation phase. The model is
fully described just by the basic parameters: black hole mass, accretion rate,
black hole spin and the viewing angle. We study how the spectral line generic
profiles correspond to this dynamics. We show that the virial factor calculated
from our model strongly depends on the black hole mass in 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 pseudo-bulges 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.
