H$β$ line shape and radius-luminosity relation in 2.5D FRADO

Galaxies with active galactic nuclei (AGN) exhibit broad emission lines as a
key spectral feature. The shape of emission-line profiles depends on the
complex dynamics of discrete clouds within a spatially extended region known as
the Broad Line Region (BLR). The distribution of cloud positions within BLR, or
the geometry of BLR indeed, is directly linked to measurements of time lags of
BLR. In this paper, we convolve a large grid of physically-based simulations of
cloud distributions in BLR with photon-flux weighted emissivity of BLR clouds
to investigate the generic shape of spectral line profiles. More importantly,
we extract the time-delay histograms of corresponding models to calculate the
size of BLR. Our physical model is based on the assumption that the clouds are
launched by the radiation pressure acting on dust in the atmosphere of the
outer disk. It has very few global parameters. The model is appropriate for the
low ionization part of the BLR, as it was shown by earlier model tests. It uses
a non-hydrodynamical single-cloud approach to the BLR dynamics. In this way we
simulate the distribution of positions and velocities of the clouds. We found
that the width of line profiles gets broader with black hole mass, or with
viewing angle, and gets narrower with accretion rate. The blue wing of the
emission line profiles becomes more pronounced with increasing black hole mass
and accretion rate, consistent with the formation and intensification of an
outflow structure. We also found that the peak time-delays rather than averaged
delay values better represents the observational trend and also the scatter in
the radius-luminosity relation.