On the orbital motion of cold clouds in BLRs

TL;DR

This paper models the orbital dynamics of cold clouds in AGN broad-line regions, incorporating gravity, radiation pressure, and drag, revealing that drag causes clouds to eventually fall inward, affecting BLR cloud longevity.

Contribution

It provides analytical and numerical solutions for cloud orbits considering drag and anisotropic radiation, highlighting the decay of orbits and the importance of cloud formation mechanisms.

Findings

Cloud orbits decay due to drag force.

Time-of-flight is inversely proportional to drag coefficient.

Clouds may need continuous formation to sustain BLR.

Abstract

We study orbit of a pressure-confined cloud in the broad-line region (BLR) of active galactic nuclei (AGNs) when the combined effects of the central gravity and anisotropic radiation pressure and the drag force are considered. Physical properties of the intercloud gas such as its pressure and dynamic viscosity are defined as power-law functions of the radial distance. For a drag force proportional to the relative velocity of a cloud and the background gas, a detailed analysis of the orbits is performed for different values of the input parameters. We also present analytical solutions for a situation where the intercloud pressure is uniform and the viscosity is proportional to the inverse square of the radial distance. Our analytical and numerical solutions demonstrate decay of the orbits because of considering the drag force so that a cloud will eventually fall onto the central region after so called time-of-flight. We found that time-of-flight of a BLR cloud is proportional to the inverse of the dimensionless drag coefficient. We discuss if time-of-flight becomes shorter than the life time of the whole system, then existence of mechanisms for continually forming BLR clouds is needed.