Effect of the drag force on the orbital motion of the broad-line region clouds

TL;DR

This paper studies how quadratic drag forces affect the orbital decay of clouds in active galactic nuclei, revealing faster infall times and implications for cloud formation mechanisms.

Contribution

It introduces a model considering quadratic drag forces on BLR clouds and quantifies their impact on orbital decay timescales, highlighting the need for continuous cloud formation.

Findings

Cloud orbital decay is faster with quadratic drag than linear drag.

Clouds typically fall onto the black hole faster than the system's age.

Continuous cloud creation mechanisms are necessary in BLR regions.

Abstract

We investigate orbital motion of cold clouds in the broad line region of active galactic nuclei subject to the gravity of a black hole and a force due to a nonisotropic central source and a drag force proportional to the velocity square. The intercloud is described using the standard solutions for the advection-dominated accretion flows. Orbit of a cloud decays because of the drag force, but the typical time scale of falling of clouds onto the central black hole is shorter comparing to the linear drag case. This time scale is calculated when a cloud is moving through a static or rotating intercloud. We show that when the drag force is a quadratic function of the velocity, irrespective of the initial conditions and other input parameters, clouds will generally fall onto the central region much faster than the age of whole system and since cold clouds present in most of the broad line regions, we suggest that mechanisms for continuous creation of the clouds must operate in these systems.