On the Virialization of Disk Winds: Implications for the Black Hole Mass
  Estimates in AGN
  Estimating the mass of a supermassive black hole (SMBH) in an active galactic
nucleus (AGN) usually relies on the assumption that the broad line region (BLR)
is virialized. However, this assumption seems invalid in BLR models that
consists of an accretion disk and its wind. The disk is likely Keplerian and
therefore virialized. However, the wind material must, beyond a certain point,
be dominated by an outward force that is stronger than gravity. Here, we
analyze hydrodynamic simulations of four different disk winds: an isothermal
wind, a thermal wind from an X-ray heated disk, and two line-driven winds, one
with and the other without X-ray heating and cooling. For each model, we check
whether gravity governs the flow properties, by computing and analyzing the
volume-integrated quantities that appear in the virial theorem: internal,
kinetic, and gravitational energies, We find that in the first two models, the
winds are non-virialized whereas the two line-driven disk winds are virialized
up to a relatively large distance. The line-driven winds are virialized because
they accelerate slowly so that the rotational velocity is dominant and the wind
base is very dense. For the two virialized winds, the so-called projected
virial factor scales with inclination angle as $1/ \sin^2{i}$. Finally, we
demonstrate that an outflow from a Keplerian disk becomes unvirialized more
slowly when it conserves the gas specific angular momentum -- as in the models
considered here, than when it conserves the angular velocity -- as in the
so-called magneto-centrifugal winds.
