  Recent modeling of the warm absorber in active galactic nuclei has proved the
usefulness of constant total (gas plus radiation) pressure models, which are
highly stratified in temperature and density. We explore the consistency of
those models when the typical variation of the flux from the central source is
taken into account. We perform a variability study of the warm absorber
response, based on timescales and our photoionization code TITAN. We show that
the ionization and recombination timescales are much shorter than the dynamical
timescale. Clouds very close to the central black hole will maintain their
equilibrium since the characteristic variability timescales of the nuclear
source are longer than cloud timescales. For more distant clouds, the density
structure has no time to vary, in response to the variations of the temperature
or ionization structure, and such clouds will show the departure from the
constant pressure equilibrium. We explore the impact of this departure on the
observed properties of the transmitted spectrum and soft X-ray variability: (i)
non uniform velocities, of the order of sound speed, appear due to pressure
gradients, up to typical values of 100 km/s. These velocities lead to the
broadening of lines. This broadening is usually observed and very difficult to
explain otherwise. (ii) Energy-dependent fractional variability amplitude in
soft X-ray range has a broader hump around ~ 1-2 keV, and (iv) the plot of the
equivalent hydrogen column density vs. ionization parameter is steeper than for
equilibrium clouds. The results have the character of a preliminary study and
should be supplemented in the future with full time-dependent radiation
transfer and dynamical computations.
