  We investigated, using spectral-timing analysis, the characterization of
highly ionized outflows in Seyfert galaxies, the so-called warm absorbers.
Here, we present our results on the extensive ~ 600 ks of XMM-Newton archival
observations of the bright and highly variable Seyfert 1 galaxy NGC 4051, whose
spectrum has revealed a complex multicomponent wind. Making use of both RGS and
EPIC-pn data, we performed a detailed analysis through a time-dependent
photoionization code in combination with spectral and Fourier spectral-timing
techniques. The source light curves and the warm absorber parameters obtained
from the data were used to simulate the response of the gas due to variations
in the ionizing flux of the central source. The resulting time variable spectra
were employed to predict the effects of the warm absorber on the time lags and
coherence of the energy dependent light curves. We have found that, in the
absence of any other lag mechanisms, a warm absorber with the characteristics
of the one observed in NGC 4051, is able to produce soft lags, up to 100 s, on
timescales of ~ hours. The time delay is associated with the response of the
gas to changes in the ionizing source, either by photoionization or radiative
recombination, which is dependent on its density. The range of radial distances
that, under our assumptions, yield longer time delays are comparable to the
existing estimates of the location of the warm absorber in NGC 4051. For this
reason, we suggest that it is likely that the observed X-ray time lags may
carry a signature of the warm absorber response time, to changes in the
ionizing continuum. These results highlight the importance of understanding the
contribution of the warm absorber to the AGN X-ray time lags, since it is also
vital information for interpreting the lags associated with propagation and
reverberation effects in the inner emitting regions.
