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 of 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 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 distances r 0.3-1.0 × 1016 cm, and hence gas densities n 0.4-3.0 × 107 cm-3. Since these ranges are comparable to the existing estimates of the location of the warm absorber in NGC 4051, 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. Our results show that the warm absorber in NGC 4051 does not introduce lags on the short timescales associated with reverberation, but will likely modify the hard continuum lags seen on longer timescales, which in this source have been measured to be on the order of 50 s. Hence, 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.
