Estimating longterm power spectral densities in AGN from simulations

The power spectral density (PSD) represents a key property quantifying the stochastic or random noise type fluctuations in variable sources like Active Galactic Nuclei (AGN). In recent years, estimates of the PSD have been refined by improvements in both, the quality of observed lightcurves and modeling them with simulations. This has aided in quantifying the variability including evaluating the significance of quasi-periodic oscillations. A central assumption in making such estimates is that of weak non-stationarity. This is violated for sources with a power-law PSD index steeper than one as the integral power diverges. As a consequence, estimates of the flux probability density function (PDF) and PSD are interlinked. In general, for evaluating parameters of both properties from lightcurves, one cannot avoid a multi-dimensional, multi-parameter model which is complex and computationally expensive, as well as harder to constrain and interpret. However, if we only wish to compute the PSD index as is often the case, we can use a simpler model. We explore a bending power-law model instead of a simple power-law as input to time-series simulations to test the quality of reconstruction. Examining the longterm variability of the classical blazar Mrk 421, extending to multiple years as is typical of Fermi-LAT or Swift-BAT lightcurves, we find that a transition from pink (PSD index one) to white noise at a characteristic timescale, $t_b \sim 500-1000$ years, comparable to the viscous timescale at the disk truncation radius, seems to provide a good model for simulations. This is both a physically motivated as well as a computationally efficient model that can be used to compute the PSD index.