Energy dependence of the X-ray power spectrum in NGC4051 and NGC4395

Abstract

Active galactic nuclei (AGNs) exhibit strong variability across the electromagnetic spectrum on a wide range of timescales, particularly in X-rays where fluctuations are both rapid and high amplitude. Power spectral density (PSD) analysis is commonly used to characterise this variability. Although AGN PSDs are typically well described by a bending power-law model, the dependence of the model parameters on photon energy has not been systematically investigated. We examine whether PSD parameters depend on energy using two highly variable, low-mass Seyfert galaxies, NGC4051 and NGC4395, as case studies. Using archival observations from XMM-Newton, Suzaku, and NuSTAR, we computed power spectra in six energy bands spanning 0.3-20 keV and fitted them with a bending power-law model to study the energy dependence of the PSD parameters. Power spectra derived from light curves obtained with different satellites and at different epochs are consistent within uncertainties, indicating that the X-ray variability process in both sources is stationary. For both AGNs we find that (i) the PSD bending frequency is consistent with being independent of energy, (ii) the high-frequency slope becomes flatter at higher energies, and (iii) the PSD amplitude decreases with increasing energy. These results place important constraints on models of AGN X-ray variability, such as the fluctuating accretion-rate model. Similar analyses of larger AGN samples are required to fully characterise the energy dependence of AGN power spectra.

Figures (5)

• Figure 1: Plot of the 0.3--0.5 and of the 1.5-5 keV keV band count rates as function of the 5--10 keV band count rate of NGC 4395 (top and bottom panels, respectively).
• Figure 2: Observed PSDs of NGC 4051 in the various energy bands we considered in this work. Open black squares and open green circles indicate the XMM-Newton and NuSTAR high frequency power spectra, respectively. Errors are plotted in all points, but they are smaller than the symbol size at high frequencies. Filled red squares and filled green circles indicate the low-frequency Suzaku and NuSTAR power spectra, respectively. The dashed lines indicate the best-fit BPL models to the PSDs at energies lower than 10 keV. For the 10--20 keV band, the dashed green lines correspond to the best-fit PL model. The bottom sub-panels display the best-fit residuals, with points colour-coded in the same manner (residuals were calculated as the difference between observed and model PSDs divided by the error of the PSDs).
• Figure 3: Same as in Fig. \ref{['fig:4051-PSD']}, but for NGC 4395.
• Figure 4: The energy dependence of the PSD parameters of NGC 4051. The solid black squares show the best-fit, BPL model parameters plotted as a function of energy for NGC 4051. Open red squares and open blue circles show the respective results from rani-etal2025, and from mchardy-etal2004, respectively. The solid lines indicate the weighted PSD$_{amp}$ of the four lowest energy points in the left panel, the best-fit log-linear model to the $\alpha_{high}-E$ data in the middle panel, and the weighted bending frequency in the right panel. Note that, for comparison reasons, the y axis limits are the same in the relevant panels in this figure and in Fig. \ref{['fig:4395-fit-params']}.
• Figure 5: Same as in Fig. \ref{['fig:4051-fit-params']}, but for NGC 4395. Open red squares in this case indicate the results of vaughan-etal2005. The solid lines indicate the best-fit log-linear model to the PSD$_{amp}$ vs $E$ plot (left panel), the weighted mean $\alpha_{high}$ and $\nu_b$ (middle and right panels, respectively). The dashed line in the middle panel indicate the best-fit log-liner model with a slope equal to the slope of the bst-fit to the $\alpha_{high}-E$ data in NGC 4051.