Energy dependence of the X-ray power spectrum in NGC 4051 and NGC 4395

¹ Department of Physics, University of Crete 71003 Heraklion, Greece
² Department of Physics and Institute of Theoretical and Computational Physics, University of Crete 71003 Heraklion, Greece
³ Institute of Astrophysics, FORTH GR-71110 Heraklion, Greece
⁴ IAASARS, National Observatory of Athens Ioannou Metaxa and Vasileos Pavlou 15236 Athens, Greece
⁵ Department of Astronomy, The University of Maryland College Park MD 20742, USA
⁶ HEASARC, Code 6601, NASA/GSFC Greenbelt MD 20771, USA
⁷ CRESST II, NASA Goddard Space Flight Center Greenbelt MD 20771, USA
⁸ Cahill Center for Astrophysics, California Institute of Technology 1216 East California Boulevard Pasadena CA 91125, USA
⁹ NASA Goddard Space Flight Center Greenbelt MD 20771, USA
¹⁰ Center for Space Science and Technology, University of Maryland Baltimore County 1000 Hilltop Circle Baltimore MD 21250, USA

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 8 October 2025
Accepted: 29 January 2026

Abstract

Context. Active galactic nuclei (AGNs) exhibit significant variability across the electromagnetic spectrum on a wide range of timescales. This variability is particularly extreme in the X–ray band, showing both high-amplitude and rapid fluctuations. Power spectral density (PSD) analysis is a common tool used to characterise the observed variability in these objects. Although PSDs of AGN are typically well described by a bending power-law model, the dependence of the model parameters on photon energy has not been systematically explored in the past.

Aims. Our objective is to investigate whether the PSD parameters of AGNs depend on energy, considering two low-mass Seyfert galaxies – NGC 4051 and NGC 4395 – as case studies. Both sources are highly variable in X-rays, and they have been observed extensively with current and past X-ray satellites. Using all archival observations, we aim to measure their power spectra over a broad frequency and energy range and investigate if and how the power spectrum evolves with energy.

Methods. We used archival data from XMM-Newton, Suzaku, and NuSTAR, and computed the power spectrum in six energy bands from 0.3 to 20 keV. Then we fitted the power spectra with a bending power-law model and investigated the energy dependence of the model parameters.

Results. The power spectra computed using light curves taken from different satellites and at different times are consistent within the errors, indicating that the X-ray variability process is stationary in these two objects. We found that, for both sources: a) the PSD bending frequency remains constant with the energy, b) the high-frequency slope becomes flatter with increasing energy, and c) the power spectrum amplitude decreases with increasing energy.

Conclusions. Our results can significantly constrain current models that explain the variability of X-rays in AGNs (such as the fluctuating accretion rate model). Similar studies of more AGNs are necessary to quantify in detail the energy dependence of the power spectrum in AGNs.