X-ray reverberation modelling of the observed UV/optical power spectra of quasars

¹ Department of Physics, University of Crete, 71003 Heraklion, Greece
² Institute of Astrophysics, FORTH, GR-71110 Heraklion, Greece
³ Department of Physics and Institute of Theoretical and Computational Physics, University of Crete, 71003 Heraklion, Greece
⁴ MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
⁵ Cahill Center for Astronomy and Astrophysics, California Institute of Technology, 1200 California Boulevard, Pasadena, CA 91125, USA
⁶ Astronomical Institute of the Academy of Sciences, Boční II 1401, CZ-14100 Prague, Czech Republic

^⋆ Corresponding author: mpapoutsis@physics.uoc.gr

Received: 21 February 2025
Accepted: 2 August 2025

Abstract

Context. Over the past decade, a significant amount of effort has been put into investigating the ultraviolet (UV) and optical variability of active galactic nuclei (AGNs). Comprehensive studies of intensive multi-wavelength monitoring and surveys of local and high-redshift AGNs have shown that X-ray illumination of AGN accretion discs is a potential explanation for the observed variability.

Aims. Our main objective is to study the UV/optical power spectra of AGNs under the assumption of X-ray reverberation and to test whether this model can explain the observed power spectra of distant quasars.

Methods. We computed the disc transfer function in the case of X-ray reverberation using a recent physical model and studied its dependence on the parameters of the model. This model allows us to explore the variability of X-ray illuminated discs under the scenario in which the X-ray corona is powered by the accretion process or by an external source. We then calculated UV/optical power spectra using the disc transfer function and assuming a bending power law for the X-ray power spectrum. We fitted our models to the observed power spectra of quasars determined by a recent power spectrum analysis of the SDSS Stripe-82 light curves.

Results. We demonstrate that X-ray reverberation can fit the power spectra of quasars in our sample well at all wavelengths, from ∼1300 Å up to 4000 Å. Our best-fit models imply that the X-ray corona is powered by the accretion disc, and that the black hole spin is probably lower than 0.7, while the X-ray corona height is in the range of 20 − 60 R_g. This is in agreement with previous findings from the application of the X-ray reverberation model to the quasar micro-lensing disc size problem, as well as recent time-lag measurements.