X-ray reverberation modelling of the continuum, optical/UV time-lags in quasars

¹ Department of Physics, University of Crete, 71003 Heraklion, Greece
² Institute of Astrophysics, FORTH, GR-71110 Heraklion, Greece
³ Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy
⁴ INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy
⁵ MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
⁶ Astronomical Institute of the Academy of Sciences, Boční II 1401, CZ-14100 Prague, Czech Republic

^⋆ Corresponding author; dlangis@physics.uoc.gr

Received: 8 May 2024
Accepted: 28 September 2024

Abstract

Context. Extensive, multi-wavelength monitoring campaigns of nearby and higher redshift active galactic nuclei (AGN) have shown that the UV/optical variations are well correlated with time delays which increase with increasing wavelength. Such behaviour is expected in the context of the X-ray thermal reverberation of the accretion disc in AGN.

Aims. Our main objective is to use time-lag measurements of luminous AGN and fit them with sophisticated X-ray reverberation time-lags models. In this way we can investigate whether X-ray reverberation can indeed explain the observed continuum time lags, and whether time-lag measurements can be used to measure physical parameters such as the X-ray corona height and the spin of the black hole (BH) in these systems.

Methods. We use archival time-lag measurements for quasars from different surveys, and we compute their rest frame, mean time-lags spectrum. We fit the data with analytical X-ray reverberation models, using χ² statistics, and fitting for both maximal and non spinning BHs, for various colour correction values and X-ray corona heights.

Results. We found that X-ray reverberation can explain very well the observed time lags, assuming the measured BH mass, accretion rate and X-ray luminosity of the quasars in the sample. The model agrees well with the data both for non-rotating and maximally rotating BHs, as long as the corona height is larger than ∼40 gravitational radii. This is in agreement with previous results which showed that X-ray reverberation can also explain the disc radius in micro-lensed quasars, for the same corona heights. The corona height we measure depends on the model assumption of a perfectly flat disc. More realistic disc models may result in lower heights for the X-ray corona.