Estimating the size of X-ray lamppost coronae in active galactic nuclei

¹ Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy
e-mail: francesco.ursini@uniroma3.it
² Astronomical Institute, Academy of Sciences of the Czech Republic, Boční II 1401, 14100 Prague, Czech Republic
³ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
⁴ Centre for Extragalactic Astronomy, Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK

Received: 11 August 2020
Accepted: 12 October 2020

Abstract

Aims. We report estimates of the X-ray coronal size of active galactic nuclei in the lamppost geometry. In this commonly adopted scenario, the corona is assumed for simplicity to be a point-like X-ray source located on the axis of the accretion disc. However, the corona must intercept a number of optical/UV seed photons from the disc consistent with the observed X-ray flux, which constrains its size.

Methods. We employ a relativistic ray-tracing code, originally developed by Dovčiak and Done, that calculates the size of a Comptonizing lamppost corona illuminated by a standard thin disc. We assume that the disc extends down to the innermost stable circular orbit of a non-spinning or a maximally spinning black hole. We apply this method to a sample of 20 Seyfert 1 galaxies using simultaneous optical/UV and X-ray archival data from XMM-Newton.

Results. At least for the sources accreting below the Eddington limit, we find that a Comptonizing lamppost corona can generally exist, but with constraints on its size and height above the event horizon of the black hole depending on the spin. For a maximally spinning black hole, a solution can almost always be found at any height, while for a non-spinning black hole the height must generally be higher than 5 gravitational radii. This is because, for a given luminosity, a higher spin implies more seed photons illuminating the corona, which is due to a larger and hotter inner disc area. The maximal spin solution is favoured, as it predicts an X-ray photon index in better agreement with the observations.