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

TL;DR

This study estimates the size of X-ray lamppost coronae in active galactic nuclei using relativistic ray-tracing, revealing that corona size and height depend on black hole spin and accretion rate, with maximal spin solutions aligning better with observations.

Contribution

It introduces a method to constrain corona sizes in AGN using ray-tracing and applies it to real data, highlighting the influence of black hole spin on corona geometry.

Findings

Coronas can exist below the Eddington limit with size constraints.

Maximally spinning black holes allow corona solutions at any height.

Higher spin correlates with more seed photon illumination and better spectral fit.

Abstract

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. We employ a relativistic ray-tracing code, originally developed by Dov\v{c}iak & Done (2016), 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. 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 due to a larger and hotter inner disc area. The maximal spin solution is favored, as it predicts an X-ray photon index in better agreement with the observations.