Relativistic reflection within an extended hot plasma geometry

Context. The reflection of X-rays at the inner accretion disk around black holes imprints relativistically broadened features in the observed spectrum. Aside from the black hole properties and the ionization and density of the accretion disk, these features also depend on the location and geometry of the primary source of X-rays, often referred to as the corona. Aims. We present a fast general relativistic model for spectral fitting of a radially extended, ring-like corona above the accretion disk. Methods. A common approach used to explain observed X-ray reflection spectra is the lamp post geometry, which assumes a point-like source on the rotational axis of the black hole. While it is typically able to explain the observations, this geometric model does not allow for any constraint to be placed on the radial size of the corona. We therefore extended the publicly available relativistic reflection model <ns0:sc>RELXILL</ns0:sc> by implementing a radially extended, ring-like primary source. Results. With the new <ns0:sc>RELXILL</ns0:sc> model allowing us to vary the position of the primary source in two dimensions, we present simulated line profiles and spectra and discuss the implications of carrying out a data fitting, in comparison to the lamp post model. We applied this extended <ns0:sc>RELXILL</ns0:sc> model to XMM-Newton and NuSTAR data of the radio-quiet Seyfert-2 active galactic nucleus (AGN) ESO 033-G002. The new model describes the data well and we are able to constrain the distance of the source to the black hole to be less than three gravitational radii, while the angular position of the source is poorly constrained. Conclusions. We show that a compact, radially extended corona close to the innermost stable circular orbit is able to explain the observed relativistic reflection as well as the lamp post corona does. This model has been made freely available to the community.