Prospects for differentiating extended coronal geometries in AGNs with the IXPE mission

X-ray polarimetry can potentially constrain the unknown geometrical shape of active galactic nucleous (AGN) coronae. We present simulations of the X-ray polarization signal expected from AGN coronae, assuming three different geometries, namely slab, spherical, and conical. We use the fully relativistic Monte Carlo Comptonization code MONK to compute the X-ray polarization degree and angle. We explore different coronal parameters such as shape, size, location, and optical depth. Different coronal geometries give a significantly different X-ray polarization signal. A slab corona yields a high polarization degree, up to 14 per cent depending on the viewing inclination; a spherical corona yields low values, about 1-3 per cent, while a conical corona yields intermediate values. We also find a difference of 90 degrees in polarization angle between the slab corona and the spherical or conical coronae. Upcoming X-ray polarimetry missions like IXPE will allow us to observationally distinguish among different coronal geometries in AGNs for the first time.