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

X-ray polarimetry can potentially constrain the unknown geometrical shape of 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% depending on the viewing inclination; a spherical corona yields low values, about 1-3%, 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.