Polarisation leakage due to errors in track reconstruction in gas pixel detectors

X-ray polarimetry based on gas pixel detectors (GPDs) has reached a high level of maturity thanks to the Imaging X-ray Polarimeter Explorer (IXPE) providing the first-ever spatially resolved polarimetric measurements. However, as this a new technique, a few unexpected effects have emerged in the course of in-flight operations. In particular, it was almost immediately found that, the unpolarized calibration sources on-board were showing radially polarized halos. The origin of these features was recognized in a correlation between the error in reconstructing the absorption point of the X-ray photon and the direction of its electric field vector. Here, we present and discuss this effect in detail, showing that it is possible to provide a simple and robust mathematical formalism to handle it. We further show its role and relevance for the recent IXPE measures as well as for the use of GPD-based techniques in general. We also illustrate how to model it in the context of studying extended sources.