Polarisation Leakage due to Errors in Track Reconstruction in Gas Pixel Detectors

X-ray polarimetry, based on Gas Pixel Detectors (GPDs), have reached a high level of maturity with the Imaging X-ray Polarimeter Explorer (IXPE) leading to the first ever spatially resolved polarimetric measures. However, being this a new technique, a few unexpected effect have emerged during in flight operations. In particular it was almost immediately found that on-board unpolarized calibration sources were showing radially polarized halos. The origin of this 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 in detail this effect, 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, and for the use of GPD-based techniques in general, and illustrate how to model it in the study of extended sources.