Robust analysis of differential Faraday rotation based on interferometric closure observables

Polarization calibration of interferometric observations is a costly procedure and, in some cases (e.g., a limited coverage of parallactic angle for the calibrator), it may not be possible to be performed. To avoid this worst-case scenario and expand the possibilities for the exploitation of polarization interferometric observations, the use of a new set of calibration-independent quantities (the closure traces) has been proposed. However, these quantities suffer from some degeneracies, so their use in practical situations may be rather limited. In this paper, we explore the use of closure traces on simulated and real observations, and show that (with the proper selection of fitting parameters) it is possible to retrieve information of the source polarization using only closure traces and constrain spatially resolved polarization. We carry out the first application of closure traces to the brightness modelling of real data, using the ALMA observations of M87 conducted on the April 2017 EHT campaign, quantifying a gradient in the Faraday rotation (FR) along the source structure (the M87 jet). This work opens the possibility to apply similar strategies to observations from any kind of interferometer (with a special focus on VLBI), from which quantities like differential Rotation Measure (RM) or the spatially resolved polarization can be retrieved.