2025A&A...696A.224F

Polarimetric observations of X-ray pulsars (XRPs) have provided us with the key to unlocking their geometrical properties. Thanks to the Imaging X-ray Polarimetry Explorer (IXPE), the geometries of several XRPs have been determined, providing new insights into their emission mechanisms and magnetic field structures. The polarimetric properties of Vela X-1 have a clear dependence on energy, showing a 90° swing in the polarization angle (PA) between low and high energies. Due to the complex energy-dependent nature of the polarization properties, until now it was not possible to determine the pulsar geometry. In this work we present the results of a detailed analysis of the pulse-phase-resolved polarization properties of Vela X-1 at different energies. By separating the polarimetric analysis into low and high energy ranges, we are able to disentangle the contributions of the soft and hard spectral components to the polarization, revealing the pulse phase dependence of the polarization degree and PA in each energy band. The PA pulse-phase dependence at high energies (5-8 keV) allows us, for the first time, to determine the pulsar geometry in Vela X-1. Based on the fit with the rotating vector model, we estimate the pulsar spin position angle to be around 127° and the magnetic obliquity to be 13°. We discuss two possible scenarios that could explain the 90° swing in the PA between high and low energies: a two-component spectral model and vacuum resonance.