The study of magnetars is of particular relevance since these objects are theonly laboratories where the physics in ultra-strong magnetic fields can bedirectly tested. Until now, spectroscopic and timing measurements at X-rayenergies in soft gamma-repeaters (SGRs) and anomalous X-ray pulsar (AXPs) havebeen the main source of information about the physical properties of a magnetarand of its magnetosphere. Spectral fitting in the ~ 0.5-10 keV range allowed tovalidate the "twisted magnetosphere" model, probing the structure of theexternal field and estimating the density and velocity of the magnetosphericcurrents. Spectroscopy alone, however, may fail in disambiguating the two keyparameters governing magnetospheric scattering (the charge velocity and thetwist angle) and is quite insensitive to the source geometry. X-raypolarimetry, on the other hand, can provide a quantum leap in the field byadding two extra observables, the linear polarization degree and thepolarization angle. Using the bright AXP 1RXS J170849.0-400910 as a template,we show that phase-resolved polarimetric measurements can unambiguouslydetermine the model parameters, even with a small X-ray polarimetry missioncarrying modern photoelectric detectors and existing X-ray optics. We also showthat polarimetric measurements can pinpoint vacuum polarization effects andthus provide an indirect evidence for ultra-strong magnetic fields.
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