The study of magnetars is of particular relevance since these objects are the
only laboratories where the physics in ultra-strong magnetic fields can be
directly tested. Until now, spectroscopic and timing measurements at X-ray
energies in soft gamma-repeaters (SGRs) and anomalous X-ray pulsar (AXPs) have
been the main source of information about the physical properties of a magnetar
and of its magnetosphere. Spectral fitting in the ~ 0.5-10 keV range allowed to
validate the "twisted magnetosphere" model, probing the structure of the
external field and estimating the density and velocity of the magnetospheric
currents. Spectroscopy alone, however, may fail in disambiguating the two key
parameters governing magnetospheric scattering (the charge velocity and the
twist angle) and is quite insensitive to the source geometry. X-ray
polarimetry, on the other hand, can provide a quantum leap in the field by
adding two extra observables, the linear polarization degree and the
polarization angle. Using the bright AXP 1RXS J170849.0-400910 as a template,
we show that phase-resolved polarimetric measurements can unambiguously
determine the model parameters, even with a small X-ray polarimetry mission
carrying modern photoelectric detectors and existing X-ray optics. We also show
that polarimetric measurements can pinpoint vacuum polarization effects and
thus provide an indirect evidence for ultra-strong magnetic fields.Comment: 12 pages, 8 figures, accepted for publication in MNRA
