Ultra-strong magnetic fields of neutron stars in binary systems are able to confine matter flowing from the donor star and channel it to the polar caps. It also shapes observed pulsed X-rays emerging from the polar cap as the pulsar spins because the radiative transport there is mostly defined by magnetic Compton scattering, which has highly anisotropic cross-section depending on angle between photon direction with respect to magnetic field lines.  This cross-section also strongly depends on photon polarization, i.e. the dominant direction of electric field oscillations. The latter fact implies that observed emission can be expected to be strongly polarized in the soft X-ray band and makes such objects a prime target for polarimetric studies with the recently launched IXPE mission.

The first X-ray pulsar observed by IXPE with counting statistics sufficient for detailed polarimetric analysis and subject of the recent Nature Astronomy paper "Determination of X-ray pulsar geometry with IXPE polarimetry" was Her X-1 - an enigmatic object discovered fifty years ago but still far from being fully understood.  Of particular interest here is the observed super-orbital variability with the period of ~35 days (orbital period is ~1.7 days) believed to be related to the precession of the accretion disk around the compact object, and possibly clocked by free precession of the neutron star itself. The latter hypothesis was prompted by the fact that complex evolution of the observed pulse profiles with phase of super-orbital cycle can indeed be modeled as a result of the precession of the neutron star and appears to be synchronized in phase with this semi-regular variability even on years-long timescales and even during periods when the source is not actively accreting. To answer whether this hypothesis holds and whether the modeling of the observed pulse profiles is solid, one needs to know, however, the geometry of the system,  including the direction of angular momenta of the neutron star and of the orbit, as well as the angle between that and the magnetic dipole axis.

That kind of information is not readily available, but that is where polarimetry really shines! IXPE observations were aimed primarily to get such constraints and also to verify the basic theoretical predictions for expected polarization degree and its energy dependence, which involve not only radiative transfer in strongly magnetized plasma but also quantum electrodynamic effects like vacuum polarization. Analysis of the data revealed a highly significant (>17σ) detection of polarized X-ray emission from the source, however, the observed polarization degree at ~8.5% turned out to be much lower than expected (60-80%).  This finding clearly signals that models of radiative transport in X-ray pulsars need to be rethinked in the coming era of X-ray polarimetry. From a practical perspective, such a low polarization is also more challenging to measure, but nevertheless it was also possible to investigate pulse phase dependence of the polarization degree and angle, and measure the angle between the spin and magnetic dipole axes of the neutron star assuming a simple rotating vector model. This measurement will serve as a valuable input for future detailed modeling of the observed pulse profile shapes. 

Combining the X-ray polarimetry constraints with the available optical polarimetry measurements, it was also possible to show that the spin of the neutron star is not aligned with the orbital angular momentum. Given that accretion torques acting on neutron stars are expected to ensure such alignment on relatively short timescales, this is a strong indication that the neutron star is indeed precessing, which has some implications on our understanding of both the astrophysics of Her X-1 as well as the internal structure of neutron stars in general. Additional observations of the source with IXPE planned closer to the end of the year at different phases of the precession cycle will unambiguously confirm this conclusion.