The X-ray pulsar Centaurus X-3 is a neutron star that spins rapidly and emits pulses of X-ray light like a lighthouse. Scientists pointed three space telescopes at it and studied the polarization of its emission — how the electric field of the light wave oscillates. It turned out that this polarization behaves very capriciously: its angle changes with both photon energy and pulse phase.
To make sense of it, astronomers built a model with two components. The first is the pulse itself, described by a rotating model, like a compass needle spinning with the star. The second is an additional component that appears only at certain phases. It turned out that if you let this second component vary in brightness but keep its polarization angle fixed, all the complex changes are explained by a single simple picture.
Additional observations showed that there is a wind of matter around the pulsar, and its density changes with pulse phase. This means that light from the pulsar passes through different layers of this wind at different times. Scattering in this wind creates the extra polarization that muddies the picture. So the capricious polarization is not a quirk of the pulsar itself, but a consequence of its surroundings.
Centaurus X-3 was the first X-ray pulsar ever discovered — found in 1971, and since then it has served as a testing ground for studying neutron stars.