Implementing and verifying a Fourier domain approach to fast stochastic X-ray polarimetry timing

ABSTRACT The launch of the Imaging X-ray Polarimetry Explorer (IXPE), the first space-based polarimeter since 1978, offers a two order of magnitude improvement to the measurement of X-ray polarization than its predecessor OSO-8, offering unprecedented precision for the measurement of linear polarization degree and polarization angle of X-ray sources. This advancement lends itself to the birth of a number of contemporary techniques to study Galactic compact objects, including X-ray polarimetry-timing, the study of how polarization properties evolve over short time-scales. However, the statistical nature of polarization measurements poses a challenge for studies on arbitrarily short time-scales, as a large number of photons are required to achieve statistically significant measurements of polarization degree and angle for time-resolved analyses. Furthermore, if the polarization variability is stochastic, then phase-folding techniques introduce systematic errors in the phase assignment of photons. Ingram and Maccarone presented a model-independent Fourier-based technique that circumvents these issues. It can be used on arbitrarily short time-scales for any kind of variability, whether aperiodic, quasi-periodic or purely periodic. Here, we implement this method on real IXPE data. We address several instrumental effects and test the technique on X-ray pulsars, RX-J0440.9 + 4431 and Hercules X-1. We verify that our technique recovers the polarization variability signal that we already know to be there from typical phase-folding techniques. It will now be possible to study fast stochastic polarization variability of X-ray sources, with applications including quasi-periodic oscillations, mass accretion rate fluctuations, and reverberation mapping.