X-ray Polarimetry in the Low Statistics Regime using the Bayesian Approach Reveals Polarization Angle Variations

X-ray polarimetry of accreting compact objects has revealed fast time variations in the polarization angle (PA), suggesting that the geometry and/or optical depth of the Comptonization region is changing rapidly. This prompts investigations into how fast such variability can be. Conventionally, the data are often binned to examine the time variability such that the measurement in each bin is above the minimum detectable polarization (MDP). Here we demonstrate that this is unnecessary, and even below the MDP, one can infer the posterior distribution of PA reliably using the Bayesian approach and still be able to place useful constraints on the physics in many cases, due to small relative uncertainties on PA (e.g., $Δ$PA $\approx$ 10--30$^\circ$ compared with a dynamical range of 180$^\circ$). With this approach, we discovered that the PA variation in one of the Imaging X-ray Polarimetry Explorer (IXPE) observations of GX 13+1 is not following a linear rotation mode as suggested previously. Instead, the PA swings between two discrete angles, suggesting that there are two emitting components, e.g., the boundary layer and the spreading layer, competing with each other. In XTE J1701-462, we confirmed previous results for a variable PA in the normal branch, and furthermore, revealed that the variation timescale could be as short as 1.5 hours. During the IXPE observation of Sco X-1, a hint is found for the PA in the highest flux level to be different from the average but consistent with previous measurement results with PolarLight and OSO-8.