What’s the Buzz about GX 13+1? Constraining Coronal Geometry with QUEEN-BEE: A Bayesian Nested Sampling Framework for X-Ray Polarization Rotation Analysis

Abstract Observations from the Imaging X-ray Polarimetry Explorer (IXPE) have revealed electric vector position angle (EVPA) rotation in several neutron star low-mass X-ray binaries, including the Galactic X-ray burster GX 13+1. We developed a novel Bayesian nested sampling framework—“Q-U Event-by-Event Nested sampling for Bayesian EVPA Evolution” (QUEEN-BEE)—to model the unbinned Stokes parameters and infer optimal EVPA rotation rates in IXPE data. We then applied this framework to three previous IXPE observations of GX 13+1. In the first observation, QUEEN-BEE recovers a rotation rate of 42° ± 4° day −1 , consistent with prior binned analysis. Energy-binned QUEEN-BEE analysis of this first observation suggests a slablike coronal geometry, providing the first constraints between slab and shell coronae for this source. We also explore alternative EVPA rotation scenarios in GX 13+1, including variable disk wind behavior. The second observation of this source shows no evidence of rotation, and the third observation shows transient rotating behavior with an EVPA rotation rate when exiting a light curve dip of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>17</mml:mn> <mml:msubsup> <mml:mn>0</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>40</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>20</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>°</mml:mo> </mml:math> day −1 . The results show marginal but consistent increases in the overall measured polarization degree for epochs where the EVPA rotation is identified. These results demonstrate that QUEEN-BEE can identify evolving polarization signatures in both time- and energy-resolved regimes, even where binned methods fall below detection thresholds. Our findings highlight the diagnostic potential of QUEEN-BEE as a tool for discriminating between competing physical models of coronal geometry and probing disk-wind-related polarization behavior, highlighting the promising potential for application of this framework in a variety of other IXPE observations.