Advanced Weights for IXPE Polarization Analysis

TL;DR

The paper tackles the challenge of extracting accurate X-ray polarization from IXPE data for faint sources by introducing a comprehensive, weight-enabled maximum-likelihood framework. It combines polarization weights from NN-informed modulations, spatial PSF-based weights, CNN-derived background de-weighting, and spectral/temporal weights into a unified likelihood, validated on simulations and real IXPE observations. The approach significantly reduces polarization uncertainty contours (by about a factor of two) and outperforms standard PCUBE and prior MLE methods, particularly in background-limited or complex-source scenarios. The methods, implemented in LeakageLib, offer a practical path to tighter polarization constraints in broad-band IXPE analyses and can be extended to extended or time-variable sources, with careful caveats for spectral interpretation.

Abstract

As the Imaging X-ray Polarimetry Explorer (IXPE) measures increasingly faint sources, the need for precise polarimetry extraction becomes paramount. In addition to previously described neural-net (NN) weights, we introduce here point-spread function weights and particle background weights, which can be critical for faint sources. In some cases these can be augmented by time/phase and energy weights. We provide a publicly available analysis tool to incorporate these new weights, validate our method on simulated data, and test it on archival IXPE observations. Together these weights decrease the area of the polarization uncertainty contour by a factor of two compared to baseline IXPE analysis and will be essential for background-limited IXPE observations.

Figures (4)

• Figure 1: The halo representing scattered prompt emission from GRB 221009A with different background removal techniques. From left: all $2-8$ keV counts; counts surviving the background cut of dimarco2023handling; counts weighted by the photon character $1-\pi_i$ this work introduces; radial profiles of the images. Green circles highlight the rings as a visual aid. The stretch, max, and min are identical between all panels. The gray curve in the rightmost panel presents a model of the true radial profile derived from the Swift GRB 221009A observation, accounting for the IXPE PSF and adding a uniform background.
• Figure 2: The average CNN particle character plotted vs. Mom track properties for PSR B0540$-$69. The dotted black and white line represents the mission-standard background cuts. 68% and 95% contours of suspected source and background events are also shown. The CNN identifies similar energy dependence of the particle track properties, but enables the use of more precise weighting methods.
• Figure 3: Uncertainties as a function of background flux, measured by the ratio of background counts within the 60$"$PCUBE radius to source counts. The number of source counts is kept constant. Dotted lines show the true Stokes coefficients, and dashed lines show the coefficients extracted by the two fit methods. Bands reflect the estimated uncertainties. Especially for faint sources, our method delivers substantially more precise fits than PCUBE.
• Figure 4: Polarization degrees extracted for four point sources using aperture-based methods in common use (left) and the weights considered in this work (right). Black results use Mom-reconstructed data while red results use NN reconstruction. Uncertainties are expressed in terms of the PD uncertainty and the area of the Q-U uncertainty contour ($\sigma_Q \sigma_U$) relative to the PCUBE area. PD Results are compared in the middle column. The weights introduced in this paper together substantially reduce polarization uncertainties. For the GRB, $\times$s indicate 99% confidence upper PD limits since polarization is not detected.