Analysis of Polarimetry Data with Angular Uncertainties

TL;DR

This paper develops a likelihood-based method to incorporate angular uncertainties from machine learning track measurements into the sensitivity analysis of polarimeters like IXPE, improving the estimation of the minimum detectable polarization.

Contribution

It introduces a revised maximum likelihood approach that accounts for event track angle uncertainties, linking them to energy-dependent modulation for better polarization sensitivity estimates.

Findings

Derived a relationship between angular uncertainties and modulation function.

Enhanced MDP estimation by including track angle uncertainties.

Applicable to energy-dependent polarimetry measurements.

Abstract

For a track based polarimeter, such as the Imaging X-ray Polarimetry Explorer (IXPE), the sensitivity to polarization depends on the modulation factor, which is a strong function of energy. In previous work, a likelihood method was developed that would account for this variation in order to estimate the minimum detectable polarization (MDP). That method essentially required that the position angles of individual events should be known precisely. In a separate work, however, it was shown that using a machine learning method for measuring event tracks can generate track angle uncertainties, which can be used in the analysis. Here, the maximum likelihood method is used as a basis for revising the estimate of the MDP in a general way that can include uncertainties in event track position angles. The resultant MDP depends solely upon the distribution of track angle uncertainties present in the input data. Due to the physics of the IXPE detectors, it is possible to derive a simple relationship between these angular uncertainties and the energy-dependent modulation function as a step in the process.