Analyzing the Data from X-ray Polarimeters with Stokes Parameters

TL;DR

This paper introduces a method using Stokes parameters to analyze X-ray polarimetry data, simplifying error calculations and improving the interpretation of polarization measurements from astrophysical sources.

Contribution

It adapts Stokes parameter analysis to X-ray polarimeters, providing formulas for error estimation, optimal observation times, and minimum detectable polarization, enhancing data analysis in X-ray polarimetry.

Findings

Stokes parameters facilitate straightforward error computation.

Derived formulas for minimum detectable polarization.

Optimized observation strategies for background contamination.

Abstract

X-ray polarimetry promises to deliver unique information about the geometry of the inner accretion flow of astrophysical black holes and the nature of matter and electromagnetism in and around neutron stars. In this paper, we discuss the possibility to use Stokes parameters - a commonly used tool in radio, infrared, and optical polarimetry - to analyze the data from X-ray polarimeters such as scattering polarimeters and photoelectric effect polarimeters, which measure the linear polarization of the detected X-rays. Based on the azimuthal scattering angle (in the case of a scattering polarimeter) or the azimuthal component of the angle of the electron ejection (in the case of a photoelectric effect polarimeter), the Stokes parameters can be calculated for each event recorded in the detector. Owing to the additive nature of Stokes parameters, the analysis reduces to adding the Stokes parameters of the individual events and subtracting the Stokes parameters characterizing the background (if present). The main strength of this kind of analysis is that the errors on the Stokes parameters can be computed easily and are well behaved - in stark contrast of the errors on the polarization fraction and polarization direction. We demonstrate the power of the Stokes analysis by deriving several useful formulae, e.g. the expected error on the polarization fraction and polarization direction for a detection of $N_S$ signal and $N_{BG}$ background events, the optimal observation times of the signal and background regions in the presence of non-negligible background contamination of the signal, and the minimum detectable polarization (MDP) that can be achieved when following this prescription.