Measuring x-ray polarization in the presence of systematic effects: Known background

TL;DR

This paper develops a mathematical framework to accurately estimate uncertainties in x-ray polarization measurements, accounting for background effects, which is crucial for advancing astronomical observations after a long hiatus.

Contribution

It introduces a formalism for calculating errors in x-ray polarization measurements considering background effects, clarifying statistical uncertainties and the distinction between MDP and measurement accuracy.

Findings

Formalism for 1- and 2-parameter errors in polarization magnitude and angle

Clarification of statistical measures like MDP and measurement accuracy

Insights into uncertainties in x-ray polarization measurements with background effects

Abstract

The prospects for accomplishing x-ray polarization measurements of astronomical sources have grown in recent years, after a hiatus of more than 37 years. Unfortunately, accompanying this long hiatus has been some confusion over the statistical uncertainties associated with x-ray polarization measurements of these sources. We have initiated a program to perform the detailed calculations that will offer insights into the uncertainties associated with x-ray polarization measurements. Here we describe a mathematical formalism for determining the 1- and 2-parameter errors in the magnitude and position angle of x-ray (linear) polarization in the presence of a (polarized or unpolarized) background. We further review relevant statistics-including clearly distinguishing between the Minimum Detectable Polarization (MDP) and the accuracy of a polarization measurement.