On understanding the figures of merit for detection and measurement of x-ray polarization

TL;DR

This paper clarifies the statistical basis of the minimum detectable polarization (MDP) in X-ray polarization measurements, addressing misconceptions and emphasizing its implications for future astronomical missions.

Contribution

It provides a detailed review and clarification of the statistical uncertainties and the proper interpretation of the MDP in X-ray polarization measurements.

Findings

Clarifies the distinction between MDP and measurement uncertainty.

Highlights the importance of correct statistical interpretation for future missions.

Addresses confusion stemming from historical misunderstandings of the MDP.

Abstract

The prospects for accomplishing X-ray polarization measurements appear to have grown in recent years after a more than 35-year hiatus. Unfortunately, this long hiatus has brought with it some confusion over the statistical uncertainties associated with polarization measurements of astronomical sources. The heart of this confusion stems from a misunderstanding (or potential misunderstanding) of a standard figure of merit-the minimum detectable polarization (MDP)-that one of us introduced many years ago. We review the relevant statistics, and quantify the differences between the MDP and the uncertainty of an actual polarization measurement. We discuss the implications for future missions.