Characterizing the Uncertainty in Cluster Magnetic Fields derived from Rotation Measures

TL;DR

This paper analyzes the uncertainties in estimating galaxy cluster magnetic fields from Faraday rotation measures, revealing an irreducible factor of about 3 and key sources of uncertainty.

Contribution

It provides a formalism to quantify uncertainties in RM-based magnetic field estimates using synthetic data from cosmological simulations.

Findings

Uncertainty factor of approximately 3 in magnetic field estimates

Principal uncertainties include line-of-sight depth and coherence length

RM estimates span over an order of magnitude in synthetic experiments

Abstract

Magnetic fields play vital roles in intracluster media (ICMs), but estimating their strengths and distributions from observations is a major challenge. Faraday rotation measures (RMs) are widely applied to this task, so it is critical to understand inherent uncertainties in RM analysis. In this paper, we seek to characterize those uncertainties given the types of information available today, independent of the specific technique used. We conduct synthetic RM observations through the ICM of a galaxy cluster drawn from an MHD cosmological simulation in which the magnetic field is known. We analyze the synthetic RM observations using an analytical formalism based on commonly used model assumptions allowing us to relate model physical variables to outcome uncertainties. Despite the simplicity of some assumptions, and unknown physical parameters, we are able to extract an approximate magnitude of the central magnetic field within an apparently irreducible uncertain factor approximately 3. Principal, largely irreducible, uncertainties come from the unknown depth along the line of sight of embedded polarized sources, the lack of robust coherence lengths from area-constrained polarization sampling, and the unknown scaling between ICM electron density and magnetic field strength. The RM-estimated central magnetic field strengths span more than an order of magnitude including the full range of synthetic experiments.