Magnetic power spectra from Faraday rotation maps - REALMAF and its use on Hydra A

TL;DR

This paper introduces a new maximum-a-posteriori method and the REALMAF code to measure magnetic power spectra from Faraday rotation data, applied to Hydra A, revealing a Kolmogorov-like spectrum and magnetic field profiles.

Contribution

The paper presents a novel Bayesian approach and a new code for analyzing magnetic power spectra from Faraday rotation data, improving upon previous methods.

Findings

Power spectrum follows a Kolmogorov-like power law between 0.3 and 8 kpc.

Magnetic field strength correlates with electron density profile.

Extrapolated magnetic field strength is 36 μG at the cluster center for a 45° jet angle.

Abstract

We develop a novel maximum-a-posteriori method to measure magnetic power spectra from Faraday rotation data and implement it in the REALMAF code. A sophisticated model for the magnetic autocorrelation in real space permits us to alleviate previously required simplifying assumptions in the processing. We also introduce a way to treat the divergence relation of the magnetic field with a multiplicative factor in Fourier space, with which we can model the magnetic autocorrelation as a spherically symmetric function. Applied to the dataset of Hydra A north, we find a power law power spectrum on spatial scales between 0.3 kpc and 8 kpc, with no visible turnover at large scales within this range and a spectral index consistent with a Kolmogorov-like power law regime. The magnetic field strength profile seems to follow the electron density profile with an index alpha=1. A variation of alpha from 0.5 to 1.5 would lead to a spectral index between 1.55 and 2.05. The extrapolated magnetic field strength in the cluster centre highly depends on the assumed projection angle of the jet. For an angle of 45 degree we derive extrapolated 36 muG in the centre and directly probed 16 muG at 50 kpc radius.