Monitoring the power spectrum of magnetic field fluctuations across the simulated intracluster medium

Thanks to the current and forthcoming radio interferometers, Faraday rotation measure maps extend out to the outskirts of galaxy clusters. Interpreted through models of the magnetic power spectrum, these maps can provide stringent constraints on the properties of the magnetic field of the intracluster medium (ICM). Our goal is to ascertain how the magnetic power spectrum varies with the environment and dynamics of the ICM in a post-merger galaxy cluster formed in a state-of-the-art non-radiative cosmological magneto-hydrodynamic simulation. We divide the simulated cluster into cubic subboxes with side length 950 kpc and compute the kinetic and magnetic power spectra in each. Starting from a "dynamo-only" functional form proposed in previous works to describe magnetic fluctuations amplified by the small-scale dynamo, we introduce an additional Kolmogorov-like component to account for the contribution of unamplified magnetic field patches. We fit this extended model to the magnetic power spectrum of each subbox individually using a Markov chain Monte Carlo method and examine scatter plots of the inferred parameters versus the local ICM properties evaluated in the corresponding subboxes. The extended model reproduces the magnetic power spectrum data well in most subboxes, whereas the "dynamo-only" model fits these data well only in subboxes not too far from the center. The inferred parameters exhibit substantial subbox-to-subbox variations that correlate significantly with the local ICM density and clumpiness. These correlations suggest that the magnetic power spectrum is closely linked to the local ICM environment, and may help observers in the interpretation of Faraday Rotation data.