Probing the origin of giant radio haloes through radio and γ-ray data: the case of the Coma cluster

Abstract

We combine for the first time all available information about the spectral shape and morphology of the radio halo of the Coma cluster with the recent γ -ray upper limits obtained by the Fermi-Large Area Telescope (LAT) and with the magnetic field strength derived from Faraday rotation measures. We explore the possibility that the radio emission is due to synchrotron emission of secondary electrons. First, we investigate the case of pure secondary models that are merely based on the mechanism of continuous injection of secondary electrons via proton-proton collisions in the intracluster medium. We use the observed spatial distribution of the halo's radio brightness to constrain the amount of cosmic ray protons and their spatial distribution in the cluster that are required by the model. Under the canonical assumption that the spectrum of cosmic rays is a power law in momentum and that the spectrum of secondaries is stationary, we find that the combination of the steep spectrum of cosmic ray protons necessary to explain the spectrum of the halo and the very broad spatial distribution (and large energy density) of cosmic rays result in a γ -ray emission in excess of present limits, unless the cluster magnetic field is relatively large. However, this large magnetic field required to not violate present γ -ray limits appears inconsistent with that derived from recent Faraday rotation measures. Secondly, we investigate more complex models in which the cosmic rays confined diffusively in the Coma cluster and their secondary electrons are all reaccelerated by magnetohydrodynamics turbulence. We show that under these conditions it is possible to explain the radio spectrum and morphology of the radio halo and to predict γ -ray fluxes in agreement with the Fermi-LAT upper limits without tension with present constraints on the cluster magnetic field. Reacceleration of secondary particles also requires a very broad cosmic ray spatial profile, much flatter than that of the intracluster medium, at least provided that both the turbulent and magnetic field energy densities scale with that of the intracluster medium. However, this requirement can be easily alleviated if we assume that a small amount of (additional) seed primary electrons is reaccelerated in the cluster's external regions, or if we adopt flatter scalings of the turbulent and magnetic field energy densities with distance from the cluster centre.

Shock Waves and Cosmic Ray Acceleration in the Outskirts of Galaxy Clusters

“…Our results indicate that the CR protons accelerated at shocks in the cluster outskirts may be capable of producing secondary electrons with the right energy spectral slope (q ss e ≈ 5.25-5.5) for the spectral index of observed radio halos. Brunetti et al (2012), however, argued that at least for the Coma cluster, the hadronic model that requires the CR proton energy 3%-5% of the thermal energy may violate the γ -ray upper limit set by Fermi-LAT observations, provided that the magnetic field is not much stronger than that measured/constrained by Faraday RM. Moreover, according to a more recent Fermi-LAT paper (Ackermann et al 2013), this limit has become even more stringent, constraining the CR proton energy down to 1% of the thermal energy in clusters.…”

“…Vazza et al (2012) also showed that the CR pressure distribution could be temporarily inverted, that is, the CR pressure can increase outward. Brunetti et al (2012), on the other hand, attempted to constrain the radial distributions of nonthermal components (including the CR proton energy density) in the Coma cluster by combining radio observations with recent Fermi-LAT γ -ray observations and with Faraday rotation measure (RM) data. They argued that the model based on the turbulent acceleration of secondary electrons would best reproduce the radio halo of the Coma cluster with the CR energy density that scales with the thermal energy density as ε CR ∝ ε θ th with θ ≈ −0.1 to −0.35, implying that ε CR is higher at lower ε th .…”

Lofar, Vla, and Chandra Observations of the Toothbrush Galaxy Cluster

“…In the turbulent re-acceleration model, electrons are re-accelerated by merger induced magnetohydrodynamical turbulence (e.g., Schlickeiser et al 1987;Brunetti et al 2001;Petrosian 2001;Pinzke et al 2015). Secondary models are challenged by the large energy content of cosmic ray protons needed to explain radio halos with very steep spectra (Brunetti 2004;Brunetti et al 2008) and by the non-detection of γ-rays (e.g., Jeltema & Profumo 2011;Brunetti et al 2012;Ackermann et al 2014).…”

THE DISCOVERY OF A RADIO HALO IN PLCK G147.3–16.6 AT Z = 0.65

“…In an alternative model, radio halos are produced by secondary electrons injected during proton-proton collisions in the ICM (e.g., Dennison 1980;Blasi & Colafrancesco 1999;Dolag & Enßlin 2000;Miniati et al 2001;Keshet & Loeb 2010). Secondary models are challenged by the large energy content of cosmic ray protons needed to explain radio halos with very steep spectra (e.g., Brunetti et al 2008) and by the non-detection of γ-rays from radio halos (e.g., Jeltema & Profumo 2011;Brunetti et al 2012). …”