Abstract
Observations of diffuse radio emission in galaxy clusters indicate that cosmic-ray electrons are accelerated on ∼ Mpc scales. However, protons appear to be accelerated less efficiently since their associated hadronic γ-ray emission has not yet been detected. Inspired by recent particle-in-cell simulations, we study the cosmic-ray production and its signatures under the hypothesis that the efficiency of shock acceleration depends on the Mach number and on the shock obliquity. For this purpose, we combine ENZO cosmological magneto-hydrodynamical simulations with a Lagrangian tracer code to follow the properties of the cosmic rays. Our simulations suggest that the distribution of obliquities in galaxy clusters is random to first order. Quasi-perpendicular shocks are able to accelerate cosmic-ray electrons to the energies needed to produce observable radio emission. However, the γ-ray emission is lowered by a factor of a few, ∼3 , if cosmic-ray protons are only accelerated by quasi-parallel shocks, reducing (yet not entirely solving) the tension with the non-detection of hadronic γ-ray emission by the Fermi-satellite.
Highlights
The existence of peripheral, elongated and often polarised radio emission in galaxy clusters, so-called radio relics, gives evidence of cosmic-ray electrons being accelerated by shock waves in the intracluster medium
In [9] we studied how linking the shock acceleration efficiency to the shock obliquity can affect the acceleration of cosmic rays by predicting the amount of radio and γ-ray emission produced by either quasi-perpendicular or quasi-parallel shocks
We found that the distribution of shock obliquities in a galaxy cluster roughly follows the distribution of random angles in three-dimensional space, ∝ sin(α)
Summary
The existence of peripheral, elongated and often polarised radio emission in galaxy clusters, so-called radio relics, gives evidence of cosmic-ray electrons being accelerated by shock waves in the intracluster medium (see [1] and references therein). Cosmic-ray protons should undergo the same acceleration mechanism, but no evidence of their presence has been found yet. Extended searches for the γ-ray emission in the Coma cluster [4] and the Virgo cluster [5] have set the flux limits above 100 MeV to. Cosmic-ray protons should be accelerated more efficiently by diffusive shock acceleration (DSA) in parallel shocks [6]. Cosmic-ray electrons should prefer a perpendicular configuration as they are first accelerated by shock drift acceleration before they are injected into the DSA cycle [7,8]
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