The thermal plasma of galaxy clusters lost most of its information on how
structure formation proceeded as a result of dissipative processes. In
contrast, non-equilibrium distributions of cosmic rays (CR) preserve the
information about their injection and transport processes and provide thus a
unique window of current and past structure formation processes. This
information can be unveiled by observations of non-thermal radiative processes,
including radio synchrotron, hard X-ray, and gamma-ray emission. To explore
this, we use high-resolution simulations of a sample of galaxy clusters
spanning a mass range of about two orders of magnitudes, and follow
self-consistent CR physics on top of the radiative hydrodynamics. We model CR
electrons that are accelerated at cosmological structure formation shocks and
those that are produced in hadronic interactions of CRs with ambient gas
protons. We find that CR protons trace the time integrated non-equilibrium
activities of clusters while shock-accelerated CR electrons probe current
accretion and merging shock waves. The resulting inhomogeneous synchrotron
emission matches the properties of observed radio relics. We propose a unified
model for the generation of radio halos. Giant radio halos are dominated in the
centre by secondary synchrotron emission with a transition to the synchrotron
radiation emitted from shock-accelerated electrons in the cluster periphery.
This model is able to explain the observed correlation of mergers with radio
halos, the larger peripheral variation of the spectral index, and the large
scatter in the scaling relation between cluster mass and synchrotron emission.
Future low-frequency radio telescopes (LOFAR, GMRT, MWA, LWA) are expected to
probe the accretion shocks of clusters. [abridged]Comment: 32 pages, 19 figures, small changes to match the version to be
published by MNRAS, full resolution version available at
http://www.cita.utoronto.ca/~pfrommer/Publications/CRs_non-thermal.pd