Acceleration of primary and secondary particles in galaxy clusters by
  compressible MHD turbulence: from radio halos to gamma rays
  Radio observations discovered large scale non thermal sources in the central
Mpc regions of dynamically disturbed galaxy clusters (radio halos). The
morphological and spectral properties of these sources suggest that the
emitting electrons are accelerated by spatially distributed and gentle
mechanisms, providing some indirect evidence for turbulent acceleration in the
inter-galactic-medium (IGM). Only deep upper limits to the energy associated
with relativistic protons in the IGM have been recently obtained through gamma
and radio observations. Yet these protons should be (theoretically) the main
non-thermal particle component in the IGM implying the unavoidable production,
at some level, of secondary particles that may have a deep impact on the gamma
ray and radio properties of galaxy clysters. Following Brunetti and Lazarian
(2007), in this paper we consider the advances in the theory of MHD turbulence
to develop a comprehensive picture of turbulence in the IGM and extend our
previous calculations of particle acceleration by compressible MHD turbulence
by considering self-consistently the reacceleration of both primary and
secondary particles. Under these conditions we expect that radio to gamma ray
emission is generated from galaxy clusters with a complex spectrum that depends
on the dynamics of the thermal gas and Dark Matter. The non-thermal emission
results in very good agreement with radio observations and with present
constraints from hard X-ray and gamma ray observations. In our model giant
radio halos are generated in merging (turbulent) clusters only. However, in
case secondaries dominate the electron component in the IGM, we expect that the
level of the Mpc-scale synchrotron emission in more relaxed clusters is already
close to that of the radio upper limits derived by present observations of
clusters without radio halos.
