Radio Halos From Simulations And Hadronic Models II: The Scaling
  Relations of Radio Halos
  We use results from a constrained, cosmological MHD simulation of the Local
Universe to predict radio halos and their evolution for a volume limited set of
galaxy clusters and compare to current observations. The simulated magnetic
field inside the clusters is a result of turbulent amplification within them,
with the magnetic seed originating from star-burst driven, galactic outflows.
We evaluate three models, where we choose different normalizations for the
Cosmic Ray proton population within clusters. Similar to our previous analysis
of the Coma cluster (Donnert et al. 2010), the radial profile and the
morphological properties of observed radio halos can not be reproduced, even
with a radially increasing energy fraction within the cosmic ray proton
population. Scaling relations between X-ray luminosity and radio power can be
reproduced by all models, however all models fail in the prediction of clusters
with no radio emission. Also the evolutionary tracks of our largest clusters in
all models fail to reproduce the observed bi-modality in radio luminosity. This
provides additional evidence that the framework of hadronic, secondary models
is disfavored to reproduce the large scale diffuse radio emission of galaxy
clusters. We also provide predictions for the unavoidable emission of
$\gamma$-rays from the hadronic models for the full cluster set. None of such
secondary models is yet excluded by the observed limits in $\gamma$-ray
emission, emphasizing that large scale diffuse radio emission is a powerful
tool to constrain the amount of cosmic ray protons in galaxy clusters.
