Magnetic fields and cosmic rays in clusters of galaxies
  We argue that the observed correlation between the radio luminosity and the
X-ray luminosity in radio emitting galaxy clusters implies that the radio
emission is due to secondary electrons that are produced by p-p interactions
and lose their energy by emitting synchrotron radiation in a strong magnetic
field, B>(8\pi a T_{CMB}^4)^{1/2}\simeq 3\muG. We construct a simple model that
naturally explains the correlation, and show that the observations provide
stringent constraints on cluster magnetic fields and cosmic rays (CRs): Within
the cores of clusters, the ratio beta_{core} between the CR energy (per
logarithmic particle energy interval) and the thermal energy is beta_{core}\sim
2*10^{-4}; The source of these CRs is most likely the cluster accretion shock,
which is inferred to deposit in CRs ~ 0.1 of the thermal energy it generates;
The diffusion time of 100 GeV CRs over scales \gtrsim100 kpc is not short
compared to the Hubble time; Cluster magnetic fields are enhanced by mergers to
\gtrsim 1 % of equipartition, and decay (to <1 muG) on 1 Gyr time scales. The
inferred value of beta_{core} implies that high energy gamma-ray emission from
secondaries at cluster cores will be difficult to detect with existing and
planned instruments.
