Constraining the population of cosmic ray protons in cooling flow
clusters with gamma-ray and radio observations: Are radio mini-halos of
hadronic origin?
We wish to constrain the cosmic-ray proton (CRp) population in galaxy
clusters. By hadronic interactions with the thermal gas of the intra-cluster
medium (ICM), the CRp produce gamma-rays for which we develop an analytic
formalism to deduce their spectral distribution. Assuming the CRp-to-thermal
energy density ratio X_CRp and the CRp spectral index to be spatially constant,
we derive an analytic relation between the gamma-ray and bolometric X-ray
fluxes, F_gamma and F_X. Based on our relation, we compile a sample of suitable
clusters which are promising candidates for future detection of gamma-rays
resulting from hadronic CRp interactions. Comparing to EGRET upper limits, we
constrain the CRp population in the cooling flow clusters Perseus and Virgo to
X_CRp < 20%. Assuming a plausible value for the CRp diffusion coefficient
kappa, we find the central CRp injection luminosity of M 87 to be limited to
10^43 erg s^-1 kappa/(10^29 cm^2 s^-1). The synchrotron emission from secondary
electrons generated in CRp hadronic interactions allows even tighter limits to
be placed on the CRp population using radio observations. We obtain excellent
agreement between the observed and theoretical radio brightness profiles for
Perseus, but not for Coma without a radially increasing CRp-to-thermal energy
density profile. Since the CRp and magnetic energy densities necessary to
reproduce the observed radio flux are very plausible, we propose synchrotron
emission from secondary electrons as an attractive explanation of the radio
mini-halos found in cooling flow clusters. This model can be tested with future
sensitive gamma-ray observations of the accompanying pi0-decays. We identify
Perseus (A 426), Virgo, Ophiuchus, and Coma (A 1656) as the most promising
candidate clusters for such observations.Comment: 20 pages, 8 figures. Corrected Figure 3 to match the erratum accepted
by A&