Constraints on Cosmic Rays, Magnetic Fields, and Dark Matter from
  Gamma-Ray Observations of the Coma Cluster of Galaxies with VERITAS and Fermi
  Observations of radio halos and relics in galaxy clusters indicate efficient
electron acceleration. Protons should likewise be accelerated, suggesting that
clusters may also be sources of very high-energy (VHE; E>100 GeV) gamma-ray
emission. We report here on VHE gamma-ray observations of the Coma galaxy
cluster with the VERITAS array of imaging Cherenkov telescopes, with
complementing Fermi-LAT observations at GeV energies. No significant gamma-ray
emission from the Coma cluster was detected. Integral flux upper limits at the
99% confidence level were measured to be on the order of (2-5)*10^-8\ ph. m^-2
s^-1 (VERITAS, >220 GeV} and ~2*10^-6 ph. m^-2 s^-1 (Fermi, 1-3 GeV),
respectively. We use the gamma-ray upper limits to constrain CRs and magnetic
fields in Coma. Using an analytical approach, the CR-to-thermal pressure ratio
is constrained to be < 16% from VERITAS data and < 1.7% from Fermi data
(averaged within the virial radius). These upper limits are starting to
constrain the CR physics in self-consistent cosmological cluster simulations
and cap the maximum CR acceleration efficiency at structure formation shocks to
be <50%. Assuming that the radio-emitting electrons of the Coma halo result
from hadronic CR interactions, the observations imply a lower limit on the
central magnetic field in Coma of (2 - 5.5) muG, depending on the radial
magnetic-field profile and on the gamma-ray spectral index. Since these values
are below those inferred by Faraday rotation measurements in Coma (for most of
the parameter space), this {renders} the hadronic model a very plausible
explanation of the Coma radio halo. Finally, since galaxy clusters are
dark-matter (DM) dominated, the VERITAS upper limits have been used to place
constraints on the thermally-averaged product of the total self-annihilation
cross section and the relative velocity of the DM particles, <\sigma v>. (abr.)
