CONSTRAINTS ON COSMIC RAYS, MAGNETIC FIELDS, AND DARK MATTER FROM GAMMA-RAY OBSERVATIONS OF THE COMA CLUSTER OF GALAXIES WITH VERITAS AND<i>FERMI</i>

Observations of radio halos and relics in galaxy clusters indicate efficient electron acceleration. Protons should likewise be accelerated and, on account of weak energy losses, can accumulate, suggesting that clusters may also be sources of very high energy (VHE; E &amp;amp;gt; 100 GeV) gamma-ray emission. We report here on VHE gamma-ray observations of the Coma galaxy cluster with the VERITAS array of imaging Cerenkov telescopes, with complementing Fermi Large Area Telescope 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) x 10(-8) photonsm(-2) s(-1) (VERITAS, &amp;amp;gt;220 GeV) and similar to 2 x 10(-6) photonsm(-2) s(-1) (Fermi, 1-3GeV), respectively. We use the gamma-ray upper limits to constrain cosmic rays (CRs) and magnetic fields in Coma. Using an analytical approach, the CR-to-thermal pressure ratio is constrained to be &amp;amp;lt; 16% from VERITAS data and &amp;amp;lt;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 &amp;amp;lt;50%. Alternatively, this may argue for non-negligible CR transport processes such as CR streaming and diffusion into the outer cluster regions. 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 similar to(2-5.5) mu G, 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, &amp;amp;lt;sigma nu &amp;amp;gt;.