The Coma cluster magnetic field from Faraday rotation measures
  The aim of the present work is to constrain the Coma cluster magnetic field
strength, its radial profile and power spectrum by comparing Faraday Rotation
Measure (RM) images with numerical simulations of the magnetic field. We have
analyzed polarization data for seven radio sources in the Coma cluster field
observed with the Very Large Array at 3.6, 6 and 20 cm, and derived Faraday
Rotation Measures with kiloparsec scale resolution. Random three dimensional
magnetic field models have been simulated for various values of the central
intensity B_0 and radial power-law slope eta, where eta indicates how the field
scales with respect to the gas density profile. We derive the central magnetic
field strength, and radial profile values that best reproduce the RM
observations. We find that the magnetic field power spectrum is well
represented by a Kolmogorov power spectrum with minimum scale ~ 2 kpc and
maximum scale ~ 34 kpc. The central magnetic field strength and radial slope
are constrained to be in the range (B_0=3.9 microG; eta=0.4) and (B_0=5.4
microG; eta=0.7) within 1sigma. The best agreement between observations and
simulations is achieved for B_0=4.7 microG; eta=0.5. Values of B_0>7 microG and
<3 microG as well as eta < 0.2 and eta > 1.0 are incompatible with RM data at
99 % confidence level.
