Quantification of Uncertainty in the Measurement of Magnetic Fields in Clusters of Galaxies

We assess the principal statistical and physical uncertainties associatedwith the determination of magnetic field strengths in clusters of galaxies frommeasurements of Faraday rotation (FR) and Compton-synchrotron emissions. In theformer case a basic limitation is noted, that the relative uncertainty in theestimation of the mean-squared FR will generally be at least one third. Evengreater uncertainty stems from the crucial dependence of the Faraday-deducedfield on the coherence length scale characterizing its random orientation; wefurther elaborate this dependence, and argue that previous estimates of thefield are likely to be too high by a factor of a few. Lack of detailed spatialinformation on the radio emission--and the recently deduced nonthermal X-rayemission in four clusters--has led to an underestimation of the mean value ofthe field in cluster cores. We conclude therefore that it is premature to drawdefinite quantitative conclusions from the previously-claimedseemingly-discrepant values of the field determined by these two methods.Comment: 31 pages including 3 figures; accepted for publication in the Astrophysical Journal as paper #5497