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

Abstract

We assess the principal statistical and physical uncertainties associated with the determination of magnetic field strengths in clusters of galaxies from measurements of Faraday rotation (FR) and Compton-synchrotron emissions. In the former case, a basic limitation is noted, that the relative uncertainty in the estimation of the mean-squared FR is generally at least . Even greater uncertainty stems from the crucial dependence of the Faraday-deduced field on the coherence length scale characterizing its random orientation; we further elaborate this dependence and argue that previous estimates of the field are likely to be too high by a factor of a few. Lack of detailed spatial information on the radio emission—and the recently deduced nonthermal X-ray emission in four clusters—has led to an underestimation of the mean value of the field in cluster cores. We conclude therefore that it is premature to draw definite quantitative conclusions from the previously claimed, seemingly discrepant values of the field determined by these two methods.