The intracluster magnetic field power spectrum in A2199

We investigate the magnetic field power spectrum in the cool core galaxy cluster A2199 by analyzing the polarized emission of the central radio source 3C338. The polarized radiation from the radio emitting plasma is modified by the Faraday rotation as it passes through the magneto-ionic intracluster medium. We use Very Large Array observations between 1665 and 8415 MHz to produce detailed Faraday rotation measure and fractional polarization images of the radio galaxy. We simulate Gaussian random three-dimensional magnetic field models with different power-law power spectra and we assume that the field strength decreases radially with the thermal gas density as n_e^{\eta}. By comparing the synthetic and the observed images with a Bayesian approach, we constrain the strength and structure of the magnetic field associated with the intracluster medium. We find that the Faraday rotation toward 3C338 in A2199 is consistent with a magnetic field power law power spectrum characterized by an index n=(2.8 \pm 1.3) between a maximum and a minimum scale of fluctuation of \Lambda_{max}=(35 \pm 28) kpc and \Lambda_{min}=(0.7 \pm 0.1) kpc, respectively. By including in the modeling X-ray cavities coincident with the radio galaxy lobes, we find a magnetic field strength of <B_0>=(11.7 \pm 9.0) \mu G at the cluster center. Further out, the field decreases with the radius following the gas density to the power of \eta=(0.9 \pm 0.5).