We report a search for linear polarization in the active galactic nucleus (AGN) 3C 84 (NGC 1275) at observed frequencies of 239 GHz and 348 GHz, corresponding to rest-frame frequencies of 243 GHz and 354 GHz. We collected polarization data with the IRAM Plateau de Bure Interferometer via Earth rotation polarimetry. We do not detect linear polarization. Our analysis finds 3-sigma upper limits on the degree of polarization of 0.5% and 1.9% at 239 GHz and 348 GHz, respectively. We regard the influence of Faraday conversion as marginal, leading to expected circular polarizations <0.3%. Assuming depolarization by a local Faraday screen, we constrain the rotation measure, as well as the fluctuations therein, to be 10^6 rad/m^2. From this we estimate line-of-sight magnetic field strengths of >100 microG. Given the physical dimensions of 3C 84 and its observed structure, the Faraday screen appears to show prominent small-scale structure, with DeltaRM > 10^6 rad/m^2 on projected spatial scales <1 pc.
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