Magnetic field at a jet base: extreme Faraday rotation in 3C 273 revealed by ALMA

We have studied the polarization behavior of the quasar 3C 273 over the 1 mm wavelength band at ALMA with a total bandwidth of 7.5 GHz across 223 to 243 GHz at 0.8" resolution, corresponding to 2.1 kpc at the distance of 3C 273. With these observations we are able to probe the optically thin polarized emission close to the jet base, and constrain the magnetic field structure at the jet launching region. We compute the Faraday rotation measure using simple linear fitting and Faraday rotation measure synthesis. In addition, we model the broadband behavior of the fractional Stokes Q and U parameters. The systematic uncertainties in the polarization observations at ALMA are assessed through Monte Carlo simulations. We find the unresolved core of 3C 273 to be 3.3% linearly polarized. We detect a very high rotation measure (RM) of ~ 3.6x10$^5$rad/m$^2$ over the 1 mm band with all the methods we have used. This results in a rotation of >30 degrees of the intrinsic electric vector position angle, which is significantly higher than typically assumed for millimeter wavelengths. Our results strongly favor depolarization models over an external Faraday screen without depolarization. For a single region dominating the polarized emission, the RM and depolarization we observe can be explained by external Faraday dispersion or an ordered RM gradient within the synthesized beam. Further multifrequency and high angular resolution observations are needed to determine the location and structure of the magnetic field of the Faraday active region. Comparing our RM estimate with values obtained at lower frequencies, the RM increases as a function of observing frequency, following a power law with an index of ~1.9 consistent with a sheath surrounding a conically expanding jet. We also detect ~0.2% circular polarization, although further observations are needed to confirm this result. (Abridged.)