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We present the results from a full polarization study carried out with ALMAduring the first VLBI campaign, which was conducted in Apr 2017 in the$\lambda$3mm and $\lambda$1.3mm bands, in concert with the Global mm-VLBI Array(GMVA) and the Event Horizon Telescope (EHT), respectively. We determine thepolarization and Faraday properties of all VLBI targets, including Sgr A*, M87,and a dozen radio-loud AGN. We detect high linear polarization fractions(2-15%) and large rotation measures (RM $>10^{3.3}-10^{5.5}$ rad m$^{-2}$). ForSgr A* we report a mean RM of $(-4.2\pm0.3) \times10^5$ rad m$^{-2}$ at 1.3 mm,consistent with measurements over the past decade, and, for the first time, anRM of $(-2.1\pm0.1) \times10^5$ rad m$^{-2}$ at 3 mm, suggesting that abouthalf of the Faraday rotation at 1.3 mm may occur between the 3 mm photosphereand the 1.3 mm source. We also report the first unambiguous measurement of RMtoward the M87 nucleus at mm wavelengths, which undergoes significant changesin magnitude and sign reversals on a one year time-scale, spanning the rangefrom -1.2 to 0.3 $\times\,10^5$ rad m$^{-2}$ at 3 mm and -4.1 to 1.5$\times\,10^5$ rad m$^{-2}$ at 1.3 mm. Given this time variability, we arguethat, unlike the case of Sgr A*, the RM in M87 does not provide an accurateestimate of the mass accretion rate onto the black hole. We put forward atwo-component model, comprised of a variable compact region and a staticextended region, that can simultaneously explain the polarimetric propertiesobserved by both the EHT and ALMA. These measurements provide criticalconstraints for the calibration, analysis, and interpretation of simultaneouslyobtained VLBI data with the EHT and GMVA.

Polarimetric properties of Event Horizon Telescope targets from ALMA