<table><caption>Table E2
Polarization Parameters of EHT Sources per Frequency Band (SPW) and per Day</caption><thead><tr><th>Frequency<br>(GHz)</th><th>I<br>(mJy)</th><th>Q<br>(mJy)</th><th>U<br>(mJy)</th><th>LP<br>(%)</th><th>EVPA<br>(deg)</th></tr></thead><tbody><tr><td colspan="6" style="text-align:center; font-weight:bold;">Apr 5</td></tr><tr><td colspan="6" style="text-align:center;">4C 01.28</td></tr><tr><td>213.1</td><td>3572.28 ± 0.11</td><td>144.5 ± 1.1</td><td>-151.7 ± 1.1</td><td>5.867 ± 0.030</td><td>-23.20 ± 0.14</td></tr><tr><td>215.1</td><td>3617.41 ± 0.11</td><td>145.8 ± 1.1</td><td>-153.3 ± 1.1</td><td>5.848 ± 0.030</td><td>-23.23 ± 0.15</td></tr><tr><td>227.1</td><td>3429.88 ± 0.11</td><td>138.9 ± 1.0</td><td>-146.7 ± 1.0</td><td>5.890 ± 0.030</td><td>-23.28 ± 0.14</td></tr><tr><td>229.1</td><td>3419.77 ± 0.11</td><td>141.9 ± 1.0</td><td>-147.0 ± 1.0</td><td>5.976 ± 0.030</td><td>-23.01 ± 0.14</td></tr><tr><td colspan="6" style="text-align:center;">OJ 287</td></tr><tr><td>213.1</td><td>4455.60 ± 0.15</td><td>-214.2 ± 1.3</td><td>-342.2 ± 1.3</td><td>9.060 ± 0.030</td><td>-61.027 ± 0.092</td></tr><tr><td>215.1</td><td>4476.37 ± 0.17</td><td>-214.8 ± 1.3</td><td>-339.6 ± 1.3</td><td>8.976 ± 0.030</td><td>-61.161 ± 0.092</td></tr><tr><td>227.1</td><td>4220.58 ± 0.15</td><td>-205.0 ± 1.3</td><td>-314.9 ± 1.3</td><td>8.902 ± 0.030</td><td>-61.53 ± 0.10</td></tr><tr><td>229.1</td><td>4198.43 ± 0.15</td><td>-203.6 ± 1.3</td><td>-325.3 ± 1.3</td><td>9.139 ± 0.030</td><td>-61.022 ± 0.093</td></tr><tr><td colspan="6" style="text-align:center;">M87</td></tr><tr><td>213.1</td><td>1336.29 ± 0.13</td><td>30.07 ± 0.40</td><td>-7.70 ± 0.40</td><td>2.323 ± 0.030</td><td>-7.17 ± 0.36</td></tr><tr><td>215.1</td><td>1325.68 ± 0.13</td><td>29.94 ± 0.40</td><td>-8.10 ± 0.40</td><td>2.338 ± 0.030</td><td>-7.57 ± 0.38</td></tr><tr><td>227.1</td><td>1236.46 ± 0.11</td><td>29.62 ± 0.37</td><td>-8.80 ± 0.37</td><td>2.500 ± 0.030</td><td>-8.29 ± 0.35</td></tr><tr><td>229.1</td><td>1227.58 ± 0.11</td><td>29.81 ± 0.37</td><td>-8.74 ± 0.37</td><td>2.530 ± 0.030</td><td>-8.15 ± 0.35</td></tr><tr><td colspan="6" style="text-align:center;">3C 279</td></tr><tr><td>213.1</td><td>9202.50 ± 0.11</td><td>-8.0 ± 2.8</td><td>1214.2 ± 2.8</td><td>13.195 ± 0.030</td><td>45.187 ± 0.066</td></tr><tr><td>215.1</td><td>9144.74 ± 0.11</td><td>-7.2 ± 2.7</td><td>1206.7 ± 2.7</td><td>13.195 ± 0.030</td><td>45.168 ± 0.065</td></tr><tr><td>227.1</td><td>8845.31 ± 0.12</td><td>-7.9 ± 2.7</td><td>1169.0 ± 2.7</td><td>13.216 ± 0.030</td><td>45.193 ± 0.063</td></tr><tr><td>229.1</td><td>8774.06 ± 0.12</td><td>-6.9 ± 2.6</td><td>1161.8 ± 2.6</td><td>13.241 ± 0.030</td><td>45.172 ± 0.066</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">Apr 6</td></tr><tr><td colspan="6" style="text-align:center;">Sgr A*</td></tr><tr><td>213.1</td><td>2631.24 ± 0.32</td><td>-130.65 ± 0.79</td><td>-113.68 ± 0.79</td><td>6.581 ± 0.030</td><td>-69.49 ± 0.13</td></tr><tr><td>215.1</td><td>2629.81 ± 0.33</td><td>-128.22 ± 0.79</td><td>-118.33 ± 0.80</td><td>6.636 ± 0.030</td><td>-68.65 ± 0.13</td></tr><tr><td>227.1</td><td>2533.72 ± 0.27<sup>a</sup></td><td>-105.98 ± 0.76</td><td>-144.59 ± 0.76</td><td>7.076 ± 0.030</td><td>-63.12 ± 0.13</td></tr><tr><td>229.1</td><td>2625.81 ± 0.28</td><td>-106.00 ± 0.79</td><td>-156.22 ± 0.79</td><td>7.188 ± 0.030</td><td>-62.07 ± 0.13</td></tr><tr><td colspan="6" style="text-align:center;">J1924-2914</td></tr><tr><td>213.1</td><td>3342.261 ± 0.089</td><td>-28.0 ± 1.0</td><td>-202.0 ± 1.0</td><td>6.101 ± 0.030</td><td>-48.95 ± 0.14</td></tr><tr><td>215.1</td><td>3313.239 ± 0.093</td><td>-28.5 ± 1.0</td><td>-199.2 ± 1.0</td><td>6.072 ± 0.030</td><td>-49.07 ± 0.14</td></tr><tr><td>227.1</td><td>3179.165 ± 0.088</td><td>-30.5 ± 1.0</td><td>-190.4 ± 1.0</td><td>6.064 ± 0.030</td><td>-49.55 ± 0.14</td></tr><tr><td>229.1</td><td>3156.545 ± 0.087</td><td>-30.65 ± 0.95</td><td>-191.3 ± 1.0</td><td>6.138 ± 0.030</td><td>-49.55 ± 0.14</td></tr><tr><td colspan="6" style="text-align:center;">J0132-1654</td></tr><tr><td>213.1</td><td>426.29 ± 0.15</td><td>7.28 ± 0.19</td><td>4.11 ± 0.19</td><td>1.963 ± 0.044</td><td>14.68 ± 0.64</td></tr><tr><td>215.1</td><td>420.00 ± 0.16</td><td>7.19 ± 0.20</td><td>4.32 ± 0.20</td><td>1.999 ± 0.047</td><td>15.48 ± 0.65</td></tr><tr><td>227.1</td><td>409.56 ± 0.16</td><td>7.16 ± 0.20</td><td>4.59 ± 0.20</td><td>2.076 ± 0.049</td><td>16.34 ± 0.66</td></tr><tr><td>229.1</td><td>404.98 ± 0.16</td><td>6.62 ± 0.19</td><td>4.05 ± 0.19</td><td>1.919 ± 0.048</td><td>15.68 ± 0.74</td></tr><tr><td colspan="6" style="text-align:center;">NGC 1052</td></tr><tr><td>213.1</td><td>437.43 ± 0.13</td><td>0.36 ± 0.14</td><td>0.17 ± 0.14</td><td>0.090 ± 0.033</td><td>13 ± 11</td></tr><tr><td>215.1</td><td>438.85 ± 0.11</td><td>0.56 ± 0.15</td><td>0.39 ± 0.15</td><td>0.154 ± 0.033</td><td>17.0 ± 6.0</td></tr><tr><td>227.1</td><td>414.12 ± 0.10</td><td>0.47 ± 0.14</td><td>0.46 ± 0.14</td><td>0.159 ± 0.033</td><td>21.9 ± 6.3</td></tr><tr><td>229.1</td><td>415.236 ± 0.062</td><td>0.05 ± 0.14</td><td>0.30 ± 0.14</td><td>0.074 ± 0.033</td><td>39 ± 18</td></tr><tr><td colspan="6" style="text-align:center;">M87</td></tr><tr><td>213.1</td><td>1361.85 ± 0.16</td><td>27.72 ± 0.41</td><td>-6.24 ± 0.41</td><td>2.088 ± 0.030</td><td>-6.34 ± 0.43</td></tr><tr><td>215.1</td><td>1349.84 ± 0.15</td><td>27.65 ± 0.41</td><td>-6.70 ± 0.41</td><td>2.108 ± 0.030</td><td>-6.83 ± 0.41</td></tr><tr><td>227.1</td><td>1269.57 ± 0.13</td><td>26.95 ± 0.38</td><td>-8.34 ± 0.38</td><td>2.224 ± 0.030</td><td>-8.61 ± 0.38</td></tr><tr><td>229.1</td><td>1257.40 ± 0.13</td><td>26.70 ± 0.38</td><td>-8.28 ± 0.38</td><td>2.224 ± 0.030</td><td>-8.61 ± 0.39</td></tr><tr><td colspan="6" style="text-align:center;">J0006-0623</td></tr><tr><td>213.1</td><td>2044.52 ± 0.32</td><td>213.57 ± 0.63</td><td>139.74 ± 0.65</td><td>12.482 ± 0.031</td><td>16.598 ± 0.071</td></tr><tr><td>215.1</td><td>2023.69 ± 0.33</td><td>212.00 ± 0.63</td><td>137.19 ± 0.64</td><td>12.480 ± 0.031</td><td>16.452 ± 0.072</td></tr><tr><td>227.1</td><td>1944.0 ± 1.1</td><td>205.43 ± 0.62</td><td>130.51 ± 0.62</td><td>12.520 ± 0.033</td><td>16.215 ± 0.073</td></tr><tr><td>229.1</td><td>1931.6 ± 1.1</td><td>204.15 ± 0.61</td><td>134.03 ± 0.62</td><td>12.645 ± 0.033</td><td>16.646 ± 0.074</td></tr><tr><td colspan="6" style="text-align:center;">3C 279</td></tr><tr><td>213.1</td><td>9571.40 ± 0.12</td><td>72.2 ± 2.9</td><td>1240.7 ± 2.9</td><td>12.984 ± 0.030</td><td>43.337 ± 0.068</td></tr><tr><td>215.1</td><td>9517.18 ± 0.13</td><td>72.4 ± 2.9</td><td>1234.1 ± 2.9</td><td>12.990 ± 0.030</td><td>43.324 ± 0.067</td></tr><tr><td>227.1</td><td>9180.18 ± 0.12</td><td>69.2 ± 2.8</td><td>1193.4 ± 2.8</td><td>13.022 ± 0.030</td><td>43.345 ± 0.066</td></tr><tr><td>229.1</td><td>9168.61 ± 0.11</td><td>69.3 ± 2.8</td><td>1193.1 ± 2.8</td><td>13.035 ± 0.030</td><td>43.338 ± 0.066</td></tr><tr><td colspan="6" style="text-align:center;">NRAO 530</td></tr><tr><td>213.1</td><td>1655.066 ± 0.071</td><td>-8.41 ± 0.50</td><td>36.58 ± 0.50</td><td>2.267 ± 0.030</td><td>51.46 ± 0.38</td></tr><tr><td>215.1</td><td>1669.741 ± 0.079</td><td>-8.95 ± 0.51</td><td>37.51 ± 0.51</td><td>2.309 ± 0.030</td><td>51.70 ± 0.38</td></tr><tr><td>227.1</td><td>1567.831 ± 0.072</td><td>-8.86 ± 0.48</td><td>36.81 ± 0.48</td><td>2.414 ± 0.030</td><td>51.76 ± 0.37</td></tr><tr><td>229.1</td><td>1554.353 ± 0.070</td><td>-8.41 ± 0.47</td><td>36.72 ± 0.47</td><td>2.424 ± 0.030</td><td>51.44 ± 0.36</td></tr></tbody></table>
<table><caption>Table E2
(Continued)</caption><thead><tr><th>Frequency<br>(GHz)</th><th>I<br>(mJy)</th><th>Q<br>(mJy)</th><th>U<br>(mJy)</th><th>LP<br>(%)</th><th>EVPA<br>(deg)</th></tr></thead><tbody><tr><td colspan="6" style="text-align:center; font-weight:bold;">3C 273</td></tr><tr><td>213.1</td><td>7744.46 ± 0.11</td><td>-58.5 ± 2.3</td><td>-191.7 ± 2.3</td><td>2.587 ± 0.030</td><td>-53.49 ± 0.33</td></tr><tr><td>215.1</td><td>7707.72 ± 0.11</td><td>-61.7 ± 2.3</td><td>-186.8 ± 2.3</td><td>2.553 ± 0.030</td><td>-54.15 ± 0.34</td></tr><tr><td>227.1</td><td>7421.16 ± 0.10</td><td>-68.4 ± 2.2</td><td>-153.4 ± 2.2</td><td>2.262 ± 0.030</td><td>-57.01 ± 0.38</td></tr><tr><td>229.1</td><td>7357.33 ± 0.10</td><td>-66.8 ± 2.2</td><td>-145.2 ± 2.2</td><td>2.170 ± 0.030</td><td>-57.36 ± 0.39</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">Apr 7<br>J1924-2914</td></tr><tr><td>213.1</td><td>3243.110 ± 0.083</td><td>-26.8 ± 1.0</td><td>-191.3 ± 1.0</td><td>5.957 ± 0.030</td><td>-48.99 ± 0.15</td></tr><tr><td>215.1</td><td>3219.06 ± 0.10</td><td>-27.3 ± 1.0</td><td>-190.0 ± 1.0</td><td>5.963 ± 0.030</td><td>-49.09 ± 0.15</td></tr><tr><td>227.1</td><td>3073.91 ± 0.11</td><td>-27.90 ± 0.92</td><td>-181.62 ± 0.93</td><td>5.978 ± 0.030</td><td>-49.37 ± 0.14</td></tr><tr><td>229.1</td><td>3048.69 ± 0.12</td><td>-28.11 ± 0.92</td><td>-180.17 ± 0.92</td><td>5.982 ± 0.030</td><td>-49.44 ± 0.15</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">J0132-1654</td></tr><tr><td>213.1</td><td>418.13 ± 0.18</td><td>6.66 ± 0.21</td><td>5.00 ± 0.21</td><td>1.990 ± 0.051</td><td>18.43 ± 0.73</td></tr><tr><td>215.1</td><td>417.76 ± 0.19</td><td>6.99 ± 0.23</td><td>4.97 ± 0.23</td><td>2.055 ± 0.055</td><td>17.75 ± 0.75</td></tr><tr><td>227.1</td><td>402.18 ± 0.20</td><td>6.82 ± 0.22</td><td>4.37 ± 0.23</td><td>2.014 ± 0.056</td><td>16.29 ± 0.80</td></tr><tr><td>229.1</td><td>394.71 ± 0.21</td><td>6.12 ± 0.23</td><td>4.77 ± 0.23</td><td>1.965 ± 0.058</td><td>18.93 ± 0.84</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">NRAO 530</td></tr><tr><td>213.1</td><td>1620.07 ± 0.10</td><td>-7.36 ± 0.49</td><td>37.57 ± 0.49</td><td>2.363 ± 0.030</td><td>50.55 ± 0.35</td></tr><tr><td>215.1</td><td>1604.64 ± 0.11</td><td>-7.57 ± 0.49</td><td>37.41 ± 0.49</td><td>2.379 ± 0.030</td><td>50.72 ± 0.36</td></tr><tr><td>227.1</td><td>1536.162 ± 0.068</td><td>-7.65 ± 0.47</td><td>36.73 ± 0.47</td><td>2.443 ± 0.030</td><td>50.89 ± 0.37</td></tr><tr><td>229.1</td><td>1526.938 ± 0.067</td><td>-7.37 ± 0.46</td><td>37.77 ± 0.46</td><td>2.520 ± 0.030</td><td>50.51 ± 0.35</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">Sgr A*</td></tr><tr><td>213.1</td><td>2418.25 ± 0.25</td><td>-124.16 ± 0.73</td><td>-113.45 ± 0.73</td><td>6.954 ± 0.030</td><td>-68.79 ± 0.12</td></tr><tr><td>215.1</td><td>2404.74 ± 0.27</td><td>-121.16 ± 0.72</td><td>-117.97 ± 0.72</td><td>7.032 ± 0.030</td><td>-67.88 ± 0.12</td></tr><tr><td>227.1</td><td>2318.41 ± 0.22<sup>a</sup></td><td>-100.51 ± 0.70</td><td>-140.51 ± 0.70</td><td>7.451 ± 0.030</td><td>-62.79 ± 0.11</td></tr><tr><td>229.1</td><td>2403.69 ± 0.23</td><td>-100.83 ± 0.72</td><td>-148.69 ± 0.72</td><td>7.472 ± 0.030</td><td>-62.07 ± 0.11</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">NGC 1052</td></tr><tr><td>213.1</td><td>398.01 ± 0.20</td><td>-0.31 ± 0.14</td><td>0.87 ± 0.14</td><td>0.231 ± 0.035</td><td>54.9 ± 4.5</td></tr><tr><td>215.1</td><td>397.25 ± 0.18</td><td>-0.10 ± 0.15</td><td>0.70 ± 0.15</td><td>0.178 ± 0.037</td><td>49.6 ± 6.0</td></tr><tr><td>227.1</td><td>369.99 ± 0.25</td><td>0.21 ± 0.14</td><td>0.12 ± 0.14</td><td>0.069 ± 0.038</td><td>13 ± 20</td></tr><tr><td>229.1</td><td>358.94 ± 0.35</td><td>-0.46 ± 0.14</td><td>0.44 ± 0.14</td><td>0.177 ± 0.039</td><td>68.1 ± 7.9</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">Apr 10<br>4C 01.28</td></tr><tr><td>213.1</td><td>3668.38 ± 0.16</td><td>154.6 ± 1.1</td><td>-102.5 ± 1.1</td><td>5.055 ± 0.030</td><td>-16.77 ± 0.16</td></tr><tr><td>215.1</td><td>3677.75 ± 0.17</td><td>153.4 ± 1.1</td><td>-102.8 ± 1.1</td><td>5.020 ± 0.030</td><td>-16.91 ± 0.17</td></tr><tr><td>227.1</td><td>3514.62 ± 0.14</td><td>147.8 ± 1.1</td><td>-99.7 ± 1.1</td><td>5.074 ± 0.030</td><td>-17.00 ± 0.18</td></tr><tr><td>229.1</td><td>3512.42 ± 0.13</td><td>152.2 ± 1.1</td><td>-99.6 ± 1.1</td><td>5.179 ± 0.030</td><td>-16.60 ± 0.17</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">OJ 287</td></tr><tr><td>213.1</td><td>4319.36 ± 0.10</td><td>-167.8 ± 1.3</td><td>-253.8 ± 1.3</td><td>7.044 ± 0.030</td><td>-61.73 ± 0.12</td></tr><tr><td>215.1</td><td>4333.61 ± 0.10</td><td>-166.9 ± 1.3</td><td>-251.3 ± 1.3</td><td>6.962 ± 0.030</td><td>-61.79 ± 0.12</td></tr><tr><td>227.1</td><td>4119.79 ± 0.10</td><td>-158.1 ± 1.2</td><td>-235.9 ± 1.2</td><td>6.894 ± 0.030</td><td>-61.91 ± 0.12</td></tr><tr><td>229.1</td><td>4105.17 ± 0.10</td><td>-162.0 ± 1.2</td><td>-243.2 ± 1.2</td><td>7.119 ± 0.030</td><td>-61.83 ± 0.12</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">Cen A</td></tr><tr><td>213.1</td><td>5710.166 ± 0.085</td><td>1.8 ± 1.7</td><td>0.5 ± 1.7</td><td>0.040 ± 0.030</td><td>6 ± 30</td></tr><tr><td>215.1</td><td>5677.690 ± 0.090</td><td>3.1 ± 1.7</td><td>2.3 ± 1.7</td><td>0.070 ± 0.030</td><td>18 ± 15</td></tr><tr><td>227.1</td><td>5621.837 ± 0.094</td><td>3.2 ± 1.7</td><td>4.7 ± 1.7</td><td>0.101 ± 0.030</td><td>27.9 ± 9.1</td></tr><tr><td>229.1</td><td>5628.36 ± 0.10</td><td>0.2 ± 1.7</td><td>3.9 ± 1.7</td><td>0.071 ± 0.030</td><td>43 ± 14</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">M87</td></tr><tr><td>213.1</td><td>1382.93 ± 0.26</td><td>37.15 ± 0.42</td><td>-0.24 ± 0.42</td><td>2.688 ± 0.030</td><td>-0.19 ± 0.32</td></tr><tr><td>215.1</td><td>1371.95 ± 0.25</td><td>37.12 ± 0.42</td><td>-0.08 ± 0.42</td><td>2.706 ± 0.030</td><td>-0.08 ± 0.31</td></tr><tr><td>227.1</td><td>1285.70 ± 0.23</td><td>35.68 ± 0.39</td><td>0.47 ± 0.39</td><td>2.777 ± 0.030</td><td>0.37 ± 0.31</td></tr><tr><td>229.1</td><td>1271.90 ± 0.23</td><td>35.24 ± 0.39</td><td>0.05 ± 0.39</td><td>2.770 ± 0.030</td><td>0.03 ± 0.31</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">3C 279</td></tr><tr><td>213.1</td><td>8750.09 ± 0.11</td><td>216.5 ± 2.6</td><td>1264.2 ± 2.6</td><td>14.659 ± 0.030</td><td>40.141 ± 0.057</td></tr><tr><td>215.1</td><td>8699.92 ± 0.11</td><td>215.5 ± 2.6</td><td>1257.5 ± 2.6</td><td>14.665 ± 0.030</td><td>40.137 ± 0.058</td></tr><tr><td>227.1</td><td>8415.64 ± 0.11</td><td>209.4 ± 2.5</td><td>1220.6 ± 2.5</td><td>14.717 ± 0.030</td><td>40.133 ± 0.058</td></tr><tr><td>229.1</td><td>8373.72 ± 0.11</td><td>208.6 ± 2.5</td><td>1216.4 ± 2.5</td><td>14.739 ± 0.030</td><td>40.135 ± 0.061</td></tr><tr><td colspan="6" style="text-align:center; font-weight:bold;">Apr 11<br>Sgr A*</td></tr><tr><td>213.1</td><td>2388.59 ± 0.31</td><td>-41.33 ± 0.72</td><td>-169.55 ± 0.72</td><td>7.307 ± 0.030</td><td>-51.85 ± 0.12</td></tr><tr><td>215.1</td><td>2383.72 ± 0.30</td><td>-37.26 ± 0.72</td><td>-169.35 ± 0.72</td><td>7.275 ± 0.030</td><td>-51.21 ± 0.12</td></tr></tbody></table>
<table><caption>**Table E2**
(Continued)</caption><thead><tr><th>Frequency<br>(GHz)</th><th>I<br>(mJy)</th><th>Q<br>(mJy)</th><th>U<br>(mJy)</th><th>LP<br>(%)</th><th>EVPA<br>(deg)</th></tr></thead><tbody><tr><td>227.1</td><td>2266.69 ± 0.26<sup>a</sup></td><td>-13.97 ± 0.68</td><td>-170.91 ± 0.68</td><td>7.565 ± 0.030</td><td>-47.34 ± 0.11</td></tr><tr><td>229.1</td><td>2362.91 ± 0.27</td><td>-12.14 ± 0.71</td><td>-181.89 ± 0.71</td><td>7.714 ± 0.030</td><td>-46.91 ± 0.12</td></tr><tr><td></td><td></td><td></td><td>4C 01.28</td><td></td><td></td></tr><tr><td>213.1</td><td>3643.15 ± 0.20</td><td>158.8 ± 1.1</td><td>-87.2 ± 1.1</td><td>4.972 ± 0.030</td><td>-14.38 ± 0.18</td></tr><tr><td>215.1</td><td>3632.17 ± 0.20</td><td>157.7 ± 1.1</td><td>-88.5 ± 1.1</td><td>4.980 ± 0.030</td><td>-14.65 ± 0.17</td></tr><tr><td>227.1</td><td>3503.45 ± 0.21</td><td>152.0 ± 1.1</td><td>-88.4 ± 1.1</td><td>5.018 ± 0.030</td><td>-15.10 ± 0.17</td></tr><tr><td>229.1</td><td>3485.19 ± 0.22</td><td>152.9 ± 1.1</td><td>-87.0 ± 1.1</td><td>5.047 ± 0.030</td><td>-14.82 ± 0.18</td></tr><tr><td></td><td></td><td></td><td>OJ 287</td><td></td><td></td></tr><tr><td>213.1</td><td>4366.345 ± 0.094</td><td>-148.7 ± 1.3</td><td>-274.2 ± 1.3</td><td>7.143 ± 0.030</td><td>-59.23 ± 0.12</td></tr><tr><td>215.1</td><td>4356.28 ± 0.10</td><td>-151.4 ± 1.3</td><td>-271.9 ± 1.3</td><td>7.143 ± 0.030</td><td>-59.56 ± 0.12</td></tr><tr><td>227.1</td><td>4170.47 ± 0.36</td><td>-149.1 ± 1.3</td><td>-258.1 ± 1.3</td><td>7.146 ± 0.030</td><td>-60.01 ± 0.12</td></tr><tr><td>229.1</td><td>4152.92 ± 0.11</td><td>-145.7 ± 1.2</td><td>-259.6 ± 1.2</td><td>7.168 ± 0.030</td><td>-59.65 ± 0.12</td></tr><tr><td></td><td></td><td></td><td>J1924-2914</td><td></td><td></td></tr><tr><td>213.1</td><td>3299.39 ± 0.19</td><td>-35.7 ± 1.0</td><td>-156.7 ± 1.0</td><td>4.870 ± 0.030</td><td>-51.42 ± 0.18</td></tr><tr><td>215.1</td><td>3289.89 ± 0.19</td><td>-36.8 ± 1.0</td><td>-155.1 ± 1.0</td><td>4.845 ± 0.030</td><td>-51.68 ± 0.18</td></tr><tr><td>227.1</td><td>3155.4 ± 1.0</td><td>-37.30 ± 0.95</td><td>-147.9 ± 1.0</td><td>4.834 ± 0.030</td><td>-52.08 ± 0.18</td></tr><tr><td>229.1</td><td>3146.13 ± 0.17</td><td>-38.04 ± 0.95</td><td>-149.99 ± 0.95</td><td>4.918 ± 0.030</td><td>-52.12 ± 0.17</td></tr><tr><td></td><td></td><td></td><td>M87</td><td></td><td></td></tr><tr><td>213.1</td><td>1393.36 ± 0.11</td><td>35.91 ± 0.42</td><td>-1.16 ± 0.42</td><td>2.579 ± 0.030</td><td>-0.94 ± 0.33</td></tr><tr><td>215.1</td><td>1380.69 ± 0.11</td><td>36.33 ± 0.42</td><td>-1.06 ± 0.42</td><td>2.634 ± 0.030</td><td>-0.85 ± 0.33</td></tr><tr><td>227.1</td><td>1290.61 ± 0.10</td><td>36.30 ± 0.39</td><td>-0.68 ± 0.39</td><td>2.813 ± 0.030</td><td>-0.54 ± 0.31</td></tr><tr><td>229.1</td><td>1278.47 ± 0.10</td><td>36.23 ± 0.39</td><td>-0.31 ± 0.39</td><td>2.833 ± 0.030</td><td>-0.25 ± 0.30</td></tr><tr><td></td><td></td><td></td><td>3C 279</td><td></td><td></td></tr><tr><td>213.1</td><td>8365.96 ± 0.23</td><td>208.5 ± 2.5</td><td>1223.0 ± 2.5</td><td>14.830 ± 0.030</td><td>40.163 ± 0.059</td></tr><tr><td>215.1</td><td>8317.40 ± 0.23</td><td>207.2 ± 2.5</td><td>1217.3 ± 2.5</td><td>14.846 ± 0.030</td><td>40.168 ± 0.058</td></tr><tr><td>227.1</td><td>8000.38 ± 0.25</td><td>201.7 ± 2.4</td><td>1180.8 ± 2.4</td><td>14.974 ± 0.030</td><td>40.154 ± 0.058</td></tr><tr><td>229.1</td><td>7972.54 ± 0.25</td><td>200.5 ± 2.4</td><td>1178.2 ± 2.4</td><td>14.991 ± 0.030</td><td>40.171 ± 0.058</td></tr></tbody></table>

**Note.**

<sup>a</sup> The flux of Sgr A* at 227 GHz (spw = 2) is systematically ~5% lower than at 229 GHz (spw = 3), owing to the presence of spectral absorption lines (see Appendix H.1). Given its flat spectral index, $F_{spw=2} = F_{spw=3}$ should be assumed for Sgr A*.

where $\sigma_I$, $\sigma_Q$, $\sigma_U$ are the uncertainties in I, Q and U, respectively. Assuming $\sigma_{QU} \sim \sigma_{QI} \sim \sigma_{UI} \sim 0$, then

$$ \sigma_{LP} = \frac{1}{I} \sqrt{\frac{(Q\sigma_Q)^2 + (U\sigma_U)^2}{Q^2 + U^2} + \left[\left(\frac{Q}{I}\right)^2 + \left(\frac{U}{I}\right)^2\right] \sigma_I^2} $$

The LP values quoted in Tables 1, 2, E1, and E2 have this debiased correction applied. The latter does not affect most of the sources studied here, but it is especially important for the low-polarization sources such as NGC 1052 and Cen A.

The absolute flux-scale calibration systematic error (5% and 10% of Stokes IQU fluxes in Band 3 and Band 6, respectively), is not included in Tables E1 and E2. The analysis on Stokes V is performed separately (see Appendix G and Tables G1 and G2).

## Appendix F
### Faraday RM Plots

We display the EVPA data as a function of $\lambda^2$ and their RM-fitted models in Figures F1–F4; EVPAs are measured in each of the four ALMA SPWs. Let us first focus on Figure F1, showing the Faraday RM of Sgr A* (upper panels), M87 (middle panels), and 3C 279 (lower panels). The EVPAs measured in Sgr A* reveal a remarkably precise $\lambda^2$ dependence both at $\lambda3$ mm (left panel) and $\lambda1.3$ mm (second to fourth panels). It is also remarkable that Sgr A* showcases a very consistent slope across all days, while in M87 the slope appears

to change sign from April 5/6 to 10/11. 3C 279 was used as polarization calibrator on April 5, 6, 10, and 11, and its measured RM (consistent with zero across all days) demonstrates the stability of the polarization measurements on M87 and on Sgr A* on the same days. On April 7, the polarization calibrator was J1924-2914, which also shows consistent RM across days (see Figure F2, upper panels). Collectively, they demonstrate the stability of the polarization measurements in 2017 April on Sgr A*, M87, and, by extension, on the remaining AGNs observed at $\lambda1.3$ mm (displayed in Figure F2) and at $\lambda3$ mm (displayed in Figure F3).

We notice that, for some of the targets, the RM fits are almost perfectly consistent with the measured EVPAs; in particular, the plots for Sgr A*, 3C 279 (Figure F1), 3C 273, J1924-2914 (Figure F2), and M87 (Figure F4), look very unlikely given the error bars. In fact, a standard $\chi^2$ analysis for these sources would give values close to 0 while for a 4-point/ 2-parameter fit, we would expect $\chi^2 \sim 2$. This apparently unexpected behavior can be explained by the fact that the EVPA uncertainties displayed in the RM plots are not just the thermal errors (which would naturally introduce scatter in the measurements) but also include a systematic error (0.03% of I into QU errors), which in fact dominates the total error budget (especially for the strongest sources with high Stokes I). We assessed that once such systematic error is removed, the EVPA data points are no longer consistent with the line to within their (thermal-noise-only) uncertainties. The fact that the thermal-only error bars are too small, but the error bars in the plots of
<figure><img src="image_20.png" /></figure>

**Figure F1.** Faraday RM of Sgr A\* (upper panels), M87 (middle panels), and 3C 279 (lower panels). The EVPA as a function of wavelength squared is presented with $1\sigma$ error bars for each SPW and for each day. The EVPAs are measured in the 1.3 mm band, except for the upper left panel, presenting the EVPAs measured at 3 mm in Sgr A\*. The error bars are derived adding in quadrature to the thermal uncertainty of the *Q* and *U* maps ($1\sigma$ image rms) a systematic error of 0.03% of Stokes *I* (error bars for Sgr A\* are smaller than the displayed points). The line is a linear fit to the data giving the RM reported inside the box. Plots in each row span the same vertical axis range in degrees in order to highlight differences in slope (the upper-left panel is an exception). It is remarkable that Sgr A\* showcases a very consistent slope across days, while in M87 the slope appears to change sign. Note also the different EVPA values between April 6/7 and 11 in Sgr A\* and between April 5/6 and 10/11 in M87 and 3C 279. The measured RM in 3C 279 (used as polarization calibrator on April 5, 6, 10, and 11) is consistent with zero across all days, demonstrating the stability of the polarization measurements on M87 and on Sgr A\* on the same days.

this Letter that include the systematic 0.03% Stokes *I* leakage into the *QU* error budget are too large, suggests that there is a real systematic error in the EVPA measurements but that it is smaller than the ALMA standard value. The fact that we are being conservative in our error estimates should ensure that we are not over-interpreting our measurements.

Finally, we notice that, for some of the targets and/or on specific days, there are > $1\sigma$ deviations between the observed EVPA and the RM fit-predicted values (e.g., OJ 287, 4C 01.28, J0006–0623, J0510+1800; see selected panels in Figures F2 and F3).

This may suggest either the presence of an additional systematic error not accounted for in our error budget or that the assumption of the EVPA $\lambda^2$-dependence is not valid in some cases. In fact, in Sections 3.3.3, 5.1.1, and 5.2 we discuss the possibility that some of the observed Faraday rotation may be partly internal, which would imply a more complex RM model than assumed in our analysis. Without a wider wavelength coverage, we cannot distinguish between the two cases. Therefore, we will not consider any additional systematic error in the RM analysis presented in this Letter.
<figure><img src="image_21.png" /><figcaption>**Figure F2.** RM fits for remaining 2017 EHT targets with EVPA measurements at 1.3 mm (see Table 2). Plots in each row span the same vertical axis range for the same source in order to highlight differences in slope.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Figure F3. RM fits for the 2017 GMVA targets with EVPA measurements at 3 mm (see Table 1).</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Figure F4. RM of M87 from observations carried out in 2015 September and November and 2016 October at 3 mm (top row) and in 2018 April at 1.3 mm (bottom row). Plots in both rows span the same vertical axis range (25° and 8° respectively) in order to highlight differences in slope (but note the different EVPA values in different panels).</figcaption></figure>

## Appendix G
### Circular Polarization and Assessment of the ALMA Polarimetry

A reliable detection of Stokes V in interferometric observations with linear-polarization feeds (i.e., the case of ALMA) strongly depends on the correct estimate of two instrumental quantities. On the one hand, the relative phase, $\Delta$, between the X and Y polarizers (i.e., the cross-polarization phase) at the reference antenna (i.e., the quantity stored in the XY0 APP table; see Goddi et al. 2019b). On the other hand, the imaginary parts of the Dterms that describe the polarization leakage of the individual ALMA elements (i.e., the quantities stored either in the Df0 APP or in the Df0 ALMA table, depending on the calibration strategy, as described in Goddi et al. 2019b). Following the standard ALMA calibration procedure, $\Delta$ is estimated by assuming a negligible Stokes V in the polarization calibrator. With this assumption, and neglecting also the effects from polarization leakage, the cross-polarization correlations ($XY^*$ and $YX^*$) between two ALMA antennas observing a

polarized point source are

$$XY^*=e^{-j\Delta}p \sin[2(\phi - \psi)] \quad \text{and} \quad YX^*=e^{j\Delta}p \sin[2(\phi - \psi)], \qquad (G1)$$

where the data are assumed to be already corrected for phase and amplitude gains, $\psi$ and $\phi$ are the feed angle of the antennas<fnref n="151" /> and the EVPA of the observed source (respectively), and $p$ is the calibrator's linearly polarized flux density ($p = LP \times I$).

The only complex quantity that appears in Equation (G1) is given by the factor $e^{j\Delta}$. Hence, the $XY^*$ (and $YX^*$) visibilities may change their amplitudes as a function of time (via the changes in $\psi$), but their phases will remain constant and equal to $\Delta$. The CASA-based calibration algorithm for ALMA (provided in the polcal task) takes advantage of this fact, and estimates the value of $\Delta$ from the fit of $XY^*$ and/or $YX^*$ (over

<footnote n="151">¹⁵¹ The parallactic angle plus the rotation of the receiver cartridge with respect to the antenna mount.</footnote>
different values of $\psi$) to a model with a constant phase. We call the phase estimated in this way as $\Delta_{QA2}$.

## G.1. Effects of an Inaccurate ALMA Polarization Calibration

### G.1.1. Polarization Calibrator

If the true value of the cross-polarization phase, $\Delta$, is offset from $\Delta_{QA2}$ by an unknown quantity, $\beta$ (i.e., $\Delta = \beta + \Delta_{QA2}$), this offset will introduce a leakage-like effect into the polconverted VLBI visibilities, which will be described by the Dterms given in Equation (13) of Goddi et al. (2019b). If $\beta$ is very small, that equation predicts an ALMA leakage for VLBI which has two remarkable properties: (1) it is pure imaginary, and (2) it is the same for the R and L polarization hands. The value of this Dterm is directly related to $\beta$ via the equation

$$D_R^{\text{VLBI}} = D_L^{\text{VLBI}} \sim j\beta.$$

Therefore, if the QA2 calibration procedure has introduced an offset $\beta$ into the cross-polarization phase, $\Delta_{QA2}$, we predict a pure imaginary Dterm in the ALMA–VLBI visibilities. The actual Dterms estimated from the ALMA–VLBI observations during the EHT 2017 campaign are reported in Event Horizon Telescope Collaboration et al. (2021a).

The phase offset $\beta$ may also introduce a spurious V signal into the data, which can be described by the equation (e.g., Hovatta et al. 2019)

$$V^{\text{tot}} = V^{\text{const}} \cos \beta + p \sin [2(\phi - \psi)] \sin \beta, \quad (\text{G2})$$

where $V^{\text{tot}}$ is the total V signal recovered from the (QA2-calibrated) data and $V^{\text{const}}$ is a constant V signal, independent of $\psi$. If the QA2 Dterm estimates for ALMA are correct, $V^{\text{const}}$ is equal to the true Stokes V of the source, (i.e., $V^{\text{const}} = V^{\text{true}}$). However, if the ALMA Dterms estimated in the QA2 are offset from their true values, there is another instrumental contribution to $XY^*$ and $YX^*$, which couples to $V^{\text{const}}$ as

$$XY^* = p \sin[2(\phi - \psi)] + jV^{\text{true}} + (D_X^a + (D_Y^b)^*)I + \mathcal{O}(pD) + \mathcal{O}(V^{\text{true}}D). \quad (\text{G3})$$

In this equation, $D_X^k$ is the part of the Dterm of the X polarizer of antenna k that remains uncalibrated after the QA2 (and similarly for the Y polarizer). Therefore, if the effects of the antenna Dterms are not fully removed from the data, the calibrator source will show a non-negligible $V^{\text{true}}$, while the CASA model assumes it to be null.

In Figure G1, we show the $V^{\text{tot}}$ signal (computed as the average real part of $(XY^* - YX^*)/j$ among all ALMA antennas) of the polarization calibrator 3C 279, as a function of parallactic angle, for the epochs where this source was observed. We have averaged the visibilities in time bins of 120 s and the data taken with antenna elevations below 30° have been discarded. In the figure we also show the simple model given by Equation (G2), where $V^{\text{const}}$ and $\Delta$ are the only two free parameters used in the fit.

The V signals from the polarization calibrator show a clear dependence with parallactic angle, which indicates that there are offsets, $\beta$ in the estimated cross-polarization phases, $\Delta_{QA2}$. Using the values of p and $\phi$ estimated for 3C 279 on different days, we fit an X–Y phase offset of $\beta = 0.2^\circ-0.5^\circ$ in all tracks except April 5, where $\beta \sim 1^\circ-2^\circ$. We notice that these ranges assume no bias in the QA2 estimates of the ALMA Dterms.

It is interesting to note that the data depart from the sinusoidal model of Equation (G2), especially for the epochs on April 6 and

<figure><img src="image_24.png" /><figcaption>Figure G1. Reconstructed Stokes V of 3C 279 as a function of feed angle, $\phi$, during the EHT campaign. Stokes V is computed as the real part of $(XY^* - YX^*)/j$. Dashed lines show the simplified model of Equation (G2), based on cross-polarization phase offset, $\beta$, of the phased-ALMA reference antenna.</figcaption></figure>

11, and for observations far from transit. These deviations may be related to other instrumental effects (e.g., the second-order leakage contributions, like $\mathcal{O}(pD)$ in Equation (G3)).

From the values of $\beta$ fitted with Equation (G2), we can estimate a rough upper bound for the Stokes V of the calibrator, assuming a perfect calibration of the ALMA Dterms. For 3C 279, our analysis yields $V = [27, 4, 4, 2]$ mJy, corresponding to CP = [0.30, 0.04, 0.07, 0.02] %, and $\beta = [2.2, 0.67, 0.57, 0.35]$ degrees, on April 5, 6, 10, 11, respectively. For J1924–2914, our analysis yields $V = 0.7$ mJy, corresponding to CP = 0.02%, and $\beta = -0.91$ degrees, on April 7 (3C 279 was not observed on April 7).

The estimated values of $V^{\text{const}}$ obtained from Equation (G2) are all of the order of 1 mJy at most. These values are small compared to the $V^{\text{true}}$ coming from the $\beta$ estimates. This is especially true for the epoch of April 5. As discussed at the beginning of this section, a low $V^{\text{const}}$ can be explained by the compensating effect of (small) biases in the QA2 estimates of the ALMA Dterms (Equation (G3)). Such systematics would force $V^{\text{const}}$ to be close to zero, regardless of the value of $V^{\text{true}}$.

In summary, two clear conclusions can be drawn from Figure G1. On the one hand, there is an offset, $\beta$, in the X–Y cross-polarization phase of the reference antenna. On the other hand, there may be other systematics in the estimates of the antenna Dterms that may compensate the imprint of a true circular polarization of the calibrator (since CASA always assumes a null Stokes V in the calibrator).

### G.1.2. Other Sources

The Dterms and cross-polarization phases discussed in the previous subsection are applied to all sources in the data. Hence, the V Stokes from the polarization calibrator, which may have introduced a cross-polarization phase offset, $\beta$, and other biases to the Dterm estimates, will be systematically put back (after applying the polarization calibration) into the Stokes V signals of the rest of the sources.

Thus, if we find different values of the fractional V Stokes among different sources, there has to be a contribution to their $V^{\text{const}}$ values (Equations (G2) and (G3)) that is independent of
<figure><img src="image_25.png" /></figure>

Apr 07 - Stokes V; $\beta = -0.91^\circ$

<figure><img src="image_26.png" /></figure>

Apr 11 - Stokes V; $\beta = 0.35^\circ$

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

Apr 10 - Stokes V; $\beta = 0.57^\circ$

<figure><img src="image_29.png" /></figure>

**Figure G2.** Reconstructed fractional Stokes V of all sources (except 3C 279), as a function of feed angle, during the EHT campaign. Stokes V is computed as the real part of $(XY^* - YX^*)/j$. Continuum lines show a simplified model based on cross-polarization phase offsets at ALMA, which have been fixed to the $\beta$ values shown on top of each figure. Note that Sgr A* is not plotted because it displays significant intrinsic variability on the timescales (of hours) plotted here (e.g., Bower et al. 2018).

that introduced by the polarization calibration. In the frame of our modeling of the instrumental polarization, such a contribution would likely be related to $V^{\text{true}}$, i.e., a true circular polarization associated to the sources.

In Figure G2, we show the fractional Stokes V values for all the sources, with the exception of 3C 279, as a function of feed angle. As with Figure G1, a time binning of 120 s has been applied and data with elevations lower than 30 degrees have not been used. We also show the model fitted with Equation (G2), where $\beta$ is fixed to the value derived from the 3C 279 data (so the only free parameter is $V^{\text{const}}$). The only exception to this modeling is for the epoch on April 7, where J1924-291 was used instead as the polarization calibrator.

Some sources show a clear dependence of $V^{\text{tot}}$ with feed angle, being 3C 273 (on April 6) and OJ 287 (on April 5) remarkable examples. However, the model prediction for such

a variability, based on the cross-polarization phase offsets, $\beta$, estimated from 3C 279, cannot reproduce all the data. A possible explanation for this discrepancy could be, for instance, a small (within 1 degree) variation of $\Delta$ with pointing direction (i.e., antenna elevation and azimuth) and/or an effect related to residual Dterms (see Equation (G3)). A deep analysis of these possibilities is out of the scope of this Letter and should indeed be carried out at the observatory level.

In any case, the fractional CPs shown in Figure G2 are very different among sources, which is a good indicator that these are not dominated by the Dterm systematics (at least, to a first-order approximation). Some sources do show the sinusoidal dependence with feed angle, whereas others (like M87) are dominated by $V^{\text{const}}$. Since we do not know the exact effects related to residual Dterms, it is not possible to derive $V^{\text{true}}$ from the estimated $V^{\text{const}}$ A robust conclusion, however, is that there
<table><caption>**Table G1**
Frequency-averaged Circular Polarization Fraction of GMVA Targets (at a Representative Frequency of 93 GHz)</caption><thead><tr><th>Source</th><th>Day<br>(2017)</th><th>I<br>(Jy)</th><th>V<sub>meas</sub><br>(mJy)</th><th>V<sub>true</sub><br>(mJy)</th><th>CP<br>(%)</th><th>LP<br>(%)</th></tr></thead><tbody><tr><td>OJ 287</td><td>Apr 2</td><td>5.97 ± 0.30</td><td>-4 ± 36</td><td>-3</td><td>-0.05 ± 0.60</td><td>8.811 ± 0.030</td></tr><tr><td>J0510+1800</td><td>Apr 2</td><td>3.11 ± 0.16</td><td>-4 ± 19</td><td>-4</td><td>-0.14 ± 0.60</td><td>4.173 ± 0.031</td></tr><tr><td>4C 01.28<sup>a</sup></td><td>Apr 2</td><td>4.86 ± 0.24</td><td>0 ± 29</td><td>1.0</td><td>0.02 ± 0.60</td><td>4.420 ± 0.030</td></tr><tr><td>Sgr A*</td><td>Apr 3</td><td>2.52 ± 0.13</td><td>-0 ± 15</td><td>-0.5</td><td>-0.02 ± 0.60</td><td>0.734 ± 0.030</td></tr><tr><td>J1924-2914</td><td>Apr 3</td><td>5.11 ± 0.26</td><td>0 ± 31</td><td>5</td><td>0.09 ± 0.60</td><td>4.841 ± 0.031</td></tr><tr><td>NRAO 530<sup>a</sup></td><td>Apr 3</td><td>2.74 ± 0.14</td><td>0 ± 16</td><td>0.0</td><td>0.00 ± 0.60</td><td>0.919 ± 0.031</td></tr><tr><td>4C 09.57</td><td>Apr 3</td><td>2.85 ± 0.14</td><td>-9 ± 17</td><td>-10</td><td>-0.34 ± 0.60</td><td>4.069 ± 0.030</td></tr><tr><td>3C 279<sup>a</sup></td><td>Apr 4</td><td>12.93 ± 0.65</td><td>-0 ± 78</td><td>-10</td><td>-0.1 ± 1.2</td><td>12.159 ± 0.030</td></tr><tr><td>3C 273</td><td>Apr 4</td><td>9.86 ± 0.49</td><td>11 ± 59</td><td>14</td><td>0.14 ± 0.60</td><td>3.984 ± 0.029</td></tr></tbody></table>

**Note.**

<table><caption>**Table G2**
Frequency-averaged Circular Polarization Fraction of EHT Targets (at a Representative Frequency of 221 GHz)</caption><thead><tr><th>Source</th><th>Day<br>(2017)</th><th>I<br>(Jy)</th><th>V<sub>meas</sub><br>(mJy)</th><th>V<sub>true</sub><br>(mJy)</th><th>CP<br>(%)</th><th>LP<br>(%)</th></tr></thead><tbody><tr><td>3C 279<sup>a</sup></td><td>Apr 5</td><td>8.99 ± 0.90</td><td>0 ± 54</td><td>27</td><td>0.30 ± 0.60</td><td>13.210 ± 0.030</td></tr><tr><td>3C 279<sup>a</sup></td><td>Apr 6</td><td>9.36 ± 0.94</td><td>0 ± 56</td><td>4</td><td>0.04 ± 0.60</td><td>13.010 ± 0.030</td></tr><tr><td>3C 279<sup>a</sup></td><td>Apr 10</td><td>8.56 ± 0.86</td><td>0 ± 51</td><td>6</td><td>0.07 ± 0.60</td><td>14.690 ± 0.030</td></tr><tr><td>3C 279<sup>a</sup></td><td>Apr 11</td><td>8.16 ± 0.82</td><td>0 ± 49</td><td>2</td><td>0.02 ± 0.60</td><td>14.910 ± 0.030</td></tr><tr><td>M87</td><td>Apr 5</td><td>1.28 ± 0.13</td><td>-1.5 ± 7.7</td><td>-2</td><td>-0.15 ± 0.60</td><td>2.420 ± 0.030</td></tr><tr><td>M87</td><td>Apr 6</td><td>1.31 ± 0.13</td><td>-4.4 ± 7.9</td><td>-5</td><td>-0.34 ± 0.60</td><td>2.160 ± 0.030</td></tr><tr><td>M87</td><td>Apr 10</td><td>1.33 ± 0.13</td><td>-3.5 ± 8.0</td><td>-4</td><td>-0.28 ± 0.60</td><td>2.730 ± 0.030</td></tr><tr><td>M87</td><td>Apr 11</td><td>1.34 ± 0.13</td><td>-5.4 ± 8.0</td><td>-6</td><td>-0.41 ± 0.60</td><td>2.710 ± 0.030</td></tr><tr><td>Sgr A*</td><td>Apr 6</td><td>2.63 ± 0.26</td><td>-40 ± 16</td><td>-40</td><td>-1.51 ± 0.61</td><td>6.870 ± 0.030</td></tr><tr><td>Sgr A*</td><td>Apr 7</td><td>2.41 ± 0.24</td><td>-27 ± 15</td><td>-27</td><td>-1.14 ± 0.61</td><td>7.230 ± 0.030</td></tr><tr><td>Sgr A*</td><td>Apr 11</td><td>2.38 ± 0.24</td><td>-24 ± 14</td><td>-24</td><td>-1.01 ± 0.60</td><td>7.470 ± 0.030</td></tr><tr><td>J1924-2914</td><td>Apr 6</td><td>3.25 ± 0.32</td><td>0 ± 19</td><td>0.1</td><td>0.00 ± 0.60</td><td>6.090 ± 0.030</td></tr><tr><td>J1924-2914<sup>a</sup></td><td>Apr 7</td><td>3.15 ± 0.31</td><td>0 ± 19</td><td>0.7</td><td>0.02 ± 0.60</td><td>5.970 ± 0.030</td></tr><tr><td>J1924-2914</td><td>Apr 11</td><td>3.22 ± 0.32</td><td>2 ± 19</td><td>2</td><td>0.05 ± 0.60</td><td>4.870 ± 0.030</td></tr><tr><td>OJ 287</td><td>Apr 5</td><td>4.34 ± 0.43</td><td>17 ± 26</td><td>20</td><td>0.46 ± 0.60</td><td>9.020 ± 0.030</td></tr><tr><td>OJ 287</td><td>Apr 10</td><td>4.22 ± 0.42</td><td>5 ± 25</td><td>5</td><td>0.12 ± 0.60</td><td>7.000 ± 0.030</td></tr><tr><td>OJ 287</td><td>Apr 11</td><td>4.26 ± 0.43</td><td>-1 ± 26</td><td>0.6</td><td>0.01 ± 0.60</td><td>7.150 ± 0.030</td></tr><tr><td>4C 01.28</td><td>Apr 5</td><td>3.51 ± 0.35</td><td>10 ± 21</td><td>9</td><td>0.25 ± 0.60</td><td>5.890 ± 0.030</td></tr><tr><td>4C 01.28</td><td>Apr 10</td><td>3.59 ± 0.36</td><td>3 ± 22</td><td>3</td><td>0.09 ± 0.60</td><td>5.080 ± 0.030</td></tr><tr><td>4C 01.28</td><td>Apr 11</td><td>3.57 ± 0.36</td><td>-1 ± 21</td><td>0.2</td><td>0.01 ± 0.60</td><td>5.000 ± 0.030</td></tr><tr><td>NRAO 530</td><td>Apr 6</td><td>1.61 ± 0.16</td><td>-0 ± 10</td><td>-0.4</td><td>-0.02 ± 0.60</td><td>2.350 ± 0.030</td></tr><tr><td>NRAO 530</td><td>Apr 7</td><td>1.57 ± 0.16</td><td>0.5 ± 9.4</td><td>0.8</td><td>0.05 ± 0.60</td><td>2.430 ± 0.030</td></tr><tr><td>J0132-1654</td><td>Apr 6</td><td>0.420 ± 0.040</td><td>-0.7 ± 2.5</td><td>-0.8</td><td>-0.19 ± 0.60</td><td>1.990 ± 0.050</td></tr><tr><td>J0132-1654</td><td>Apr 7</td><td>0.410 ± 0.040</td><td>-0.1 ± 2.5</td><td>-0.2</td><td>-0.04 ± 0.60</td><td>2.000 ± 0.050</td></tr><tr><td>NGC 1052</td><td>Apr 6</td><td>0.430 ± 0.040</td><td>0.2 ± 2.6</td><td>0.2</td><td>0.05 ± 0.60</td><td>0.110 ± 0.030</td></tr><tr><td>NGC 1052</td><td>Apr 7</td><td>0.380 ± 0.040</td><td>0.4 ± 2.3</td><td>0.3</td><td>0.08 ± 0.60</td><td>0.150 ± 0.040</td></tr><tr><td>Cen A</td><td>Apr 10</td><td>5.66 ± 0.57</td><td>-2 ± 34</td><td>-2</td><td>-0.04 ± 0.60</td><td>0.060 ± 0.030</td></tr><tr><td>3C 273</td><td>Apr 6</td><td>7.56 ± 0.76</td><td>10 ± 45</td><td>9</td><td>0.12 ± 0.60</td><td>2.390 ± 0.030</td></tr><tr><td>J0006-0623</td><td>Apr 6</td><td>1.99 ± 0.20</td><td>-1 ± 12</td><td>-3</td><td>-0.16 ± 0.60</td><td>12.530 ± 0.030</td></tr></tbody></table>

**Note.**

is CP detected in most of the sources (with amplitudes of the order of a few 0.1%) and that, to our understanding, the instrumental effects alone cannot explain the results for all

sources in a self-consistent way. The “true” Stokes V and CP reconstructed with this analysis are reported in Tables G1 and G2 for all the GMVA and EHT sources, respectively.

<footnote><sup>a</sup> The polarization calibrator is assumed to have Stokes V = 0 for polarization calibration purposes (see Goddi et al. 2019b).</footnote>

<footnote><sup>a</sup> The polarization calibrator is assumed to have Stokes V = 0 for polarization calibration purposes (see Goddi et al. 2019b).</footnote>
# Appendix H
## Spectral Indices of Total Intensity

We compute the total intensity spectral index for all the sources observed in the VLBI campaign at 3 mm and 1.3 mm. For each source, the spectral index $\alpha$, defined as $I(\nu) \propto \nu^{\alpha}$, is derived “in-band,” performing a weighted least-squares fit across the four flux-density values estimated with UVMULTIFIT in each SPW, i.e., at frequencies of 213, 215, 227, 229 GHz in the 1.3 mm band, and 86, 88, 98, and 100 GHz in the 3 mm band, respectively. For Sgr A*, the spectral index of the compact core is around 0 both at 3 mm ($\alpha = 0.01 \pm 0.1$) and 1.3 mm ($\alpha = [-0.03, -0.15] \pm 0.06$). For M87, the spectral index of the compact core at 1.3 mm is negative ($\alpha = [-1.2, -1.1]$). Cycle 0 ALMA observations at 3 mm at a comparable angular resolution ($2''6 \times 1''4$) yield a much flatter $\alpha = [-0.2, -0.3]$ (Doi et al. 2013), consistent with VLA measurements at radio-frequency bands (8.4–43 GHz). VLBA observations revealed a flat-spectrum ($\alpha = 0$) compact core (e.g., Kravchenko et al. 2020). The steeper spectrum measured in the 1.3 mm band suggests that a spectral break must occur between 3 and 1.3 mm. Spectral steepening is also observed in other AGN sources in the sample, which vary in the range $\alpha = [-0.7, -0.3]$ at 3 mm and $\alpha = [-1.3, -0.6]$ at 1.3 mm (Cen A being the only exception, with $\alpha = -0.2$). When put together, these results indicate that the spectrum of AGN cores becomes progressively more optically thin at millimeter wavelengths (see Section 5.1.1).

### H.1. Foreground Absorption at 226.91 GHz toward Sgr A*

Figure H1 shows the spectrum of Sgr A* in SPW = 2 on 2017 April 7. The spectrum is virtually the same in the remainder days of observation in 2017 April, suggesting that the absorption is probably associated with material that is in front of the Galactic center core. Cyanide radical and its hyperfine structure at 226.3600 GHz ($N = 2-1, J = 3/2-3/2$), 226.6595 GHz ($N = 2-1, J = 3/2-1/2$), and 226.8748 GHz ($N = 2-1, J = 5/2-3/2$)<fnref n="152" /> are identified as the carriers of the absorption features. The lines predict a loss of integrated emission over the 1.8 GHz bandwidth of about 2%, in reasonable agreement with the decrements seen in SPW = 2 in Figure H1.

<figure><img src="image_30.png" /><figcaption>**Figure H1.** Bandpass for Sgr A* core (after removing instrumental bandpass with the calibrator NRAO 530) for 2017 April 7 observations. Only baselines longer than 60 m were used to remove virtually all of the extended arcsecond emission. For each channel, every antenna bandpass amplitude is plotted (represented by different colors). All three April observations show virtually the same “bandpass.”</figcaption></figure>

# Appendix I
## Two-component Polarization Model for M87

Here we present the two-component polarization model for M87 summarized in Section 5.2.2 and shown schematically in Figure 6. Details of the model itself, analysis, and parameter constraints can be found below. Note that unlike the detailed image models presented in Event Horizon Telescope Collaboration et al. (2021b), these models seek to reconstruct only the Stokes I, Q, and U integrated over the EHT map and within the ALMA core.

The motivation of this modeling is to assess whether or not the significant interday variations seen in the RMs of M87 can be accommodated by a model in which the only variable element is the intrinsic polarization of the horizon-scale emission, holding all other properties of the Faraday rotation and a putative large-scale polarized component fixed. In summary, we find that it is possible to do so, though it does require the RM of the horizon-scale component to be significantly larger than the RMs associated with the ALMA core in M87 reported in Table 2.

<footnote n="152">¹⁵² NIST Recommended Rest Frequencies for Observed Interstellar Molecular Microwave Transitions; https://physics.nist.gov/cgi-bin/micro/table5/start.pl.</footnote>
<table><caption>**Table II**
Two-component Model MCMC Analysis Priors and Results</caption><thead><tr><th>Parameter</th><th>Unit</th><th>Prior<sup>a</sup></th><th>External Screen<sup>b</sup></th><th>Internal Screen<sup>b,c</sup></th></tr></thead><tbody><tr><td>I<sub>0,ext</sub></td><td>Jy</td><td>L(0, ∞)</td><td>0.813 ± 0.044</td><td>0.811 ± 0.049</td></tr><tr><td>α<sub>ext</sub></td><td>...</td><td>U[0, 2.5]</td><td>2.14 ± 0.32</td><td>1.12 ± 0.62</td></tr><tr><td>m<sub>ext</sub></td><td>%</td><td>U[0, 100]</td><td>3.03 ± 0.37</td><td>3.43 ± 0.36</td></tr><tr><td>EVPA<sub>ext</sub></td><td>deg</td><td>U[-90, 90]</td><td>5.7 ± 2.1</td><td>-0.5 ± 2.4</td></tr><tr><td>RM<sub>ext</sub></td><td>10<sup>5</sup> rad m<sup>-2</sup></td><td>U[-100, 100]</td><td>0.87 ± 0.64</td><td>0.55 ± 0.53</td></tr><tr><td>I<sub>0,com</sub></td><td>Jy</td><td>L(0, ∞)</td><td>0.439 ± 0.032</td><td>0.454 ± 0.032</td></tr><tr><td>α<sub>com</sub></td><td>...</td><td>U[0, 2.5]</td><td>0.31 ± 0.27</td><td>1.31 ± 0.66</td></tr><tr><td>RM<sub>com</sub></td><td>10<sup>5</sup> rad m<sup>-2</sup></td><td>U[-100, 100]</td><td>-4.92 ± 0.91</td><td>-4.98 ± 0.43</td></tr><tr><td>m<sub>com, Apr 5</sub></td><td>%</td><td>U[0, 100]</td><td>3.48 ± 0.41</td><td>3.66 ± 0.66</td></tr><tr><td>m<sub>com, Apr 6</sub></td><td>%</td><td>U[0, 100]</td><td>3.06 ± 0.43</td><td>3.17 ± 0.82</td></tr><tr><td>m<sub>com, Apr 10</sub></td><td>%</td><td>U[0, 100]</td><td>2.73 ± 0.54</td><td>3.2 ± 1.2</td></tr><tr><td>m<sub>com, Apr 11</sub></td><td>%</td><td>U[0, 100]</td><td>2.78 ± 0.51</td><td>3.0 ± 1.1</td></tr><tr><td>EVPA<sub>com, Apr 5</sub></td><td>deg</td><td>U[-90, 90]</td><td>-32.9 ± 5.6</td><td>14 ± 10</td></tr><tr><td>EVPA<sub>com, Apr 6</sub></td><td>deg</td><td>U[-90, 90]</td><td>-38.5 ± 6.3</td><td>3.0 ± 10.0</td></tr><tr><td>EVPA<sub>com, Apr 10</sub></td><td>deg</td><td>U[-90, 90]</td><td>-12.4 ± 6.5</td><td>53 ± 13</td></tr><tr><td>EVPA<sub>com, Apr 11</sub></td><td>deg</td><td>U[-90, 90]</td><td>-14.8 ± 6.6</td><td>48 ± 13</td></tr></tbody></table>

**Notes.**

<sup>a</sup> Priors types are logarithmic (L) and uniform (U), with ranges indicated afterward.

<sup>b</sup> Means and standard deviations of parameter values are provided.

<sup>c</sup> Note that LP (m) and EVPA refer to those of the emission process, not observed at the surface of the emission region.

## 1.1. Model Definitions

We consider two two-component models for the polarimetric properties of M87, differing in the location of the small-scale Faraday screen. For both components, we construct the set of Stokes I, Q, U, which may depend on observation day and wavelength. The directly compared quantities that comprise the model are the integrated Stokes parameters of the compact component, $I_{\text{com,day},\lambda}$, $Q_{\text{com,day},\lambda}$, and $U_{\text{com,day},\lambda}$, and of the combination of the compact and extended components, $I_{\text{tot,day},\lambda} = I_{\text{com,day},\lambda} + I_{\text{ext},\lambda}$, $Q_{\text{tot,day},\lambda} = Q_{\text{com,day},\lambda} + Q_{\text{ext},\lambda}$, and $U_{\text{tot,day},\lambda} = U_{\text{com,day},\lambda} + U_{\text{ext},\lambda}$. A summary list of the model parameters for the models described in Appendix I.1.1–I.1.3 is contained in Table II.

### 1.1.1. Extended Component

Both models contain a large-scale component defined by an intensity normalization $I_{0,ext}$ at a reference wavelength $\lambda_0$, spectral index $\alpha_{0,ext}$, polarization fraction $m_{\text{ext}}$, and EVPA $\psi_{\text{ext}}$ at $\lambda_0$. This is further processed through an external Faraday screen with a rotation measure of RM$_{\text{ext}}$. The contribution to the Stokes I, Q, and U are then

$$ 
\begin{aligned}
I_{\text{ext},\lambda} &= I_{0,\text{ext}}(\lambda/\lambda_0)^{\alpha_{\text{ext}}} \\
Q_{\text{ext},\lambda} &= m_{\text{ext}} I_{\text{ext},\lambda} \cos[2\psi + 2\text{RM}_{\text{ext}}(\lambda^2 - \lambda_0^2)] \\
U_{\text{ext},\lambda} &= m_{\text{ext}} I_{\text{ext},\lambda} \sin[2\psi + 2\text{RM}_{\text{ext}}(\lambda^2 - \lambda_0^2)].
\end{aligned} 
\quad (11) 
$$

This introduces five parameters: $I_{0,ext}$, $\alpha_{\text{ext}}$, RM$_{\text{ext}}$, $m_{\text{ext}}$, and $\psi$.

### 1.1.2. Compact Component: External Faraday Screen

For each day on which M87 was observed by ALMA and the EHT (i.e., April 5, 6, 10 and 11) we specify a similar model for the compact component. When the screen is assumed to be external, we adopt a similar model to the large-scale component

with the exception that the rotation is due to both screens:

$$ 
\begin{aligned}
I_{\text{com,day},\lambda}^{\text{Ex}} &= I_{0,\text{com}}(\lambda/\lambda_0)^{\alpha_{\text{com}}} \\
Q_{\text{com,day},\lambda}^{\text{Ex}} &= m_{\text{com, day}} I_{\text{com,day},\lambda}^{\text{Ex}} \\
& \quad \times \cos[2\psi_{\text{com, day}} + 2(\text{RM}_{\text{com}} + \text{RM}_{\text{ext}})(\lambda^2 - \lambda_0^2)] \\
& \quad (12) \\
U_{\text{com,day},\lambda}^{\text{Ex}} &= m_{\text{com, day}} I_{\text{com,day},\lambda}^{\text{Ex}} \\
& \quad \sin[2\psi_{\text{com, day}} + 2(\text{RM}_{\text{com}} + \text{RM}_{\text{ext}})(\lambda^2 - \lambda_0^2)].
\end{aligned} 
$$

This introduces an additional 11 parameters: $I_{0,com}$, $\alpha_{com}$, RM$_{com}$, and four each of $m_{com, day}$ and $\psi_{com, day}$. The polarization fraction and EVPA of the compact component, $m_{com,day}$ and $\psi_{com,day}$, are distinct from all of the other parameters in the model in that they vary among observation days. Therefore, where useful, we will distinguish these as “dynamic” parameters, with the remainder of the parameters being “static” in the limited sense that they do not vary across the observation campaign.

### 1.1.3. Compact Component: Internal Faraday Screen Model

Many simulations of M87 indicate the presence of large Faraday depths in the emission region (Broderick & McKinney 2010; Mościbrodzka et al. 2017; Ricarte et al. 2020). Therefore, we also consider a simple model for the compact component in which the emission and rotation are co-located, i.e., an internal Faraday screen. In principle, this is inextricably linked to the detailed properties of the emission region. Here we employ the gross simplification of a single-zone, or slab, model: the emission and Faraday rotation within the compact component occur within a homogeneous region. We begin with a summary of the polarimetric properties of such a slab.

For a plane-parallel source with physical depth L and at some reference wavelength $\lambda_0$, a uniform emissivity j, polarization fraction $m_{em}$ at emission, EVPA at emission $\psi_{em}$,
Faraday rotativity $R$, we have total intensity,

$$I = \int_{0}^{L} j dz = jL, \qquad (13)$$

and Stokes $Q$ and $U$,

$$ \begin{aligned} Q + iU &= \int_{0}^{L} j m_{em} e^{2i[Rx\lambda^{2} + \psi_{em}]} dx \\ &= \frac{m_{em}I}{2RL\lambda^{2}}[\sin(2\psi_{em} + 2RL\lambda^{2}) - \sin(2\psi_{em})] \\ &\quad + i \frac{m_{em}I}{2RL\lambda^{2}}[\cos(2\psi_{em}) - \cos(2\psi_{em} + 2RL\lambda^{2})] \end{aligned} \qquad (14) \\ &= \frac{1}{2} m_{em} I \sinh(RL\lambda^{2}) \\ &\quad \times [\cos(2\psi_{em} + RL\lambda^{2}) + i \sin(2\psi_{em} + RL\lambda^{2})] \end{aligned} $$

from which we can immediately read off $Q$ and $U$. The EVPA at the top of the slab is

$$ \tan(2\psi) = \frac{Q}{U} = \tan[2\psi_{em} + RL(\lambda^2 - \lambda_0^2)], \qquad (15) $$

from which it is apparent that the effective contribution to the compact RM is $RM_{com} = RL/2$.

The internal Faraday screen model is then defined by

$$ \begin{aligned} I_{\text{com,day},\lambda}^{\text{In}} &= I_{0,\text{com}}(\lambda/\lambda_0)^{\alpha_{\text{com}}} \\ Q_{\text{com,day},\lambda}^{\text{In}} &= \frac{1}{2} m_{\text{com, day}} I_{\text{com,day},\lambda}^{\text{In}} \text{sinc}(2RM_{\text{com}}\lambda^2) \\ & \quad \times \cos[2\psi_{\text{com,day}} + 2(RM_{\text{com}} + RM_{\text{ext}})\lambda^2] \\ U_{\text{com,day},\lambda}^{\text{In}} &= \frac{1}{2} m_{\text{com, day}} I_{\text{com,day},\lambda}^{\text{In}} \text{sinc}(2RM_{\text{com}}\lambda^2) \\ & \quad \times \sin[2\psi_{\text{com,day}} + 2(RM_{\text{com}} + RM_{\text{ext}})\lambda^2], \end{aligned} \qquad (16) $$

where, as with the external model, we have added the Faraday rotation from the large-scale Faraday screen. As with the external Faraday screen model, this introduces 11 parameters, though the interpretations of the polarization fraction, and EVPA subtly differ, here referring to those of the emission process instead of derotated values.

As with the external Faraday screen model, where useful, we will refer to $m_{com,day}$ and $\psi_{com,day}$, which differ among observation days, as “dynamic” parameters to distinguish them from the remaining “static” parameters.

## 1.2. Markov Chain Monte Carlo Analysis

From the models described above and the integrated EHT Stokes parameter ranges presented in Table 7 in Appendix H2 of Event Horizon Telescope Collaboration et al. (2021a) ($I_{EHT}$, $Q_{EHT}$, $U_{EHT}$) and the ALMA core Stokes parameter values for the individual SPWs in Table E2 ($I_{spw}$, $Q_{spw}$, $U_{spw}$), we construct a log-likelihood for each set of model parameters. These comprise 60 data values in total: three ($I_{EHT}$, $Q_{EHT}$, $U_{EHT}$) on each of four days from the EHT observations (3 × 4 data points), three ($I_{spw}$, $Q_{spw}$, $U_{spw}$) in four SPWs on each of four days presented here (3 × 4 × 4 data points).

We assume that the integrated EHT Stokes parameters are distributed normally with means and standard deviations set by the centers and half-widths of the ranges; this likely over-estimates the true uncertainty on the $I_{EHT}$, $Q_{EHT}$, and $U_{EHT}$.

The resulting log-likelihood is

$$ \mathcal{L} = \sum_{\text{day}} \left[ -\frac{(I_{\text{EHT}} - I_{\text{com,day},\lambda_0})^2}{2\sigma_{I_{\text{EHT}}}^2} - \frac{(Q_{\text{EHT}} - Q_{\text{com,day},\lambda_0})^2}{2\sigma_{Q_{\text{EHT}}}^2} - \frac{(U_{\text{EHT}} - U_{\text{com,day},\lambda_0})^2}{2\sigma_{U_{\text{EHT}}}^2} \right. \\ \left. - \sum_{\text{spw}=1}^{4} \frac{(I_{\text{spw}} - I_{\text{tot,day},\lambda_{\text{spw}}})^2}{2\sigma_{I_{\text{spw}}}^2} - \sum_{\text{spw}=1}^{4} \frac{(Q_{\text{spw}} - Q_{\text{tot,day},\lambda_{\text{spw}}})^2}{2\sigma_{Q_{\text{spw}}}^2} - \sum_{\text{spw}=1}^{4} \frac{(U_{\text{spw}} - U_{\text{tot,day},\lambda_{\text{spw}}})^2}{2\sigma_{U_{\text{spw}}}^2} \right] \qquad (17) $$

Linear or “uniform” priors in the natural ranges are imposed on all parameters with the exception of the compact and extended component intensity normalizations, for which logarithmic priors are chosen. See Table II for details.

The likelihood is sampled with the ensemble Markov chain MC (MCMC) method provided by the EMCEE python package (Foreman-Mackey et al. 2013). We use 256 independent walkers, and run for 10⁵ steps, discarding the first half of the chains. Explorations with fewer walkers and steps indicate that by this time the MCMC chains are well converged.

In addition to the models described in Appendix I.1, we also considered versions of the two-component model applied to each day independently, i.e., keeping only one day in the sum in Equation (17). In these, on each day the five parameters of the external screen and five parameters of the internal screen (a single $m_{com}$ and $\psi_{com}$) are independently fit on each observation day. Effectively, this corresponds to a 40-parameter model across the four observation days, permitting Faraday screens and emission from both the compact and extended Faraday screens to vary independently across the four observation days.

On any given observation day, the parameters are less well constrained in this case and, with the notable exceptions of the compact component polarization fraction and EVPA, are consistent with a single set of values across all days. The variable polarization properties of the compact component matches the expectation from the EHT measurements in Event Horizon Telescope Collaboration et al. (2021a). The consistency with a single set of values for the remaining model parameters serves as a partial motivation for the more restricted variability in the models presented in Appendix I.1.

## 1.3. Two-component Model Results

Excellent fits are found for both the external and internal Faraday screen models. For 44 degrees of freedom, the best-fit external and internal screen models have reduced $\chi^2 = 3.96$ and $\chi^2 = 2.54$, respectively, both modestly small and possibly indicating that the uncertainties on the integrated EHT Stokes parameters are indeed over-estimated by their half-range values. Thus, it is possible to reproduce the variable
## Internal Compact Faraday Screen

<figure><img src="image_31.png" /></figure>

## External Compact Faraday Screen

<caption>**Figure 11.** Joint posteriors for static parameters of two-component polarimetric models with external (lower left; blue) and internal (upper right; red) small-scale Faraday screens. Contours indicate 50%, 90%, and 95% quantiles.</caption>

polarimetric properties observed by ALMA with a model in which only the compact emission evolves.

Figures I1 and I2 show the joint posteriors for the external (lower-left) and internal (upper-right) Faraday screen models for the static and dynamic model components, respectively. To facilitate a direct comparison with the external Faraday screen model, in Figure 12, the polarization fractions and EVPAs of the internal Faraday screen model have been depolarized and rotated to show the corresponding posteriors on their observed analogs. Model parameter estimates, marginalized over all other parameters, are contained in Table I1.

After adjusting the polarization fraction and EVPA of the compact component, the properties of the two-component models are consistent among the external and internal Faraday

screen models. Strong correlations exist between many of the compact component features. These are very strong for the polarization fractions and EVPAs on neighboring observation days, i.e., April 5 and 6, and April 10 and 11. This is anticipated by the similarities in the integrated polarimetric properties reported in Event Horizon Telescope Collaboration et al. (2021a) between neighboring observation days, which naturally constrain the two-component polarization models accordingly.

The flux normalizations, polarization fractions, and EVPAs are well constrained. RM<sub>ext</sub> is restricted to small magnitudes in both cases, typically less than 1.5 × 10<sup>5</sup> rad m<sup>-2</sup>, and remains consistent with vanishing altogether. In contrast, RM<sub>com</sub> is significantly non-zero, and typically of order -5 × 10<sup>5</sup> rad m<sup>-2</sup>,
Internal Compact Faraday Screen

<figure><img src="image_32.png" /></figure>

External Compact Faraday Screen

**Figure 12.** Joint posteriors for dynamic parameters of two-component polarimetric models with external (lower left; blue) and internal (upper right; red) small-scale Faraday screens. For the internal Faraday screen model, the polarization fractions have been depolarized by a factor of sinc(2RM<sub>com</sub>λ<sub>0</sub><sup>2</sup>) and the EVPAs have been rotated by (RM<sub>com</sub> + RM<sub>ext</sub>)λ<sub>0</sub><sup>2</sup>, corresponding to observed values, concordant with the definition for the external Faraday screen model. Contours indicate 50%, 90%, and 95% quantiles.

factors of 3–10 larger than those reported in Table 2, implying a
significant degree of competition between the spectral variations
in the two components and the residual Faraday rotation. In
neither model are the spectral indexes of the components well
constrained.

By construction, these are necessarily consistent with the
results from ALMA-only RM measurements reported in
Table 2. Figure 13 shows a number of realizations drawn from
the posteriors for the wavelength-dependence of the EVPAs
on each of the observation days in comparison to the

measured values listed in Table E2. The interday evolution
in the ALMA RMs is well reproduced, despite restricting the
variable elements of the model to the compact component.
Within the ALMA SPWs the EVPAs only weakly depart from
the linear dependence on λ², indicative of Faraday rotation;
outside of the ALMA SPWs this divergence can become
considerably larger, implying that additional coincident
polarimetric measurements at longer (and shorter) wave-
lengths will significantly improve constraints on the elements
of the two-component model.
<figure><img src="image_33.png" /><figcaption>External Compact Faraday Screen</figcaption></figure>

**Figure 13.** EVPA as a function of $\lambda^2$ for 10$^3$ draws from the two-component model posterior of the external (top) and internal (bottom) Faraday screen models. The highest-likelihood models are shown by the black lines. The blue data points are the ALMA measurements (same as Figure F1).

<caption>Internal Compact Faraday Screen</caption>

ORCID iDs

Ciriaco Goddi https://orcid.org/0000-0002-2542-7743

Iván Martí-Vidal https://orcid.org/0000-0003-3708-9611

Hugo Messias https://orcid.org/0000-0002-2985-7994

Geoffrey C. Bower https://orcid.org/0000-0003-4056-9982

Avery E. Broderick https://orcid.org/0000-0002-3351-760X

Jason Dexter https://orcid.org/0000-0003-3903-0373

Daniel P. Marrone https://orcid.org/0000-0002-2367-1080

Monika Moscibrodzka https://orcid.org/0000-0002-4661-6332

Hiroshi Nagai https://orcid.org/0000-0003-0292-3645

Juan Carlos Algaba https://orcid.org/0000-0001-6993-1696

Geoffrey B. Crew https://orcid.org/0000-0002-2079-3189

José L. Gómez https://orcid.org/0000-0003-4190-7613

C. M. Violette Impellizzeri https://orcid.org/0000-0002-3443-2472

Michael Janssen https://orcid.org/0000-0001-8685-6544

Matthias Kadler https://orcid.org/0000-0001-5606-6154

Thomas P. Krichbaum https://orcid.org/0000-0002-4892-9586

Rocco Lico https://orcid.org/0000-0001-7361-2460

Lynn D. Matthews https://orcid.org/0000-0002-3728-8082

Angelo Ricarte https://orcid.org/0000-0001-5287-0452

Eduardo Ros https://orcid.org/0000-0001-9503-4892

Ziri Younsi https://orcid.org/0000-0001-9283-1191

Kazunori Akiyama https://orcid.org/0000-0002-9475-4254

Antxon Alberdi https://orcid.org/0000-0002-9371-1033

Richard Anantua https://orcid.org/0000-0003-3457-7660

Rebecca Azulay https://orcid.org/0000-0002-2200-5393

Anne-Kathrin Baczko https://orcid.org/0000-0003-3090-3975

Mislav Baloković https://orcid.org/0000-0003-0476-6647

John Barrett https://orcid.org/0000-0002-9290-0764

Bradford A. Benson https://orcid.org/0000-0002-5108-6823

Lindy Blackburn https://orcid.org/0000-0002-9030-642X

Raymond Blundell https://orcid.org/0000-0002-5929-5857

Katherine L. Bouman https://orcid.org/0000-0003-0077-4367

Hope Boyce https://orcid.org/0000-0002-6530-5783

Christiaan D. Brinkerink https://orcid.org/0000-0002-2322-0749

Roger Brissenden https://orcid.org/0000-0002-2556-0894

Silke Britzen https://orcid.org/0000-0001-9240-6734

Do-Young Byun https://orcid.org/0000-0003-1157-4109

Andrew Chael https://orcid.org/0000-0003-2966-6220

Chi-kwan Chan https://orcid.org/0000-0001-6337-6126

Shami Chatterjee https://orcid.org/0000-0002-2878-1502

Koushik Chatterjee https://orcid.org/0000-0002-2825-3590

Paul M. Chesler https://orcid.org/0000-0001-6327-8462

Ilje Cho https://orcid.org/0000-0001-6083-7521

Pierre Christian https://orcid.org/0000-0001-6820-9941

John E. Conway https://orcid.org/0000-0003-2448-9181

James M. Cordes https://orcid.org/0000-0002-4049-1882

Thomas M. Crawford https://orcid.org/0000-0001-9000-5013

Alejandro Cruz-Osorio https://orcid.org/0000-0002-3945-6342

Yuzhu Cui https://orcid.org/0000-0001-6311-4345

Jordy Davelaar https://orcid.org/0000-0002-2685-2434

Mariafelicia De Laurentis https://orcid.org/0000-0002-9945-682X

Roger Deane https://orcid.org/0000-0003-1027-5043

Jessica Dempsey https://orcid.org/0000-0003-1269-9667

Gregory Desvignes https://orcid.org/0000-0003-3922-4055

Sheperd S. Doeleman https://orcid.org/0000-0002-9031-0904

Ralph P. Eatough https://orcid.org/0000-0001-6196-4135

Heino Falcke https://orcid.org/0000-0002-2526-6724

Joseph Farah https://orcid.org/0000-0003-4914-5625

Vincent L. Fish https://orcid.org/0000-0002-7128-9345

Ed Fomalont https://orcid.org/0000-0002-9036-2747

H. Alyson Ford https://orcid.org/0000-0002-9797-0972

Raquel Fraga-Encinas https://orcid.org/0000-0002-5222-1361

Per Friberg https://orcid.org/0000-0002-8010-8454

Antonio Fuentes https://orcid.org/0000-0002-8773-4933

Peter Galison https://orcid.org/0000-0002-6429-3872

Charles F. Gammie https://orcid.org/0000-0001-7451-8935
Roberto García https://orcid.org/0000-0002-6584-7443

Boris Georgiev https://orcid.org/0000-0002-3586-6424

Roman Gold https://orcid.org/0000-0003-2492-1966

Arturo I. Gómez-Ruiz https://orcid.org/0000-0001-9395-1670

Minfeng Gu (顾敏峰) https://orcid.org/0000-0002-4455-6946

Mark Gurwell https://orcid.org/0000-0003-0685-3621

Kazuhiro Hada https://orcid.org/0000-0001-6906-772X

Daryl Haggard https://orcid.org/0000-0001-6803-2138

Ronald Hesper https://orcid.org/0000-0003-1918-6098

Luis C. Ho (何子山) https://orcid.org/0000-0001-6947-5846

Mareki Honma https://orcid.org/0000-0003-4058-9000

Chih-Wei L. Huang https://orcid.org/0000-0001-5641-3953

Lei Huang (黄磊) https://orcid.org/0000-0002-1923-227X

Sara Issaoun https://orcid.org/0000-0002-5297-921X

David J. James https://orcid.org/0000-0001-5160-4486

Britton Jeter https://orcid.org/0000-0003-2847-1712

Wu Jiang (江悟) https://orcid.org/0000-0001-7369-3539

Michael D. Johnson https://orcid.org/0000-0002-4120-3029

Svetlana Jorstad https://orcid.org/0000-0001-6158-1708

Taehyun Jung https://orcid.org/0000-0001-7003-8643

Mansour Karami https://orcid.org/0000-0001-7387-9333

Ramesh Karuppusamy https://orcid.org/0000-0002-5307-2919

Tomohisa Kawashima https://orcid.org/0000-0001-8527-0496

Garrett K. Keating https://orcid.org/0000-0002-3490-146X

Mark Kettenis https://orcid.org/0000-0002-6156-5617

Dong-Jin Kim https://orcid.org/0000-0002-7038-2118

Jae-Young Kim https://orcid.org/0000-0001-8229-7183

Jongsoo Kim https://orcid.org/0000-0002-1229-0426

Junhan Kim https://orcid.org/0000-0002-4274-9373

Motoki Kino https://orcid.org/0000-0002-2709-7338

Jun Yi Koay https://orcid.org/0000-0002-7029-6658

Patrick M. Koch https://orcid.org/0000-0003-2777-5861

Shoko Koyama https://orcid.org/0000-0002-3723-3372

Michael Kramer https://orcid.org/0000-0002-4175-2271

Carsten Kramer https://orcid.org/0000-0002-4908-4925

Cheng-Yu Kuo https://orcid.org/0000-0001-6211-5581

Tod R. Lauer https://orcid.org/0000-0003-3234-7247

Sang-Sung Lee https://orcid.org/0000-0002-6269-594X

Aviad Levis https://orcid.org/0000-0001-7307-632X

Yan-Rong Li (李彦荣) https://orcid.org/0000-0001-5841-9179

Zhiyuan Li (李志远) https://orcid.org/0000-0003-0355-6437

Michael Lindqvist https://orcid.org/0000-0002-3669-0715

Greg Lindahl https://orcid.org/0000-0002-6100-4772

Jun Liu (刘俊) https://orcid.org/0000-0002-7615-7499

Kuo Liu https://orcid.org/0000-0002-2953-7376

Elisabetta Liuzzo https://orcid.org/0000-0003-0995-5201

Laurent Loinard https://orcid.org/0000-0002-5635-3345

Ru-Sen Lu (路如森) https://orcid.org/0000-0002-7692-7967

Nicholas R. MacDonald https://orcid.org/0000-0002-6684-8691

Jirong Mao (毛基荣) https://orcid.org/0000-0001-8339-1294

Nicola Marchili https://orcid.org/0000-0002-5523-7588

Sera Markoff https://orcid.org/0000-0001-9564-0876

Alan P. Marscher https://orcid.org/0000-0001-7396-3332

Satoshi Matsushita https://orcid.org/0000-0002-2127-7880

Lia Medeiros https://orcid.org/0000-0003-2342-6728

Karl M. Menten https://orcid.org/0000-0001-6459-0669

Izumi Mizuno https://orcid.org/0000-0002-7210-6264

Yosuke Mizuno https://orcid.org/0000-0002-8131-6730

James M. Moran https://orcid.org/0000-0002-3882-4414

Kotaro Moriyama https://orcid.org/0000-0003-1364-3761

Cornelia Müller https://orcid.org/0000-0002-2739-2994

Gibwa Musoke https://orcid.org/0000-0003-1984-189X

Alejandro Mus Mejías https://orcid.org/0000-0003-0329-6874

Neil M. Nagar https://orcid.org/0000-0001-6920-662X

Masanori Nakamura https://orcid.org/0000-0001-6081-2420

Ramesh Narayan https://orcid.org/0000-0002-1919-2730

Iniyan Natarajan https://orcid.org/0000-0001-8242-4373

Joey Neilsen https://orcid.org/0000-0002-8247-786X

Roberto Neri https://orcid.org/0000-0002-7176-4046

Chunchong Ni https://orcid.org/0000-0003-1361-5699

Aristeidis Noutsos https://orcid.org/0000-0002-4151-3860

Michael A. Nowak https://orcid.org/0000-0001-6923-1315

Héctor Olivares https://orcid.org/0000-0001-6833-7580

Gisela N. Ortiz-León https://orcid.org/0000-0002-2863-676X

Daniel C. M. Palumbo https://orcid.org/0000-0002-7179-3816

Jongho Park https://orcid.org/0000-0001-6558-9053

Ue-Li Pen https://orcid.org/0000-0003-2155-9578

Dominic W. Pesce https://orcid.org/0000-0002-5278-9221

Richard Plambeck https://orcid.org/0000-0001-6765-9609

Oliver Porth https://orcid.org/0000-0002-4584-2557

Felix M. Pötzl https://orcid.org/0000-0002-6579-8311

Ben Prather https://orcid.org/0000-0002-0393-7734

Jorge A. Preciado-López https://orcid.org/0000-0002-4146-0113

Dimitrios Psaltis https://orcid.org/0000-0003-4058-2837

Hung-Yi Pu https://orcid.org/0000-0001-9270-8812

Venkatessh Ramakrishnan https://orcid.org/0000-0002-9248-086X

Ramprasad Rao https://orcid.org/0000-0002-1407-7944

Mark G. Rawlings https://orcid.org/0000-0002-6529-202X

Alexander W. Raymond https://orcid.org/0000-0002-5779-4767

Luciano Rezzolla https://orcid.org/0000-0002-1330-7103

Bart Ripperda https://orcid.org/0000-0002-7301-3908

Freek Roelofs https://orcid.org/0000-0001-5461-3687

Mel Rose https://orcid.org/0000-0002-2016-8746

Alan L. Roy https://orcid.org/0000-0002-1931-0135

Chet Ruszczyk https://orcid.org/0000-0001-7278-9707

Kazi L. J. Rygl https://orcid.org/0000-0003-4146-9043

David Sánchez-Arguelles https://orcid.org/0000-0002-7344-9920

Mahito Sasada https://orcid.org/0000-0001-5946-9960

Tuomas Savolainen https://orcid.org/0000-0001-6214-1085

Lijing Shao https://orcid.org/0000-0002-1334-8853

Zhiqiang Shen (沈志强) https://orcid.org/0000-0003-3540-8746

Des Small https://orcid.org/0000-0003-3723-5404

Bong Won Sohn https://orcid.org/0000-0002-4148-8378

Jason SooHoo https://orcid.org/0000-0003-1938-0720

He Sun (孙赫) https://orcid.org/0000-0003-1526-6787

Fumie Tazaki https://orcid.org/0000-0003-0236-0600
Alexandra J. Tetarenko https://orcid.org/0000-0003-3906-4354

Paul Tiede https://orcid.org/0000-0003-3826-5648

Remo P. J. Tilanus https://orcid.org/0000-0002-6514-553X

Michael Titus https://orcid.org/0000-0002-3423-4505

Kenji Toma https://orcid.org/0000-0002-7114-6010

Pablo Torne https://orcid.org/0000-0001-8700-6058

Efthalia Traianou https://orcid.org/0000-0002-1209-6500

Sascha Trippe https://orcid.org/0000-0003-0465-1559

Ilse van Bemmel https://orcid.org/0000-0001-5473-2950

Huib Jan van Langevelde https://orcid.org/0000-0002-0230-5946

Daniel R. van Rossum https://orcid.org/0000-0001-7772-6131

Jan Wagner https://orcid.org/0000-0003-1105-6109

Derek Ward-Thompson https://orcid.org/0000-0003-1140-2761

John Wardle https://orcid.org/0000-0002-8960-2942

Jonathan Weintroub https://orcid.org/0000-0002-4603-5204

Norbert Wex https://orcid.org/0000-0003-4058-2837

Robert Wharton https://orcid.org/0000-0002-7416-5209

Maciek Wielgus https://orcid.org/0000-0002-8635-4242

George N. Wong https://orcid.org/0000-0001-6952-2147

Qingwen Wu (吴庆文) https://orcid.org/0000-0003-4773-4987

Doosoo Yoon https://orcid.org/0000-0001-8694-8166

André Young https://orcid.org/0000-0003-0000-2682

Ken Young https://orcid.org/0000-0002-3666-4920

Feng Yuan (袁峰) https://orcid.org/0000-0003-3564-6437

Ye-Fei Yuan (袁业飞) https://orcid.org/0000-0002-7330-4756

J. Anton Zensus https://orcid.org/0000-0001-7470-3321

Guang-Yao Zhao https://orcid.org/0000-0002-4417-1659

Shan-Shan Zhao https://orcid.org/0000-0002-9774-3606

Gabriele Bruni https://orcid.org/0000-0002-5182-6289

Antonio Hernández-Gómez https://orcid.org/0000-0001-7520-4305

Adam Ingram https://orcid.org/0000-0002-5311-9078

S. Komossa https://orcid.org/0000-0002-9214-4428

Y. Y. Kovalev https://orcid.org/0000-0001-9303-3263

Dirk Muders https://orcid.org/0000-0002-2315-2571

Manel Perucho https://orcid.org/0000-0003-2784-0379

Mauri Valtonen https://orcid.org/0000-0001-8580-8874

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