<table><caption>**Table C.1. Atmospheric parameters and metallicity [Fe/H] for the GK star sample.**</caption><thead><tr><th>Star</th><th><i>T</i><sub>eff</sub><br>(K)</th><th>log <i>g</i><br>(dex)</th><th><i>V</i><sub>t</sub><br>(km s<sup>-1</sup>)</th><th>[Fe/H]<br>(dex)</th><th>Spectrum</th><th><i>S</i>/<i>N</i><br>(per pixel)</th></tr></thead><tbody><tr><td>HD 3651</td><td>5274 ± 107</td><td>4.42 ± 0.20</td><td>0.87 ± 0.25</td><td>+0.08 ± 0.06</td><td>HARPN</td><td>280</td></tr><tr><td>HD 20794</td><td>5501 ± 66</td><td>4.49 ± 0.15</td><td>0.88 ± 0.11</td><td>-0.36 ± 0.05</td><td>HARPS</td><td>350</td></tr><tr><td>HD 38858</td><td>5788 ± 75</td><td>4.56 ± 0.11</td><td>0.95 ± 0.11</td><td>-0.21 ± 0.05</td><td>HARPS</td><td>400</td></tr><tr><td>HD 69830</td><td>5458 ± 72</td><td>4.55 ± 0.12</td><td>0.76 ± 0.15</td><td>-0.03 ± 0.05</td><td>HARPS</td><td>380</td></tr><tr><td>HD 99492</td><td>5562 ± 120</td><td>4.58 ± 0.19</td><td>1.06 ± 20</td><td>+0.27 ± 0.09</td><td>HARPS</td><td>250</td></tr><tr><td>HD 102365</td><td>5608 ± 50</td><td>4.27 ± 0.12</td><td>0.91 ± 0.07</td><td>-0.35 ± 0.03</td><td>HARPS</td><td>350</td></tr><tr><td>61 Vir</td><td>5557 ± 48</td><td>4.40 ± 0.12</td><td>0.82 ± 0.10</td><td>-0.03 ± 0.04</td><td>HARPS</td><td>300</td></tr><tr><td>HD 136352</td><td>5655 ± 48</td><td>4.24 ± 0.12</td><td>0.88 ± 0.06</td><td>-0.37 ± 0.03</td><td>HARPS</td><td>345</td></tr><tr><td>HD 154088</td><td>5416 ± 70</td><td>4.46 ± 0.20</td><td>0.96 ± 0.20</td><td>+0.25 ± 0.06</td><td>HARPS</td><td>312</td></tr><tr><td>HD 189567</td><td>5715 ± 45</td><td>4.36 ± 0.13</td><td>0.92 ± 0.07</td><td>-0.27 ± 0.03</td><td>HARPS</td><td>330</td></tr><tr><td>BD-061339</td><td>4061 ± 52</td><td>4.68 ± 0.05</td><td>0.79 ± 0.12</td><td>-0.20 ± 0.10</td><td>HARPS</td><td>60</td></tr><tr><td>GJ 667 C</td><td>4939 ± 41</td><td>4.50 ± 0.10</td><td>0.90 ± 0.10</td><td>-0.48 ± 0.10</td><td>HARPS</td><td>290</td></tr><tr><td>HD 40307</td><td>4871 ± 65</td><td>4.61 ± 0.05</td><td>0.89 ± 0.10</td><td>-0.30 ± 0.05</td><td>ESPRESSO</td><td>1000</td></tr><tr><td>HD 85512</td><td>4389 ± 115</td><td>4.48 ± 0.10</td><td>0.75 ± 0.10</td><td>-0.28 ± 0.12</td><td>HARPS</td><td>195</td></tr></tbody></table>

<table><caption>**Table C.2. Elemental abundances with corresponding errors for the G-type stars in our sample.**</caption><thead><tr><th>Star</th><th>[Na/Fe]<sub>NLTE</sub></th><th>[Mg/Fe]</th><th>[Si/Fe]</th><th>[Ca/Fe]</th><th>[Ti/Fe]</th><th>[Cr/Fe]</th><th>[Ni/Fe]</th></tr></thead><tbody><tr><td>HD 3651</td><td>0.11 ± 0.05</td><td>0.10 ± 0.07</td><td>0.00 ± 0.05</td><td>0.04 ± 0.06</td><td>0.04 ± 0.05</td><td>0.11 ± 0.08</td><td>0.10 ± 0.08</td></tr><tr><td>HD 20794</td><td>0.06 ± 0.05</td><td>0.25 ± 0.04</td><td>0.14 ± 0.05</td><td>0.18 ± 0.07</td><td>0.28 ± 0.05</td><td>0.04 ± 0.05</td><td>0.08 ± 0.04</td></tr><tr><td>HD 69830</td><td>0.03 ± 0.05</td><td>-0.01 ± 0.04</td><td>-0.01 ± 0.04</td><td>0.00 ± 0.05</td><td>0.05 ± 0.06</td><td>0.05 ± 0.06</td><td>0.04 ± 0.05</td></tr><tr><td>HD 38858</td><td>-0.01 ± 0.05</td><td>-0.03 ± 0.06</td><td>-0.03 ± 0.07</td><td>0.03 ± 0.08</td><td>0.04 ± 0.04</td><td>0.04 ± 0.08</td><td>-0.01 ± 0.08</td></tr><tr><td>HD 99492</td><td>0.12 ± 0.04</td><td>-0.03 ± 0.06</td><td>0.06 ± 0.06</td><td>-0.04 ± 0.07</td><td>0.05 ± 0.06</td><td>0.08 ± 0.06</td><td>0.10 ± 0.06</td></tr><tr><td>HD 102365</td><td>0.08 ± 0.05</td><td>0.18 ± 0.04</td><td>0.11 ± 0.05</td><td>0.12 ± 0.16</td><td>0.13 ± 0.05</td><td>0.01 ± 0.03</td><td>0.06 ± 0.07</td></tr><tr><td>61 Vir</td><td>0.06 ± 0.05</td><td>-0.01 ± 0.06</td><td>-0.01 ± 0.05</td><td>0.03 ± 0.05</td><td>0.06 ± 0.05</td><td>0.00 ± 0.05</td><td>0.03 ± 0.06</td></tr><tr><td>HD 136352</td><td>0.13 ± 0.06</td><td>0.24 ± 0.05</td><td>0.13 ± 0.06</td><td>0.14 ± 0.10</td><td>0.17 ± 0.06</td><td>0.05 ± 0.04</td><td>0.05 ± 0.06</td></tr><tr><td>HD 154088</td><td>0.15 ± 0.06</td><td>0.07 ± 0.06</td><td>0.12 ± 0.04</td><td>0.04 ± 0.05</td><td>0.07 ± 0.08</td><td>0.16 ± 0.07</td><td>0.10 ± 0.10</td></tr><tr><td>HD 189567</td><td>0.08 ± 0.09</td><td>0.05 ± 0.04</td><td>0.05 ± 0.04</td><td>0.06 ± 0.10</td><td>0.08 ± 0.10</td><td>0.01 ± 0.05</td><td>0.01 ± 0.07</td></tr></tbody></table>

## Appendix D: Log of the VLT/SPHERE observations

Table D.1 lists the 94 observations with VLT/SPHERE, including the observational conditions, represented in Fig. D.1 too.

<figure><img src="image_25.png" /><figcaption>**Fig. D.1.** Distribution of the observing conditions: seeing, coherence time of the adaptive optic system, strehl, and parallactic angle variation.</figcaption></figure>
<table><caption>**Table D.1.** Log of the 94 observations with the instrument VLT/SPHERE.</caption><thead><tr><th>System</th><th>Date</th><th>Instru.</th><th>Filter</th><th>N<sub>exp</sub></th><th>DIT (s)</th><th>Grade</th><th>Δπ (°)</th><th>ε (")</th><th>τ<sub>0</sub> (ms)</th><th>Sr (%)</th><th>airmass</th></tr></thead><tbody><tr><td>GJ 163</td><td>2018-10-12</td><td>IRDIS</td><td>H23</td><td>32</td><td>96</td><td>B</td><td>23.7</td><td>0.68</td><td>2.4</td><td>30</td><td>1.14</td></tr><tr><td>GJ 163</td><td>2018-10-12</td><td>IFS</td><td>YJ</td><td>32</td><td>96</td><td>B</td><td>23.8</td><td>0.70</td><td>2.4</td><td>—</td><td>1.14</td></tr><tr><td>GJ 176</td><td>2018-10-08</td><td>IRDIS</td><td>H23</td><td>64</td><td>48</td><td>A</td><td>16.9</td><td>0.90</td><td>3.7</td><td>77</td><td>1.38</td></tr><tr><td>GJ 176</td><td>2018-10-08</td><td>IFS</td><td>YJ</td><td>32</td><td>96</td><td>A</td><td>16.6</td><td>0.88</td><td>3.8</td><td>—</td><td>1.39</td></tr><tr><td>GJ 180</td><td>2018-10-09</td><td>IRDIS</td><td>H23</td><td>32</td><td>96</td><td>A</td><td>78.3</td><td>0.77</td><td>3.2</td><td>73</td><td>1.01</td></tr><tr><td>GJ 180</td><td>2018-10-09</td><td>IFS</td><td>YJ</td><td>32</td><td>96</td><td>A</td><td>78.4</td><td>0.84</td><td>2.5</td><td>—</td><td>1.01</td></tr><tr><td>BD-061339</td><td>2018-11-24</td><td>IRDIS</td><td>H23</td><td>32</td><td>96</td><td>A</td><td>31.3</td><td>0.59</td><td>12.0</td><td>84</td><td>1.06</td></tr><tr><td>BD-061339</td><td>2018-11-24</td><td>IFS</td><td>YJ</td><td>32</td><td>96</td><td>A</td><td>31.7</td><td>0.53</td><td>14.2</td><td>—</td><td>1.07</td></tr><tr><td>GJ 229</td><td>2018-11-27</td><td>IRDIS</td><td>H23</td><td>48</td><td>64</td><td>A</td><td>9.0</td><td>0.59</td><td>4.4</td><td>87</td><td>1.03</td></tr><tr><td>GJ 229</td><td>2018-11-27</td><td>IFS</td><td>YJ</td><td>32</td><td>96</td><td>A</td><td>9.2</td><td>0.63</td><td>4.0</td><td>—</td><td>1.03</td></tr><tr><td>GJ 422</td><td>2018-01-28</td><td>IRDIS</td><td>H23</td><td>30</td><td>96</td><td>A</td><td>19.4</td><td>0.38</td><td>10.2</td><td>75</td><td>1.20</td></tr><tr><td>GJ 422</td><td>2018-01-28</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>A</td><td>19.6</td><td>0.38</td><td>10.2</td><td>—</td><td>1.20</td></tr><tr><td>GJ 422</td><td>2019-11-25</td><td>IRDIS</td><td>K12</td><td>24</td><td>96</td><td>C</td><td>8.4</td><td>0.57</td><td>5.8</td><td>84</td><td>1.79</td></tr><tr><td>GJ 422</td><td>2019-11-25</td><td>IFS</td><td>YJH</td><td>24</td><td>96</td><td>C</td><td>8.4</td><td>0.65</td><td>3.9</td><td>—</td><td>1.79</td></tr><tr><td>GJ 422</td><td>2020-01-18</td><td>IRDIS</td><td>K12</td><td>24</td><td>96</td><td>A</td><td>15.4</td><td>0.47</td><td>10.7</td><td>87</td><td>1.20</td></tr><tr><td>GJ 422</td><td>2020-01-18</td><td>IFS</td><td>YJH</td><td>24</td><td>96</td><td>A</td><td>15.4</td><td>0.44</td><td>8.7</td><td>—</td><td>1.20</td></tr><tr><td>GJ 433</td><td>2018-02-02</td><td>IRDIS</td><td>H23</td><td>30</td><td>96</td><td>A</td><td>68.0</td><td>1.01</td><td>6.7</td><td>84</td><td>1.01</td></tr><tr><td>GJ 433</td><td>2018-02-02</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>A</td><td>68.4</td><td>1.01</td><td>6.7</td><td>—</td><td>1.01</td></tr><tr><td>GJ 433</td><td>2019-06-08</td><td>IRDIS</td><td>K12</td><td>15</td><td>64</td><td>C</td><td>23.9</td><td>0.86</td><td>3.7</td><td>82</td><td>1.01</td></tr><tr><td>GJ 433</td><td>2019-06-08</td><td>IFS</td><td>YJH</td><td>10</td><td>96</td><td>C</td><td>23.3</td><td>0.86</td><td>3.7</td><td>—</td><td>1.01</td></tr><tr><td>GJ 433</td><td>2020-01-20</td><td>IRDIS</td><td>K12</td><td>15</td><td>64</td><td>C</td><td>21.6</td><td>0.36</td><td>12.3</td><td>91</td><td>1.01</td></tr><tr><td>GJ 433</td><td>2020-01-20</td><td>IFS</td><td>YJH</td><td>10</td><td>96</td><td>C</td><td>20.6</td><td>0.36</td><td>12.3</td><td>—</td><td>1.01</td></tr><tr><td>GJ 581</td><td>2017-07-21</td><td>IRDIS</td><td>H23</td><td>30</td><td>96</td><td>A</td><td>35.3</td><td>0.55</td><td>6.9</td><td>81</td><td>1.05</td></tr><tr><td>GJ 581</td><td>2017-07-21</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>A</td><td>35.6</td><td>0.56</td><td>6.4</td><td>—</td><td>1.05</td></tr><tr><td>Wolf 1061</td><td>2017-07-28</td><td>IRDIS</td><td>H23</td><td>120</td><td>24</td><td>A</td><td>34.9</td><td>0.82</td><td>4.0</td><td>79</td><td>1.04</td></tr><tr><td>Wolf 1061</td><td>2017-07-28</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>A</td><td>34.1</td><td>0.78</td><td>4.5</td><td>—</td><td>1.04</td></tr><tr><td>GJ 649</td><td>2017-08-20</td><td>IRDIS</td><td>H23</td><td>60</td><td>48</td><td>B</td><td>14.1</td><td>0.84</td><td>5.6</td><td>81</td><td>1.57</td></tr><tr><td>GJ 649</td><td>2017-08-20</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>B</td><td>13.9</td><td>0.84</td><td>5.6</td><td>—</td><td>1.57</td></tr><tr><td>GJ 667</td><td>2017-06-27</td><td>IRDIS</td><td>H23</td><td>30</td><td>96</td><td>A</td><td>53.6</td><td>1.36</td><td>2.6</td><td>66</td><td>1.02</td></tr><tr><td>GJ 667</td><td>2017-06-27</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>A</td><td>54.2</td><td>1.36</td><td>2.6</td><td>—</td><td>1.02</td></tr><tr><td>GJ 674</td><td>2017-07-14</td><td>IRDIS</td><td>H23</td><td>30</td><td>96</td><td>A</td><td>27.2</td><td>0.67</td><td>3.2</td><td>73</td><td>1.08</td></tr><tr><td>GJ 674</td><td>2017-07-14</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>A</td><td>27.4</td><td>0.67</td><td>3.2</td><td>—</td><td>1.08</td></tr><tr><td>GJ 674</td><td>2021-07-04</td><td>IRDIS</td><td>K12</td><td>68</td><td>32</td><td>A</td><td>21.2</td><td>0.54</td><td>5.8</td><td>85</td><td>1.08</td></tr><tr><td>GJ 674</td><td>2021-07-04</td><td>IFS</td><td>YJH</td><td>23</td><td>96</td><td>A</td><td>21.2</td><td>0.54</td><td>5.8</td><td>—</td><td>1.08</td></tr><tr><td>GJ 682</td><td>2017-06-23</td><td>IRDIS</td><td>H23</td><td>60</td><td>48</td><td>C</td><td>31.5</td><td>1.95</td><td>1.4</td><td>58</td><td>1.07</td></tr><tr><td>GJ 682</td><td>2017-06-23</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>C</td><td>31.0</td><td>1.95</td><td>1.4</td><td>—</td><td>1.07</td></tr><tr><td>GJ 682</td><td>2017-07-20</td><td>IRDIS</td><td>H23</td><td>30</td><td>96</td><td>B</td><td>30.7</td><td>0.55</td><td>6.5</td><td>72</td><td>1.07</td></tr><tr><td>GJ 682</td><td>2017-07-20</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>B</td><td>31.0</td><td>0.55</td><td>6.5</td><td>—</td><td>1.07</td></tr><tr><td>GJ 682</td><td>2019-07-05</td><td>IRDIS</td><td>K12</td><td>24</td><td>96</td><td>B</td><td>25.0</td><td>0.54</td><td>6.5</td><td>88</td><td>1.06</td></tr><tr><td>GJ 682</td><td>2019-07-05</td><td>IFS</td><td>YJH</td><td>24</td><td>96</td><td>B</td><td>25.1</td><td>0.52</td><td>6.5</td><td>—</td><td>1.06</td></tr><tr><td>GJ 832</td><td>2017-05-27</td><td>IRDIS</td><td>H23</td><td>46</td><td>64</td><td>A</td><td>26.7</td><td>1.06</td><td>2.5</td><td>78</td><td>1.10</td></tr></tbody></table>
Table D.1. continued.

<table><thead><tr><th>System</th><th>Date</th><th>Instru.</th><th>Filter</th><th>N<sub>exp</sub></th><th>DIT (s)</th><th>Grade</th><th>Δπ (°)</th><th>ε (")</th><th>τ<sub>0</sub> (ms)</th><th>Sr (%)</th><th>airmass</th></tr></thead><tbody><tr><td>GJ 832</td><td>2017-05-27</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>A</td><td>25.9</td><td>0.97</td><td>2.9</td><td>—</td><td>1.10</td></tr><tr><td>GJ 832</td><td>2017-06-21</td><td>IRDIS</td><td>H23</td><td>184</td><td>16</td><td>C</td><td>27.7</td><td>2.30</td><td>1.1</td><td>61</td><td>1.10</td></tr><tr><td>GJ 832</td><td>2017-06-21</td><td>IFS</td><td>YJ</td><td>90</td><td>32</td><td>C</td><td>26.9</td><td>2.30</td><td>1.4</td><td>—</td><td>1.10</td></tr><tr><td>GJ 832</td><td>2017-06-27</td><td>IRDIS</td><td>H23</td><td>46</td><td>64</td><td>C</td><td>26.7</td><td>1.50</td><td>1.9</td><td>71</td><td>1.10</td></tr><tr><td>GJ 832</td><td>2017-06-27</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>C</td><td>25.9</td><td>1.50</td><td>1.9</td><td>—</td><td>1.10</td></tr><tr><td>GJ 832</td><td>2017-07-03</td><td>IRDIS</td><td>H23</td><td>46</td><td>64</td><td>B</td><td>25.9</td><td>1.42</td><td>1.8</td><td>75</td><td>1.10</td></tr><tr><td>GJ 832</td><td>2017-07-03</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>B</td><td>25.0</td><td>1.30</td><td>1.9</td><td>—</td><td>1.10</td></tr><tr><td>GJ 832</td><td>2022-07-29</td><td>IRDIS</td><td>H23</td><td>95</td><td>64</td><td>A</td><td>55.4</td><td>0.53</td><td>7.6</td><td>83</td><td>1.10</td></tr><tr><td>GJ 832</td><td>2022-07-29</td><td>IFS</td><td>YJ</td><td>56</td><td>96</td><td>A</td><td>47.3</td><td>0.56</td><td>7.2</td><td>—</td><td>1.10</td></tr><tr><td>GJ 3998</td><td>2017-05-14</td><td>IRDIS</td><td>H23</td><td>30</td><td>96</td><td>B</td><td>18.2</td><td>1.29</td><td>2.5</td><td>67</td><td>1.23</td></tr><tr><td>GJ 3998</td><td>2017-05-14</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>B</td><td>18.3</td><td>1.37</td><td>1.9</td><td>—</td><td>1.23</td></tr><tr><td>GJ 3998</td><td>2019-07-27</td><td>IRDIS</td><td>K12</td><td>24</td><td>96</td><td>B</td><td>14.4</td><td>0.59</td><td>4.8</td><td>85</td><td>1.23</td></tr><tr><td>GJ 3998</td><td>2019-07-27</td><td>IFS</td><td>YJH</td><td>24</td><td>96</td><td>B</td><td>14.4</td><td>0.68</td><td>3.6</td><td>—</td><td>1.24</td></tr><tr><td>HD 3651</td><td>2017-07-11</td><td>IRDIS</td><td>H23</td><td>332</td><td>10</td><td>A</td><td>18.8</td><td>1.22</td><td>2.0</td><td>78</td><td>1.45</td></tr><tr><td>HD 3651</td><td>2017-07-11</td><td>IFS</td><td>YJ</td><td>66</td><td>48</td><td>A</td><td>16.8</td><td>1.08</td><td>2.4</td><td>—</td><td>1.45</td></tr><tr><td>HD 20794</td><td>2017-09-03</td><td>IRDIS</td><td>H23</td><td>736</td><td>3</td><td>C</td><td>34.4</td><td>0.45</td><td>7.2</td><td>89</td><td>1.06</td></tr><tr><td>HD 20794</td><td>2017-09-03</td><td>IFS</td><td>YJ</td><td>406</td><td>6</td><td>C</td><td>37.5</td><td>0.47</td><td>6.8</td><td>—</td><td>1.06</td></tr><tr><td>HD 20794</td><td>2017-09-04</td><td>IRDIS</td><td>H23</td><td>552</td><td>6</td><td>B</td><td>44.9</td><td>0.88</td><td>2.2</td><td>87</td><td>1.06</td></tr><tr><td>HD 20794</td><td>2017-09-04</td><td>IFS</td><td>YJ</td><td>261</td><td>12</td><td>B</td><td>42.3</td><td>0.90</td><td>2.1</td><td>—</td><td>1.06</td></tr><tr><td>HD 38858</td><td>2018-11-23</td><td>IRDIS</td><td>H23</td><td>48</td><td>64</td><td>A</td><td>26.2</td><td>0.31</td><td>6.6</td><td>89</td><td>1.09</td></tr><tr><td>HD 38858</td><td>2018-11-23</td><td>IFS</td><td>YJ</td><td>32</td><td>96</td><td>A</td><td>26.1</td><td>0.32</td><td>7.7</td><td>—</td><td>1.09</td></tr><tr><td>HD 40307</td><td>2018-12-22</td><td>IRDIS</td><td>H23</td><td>48</td><td>64</td><td>A</td><td>18.2</td><td>0.48</td><td>8.7</td><td>89</td><td>1.27</td></tr><tr><td>HD 40307</td><td>2018-12-22</td><td>IFS</td><td>YJ</td><td>32</td><td>96</td><td>A</td><td>18.1</td><td>0.52</td><td>8.1</td><td>—</td><td>1.27</td></tr><tr><td>HD 69830</td><td>2018-12-18</td><td>IRDIS</td><td>H23</td><td>96</td><td>32</td><td>A</td><td>37.2</td><td>0.64</td><td>5.8</td><td>84</td><td>1.04</td></tr><tr><td>HD 69830</td><td>2018-12-18</td><td>IFS</td><td>YJ</td><td>32</td><td>96</td><td>A</td><td>36.7</td><td>0.70</td><td>5.5</td><td>—</td><td>1.04</td></tr><tr><td>HD 85512</td><td>2017-04-01</td><td>IRDIS</td><td>H23</td><td>60</td><td>48</td><td>C</td><td>32.8</td><td>1.04</td><td>2.4</td><td>80</td><td>1.06</td></tr><tr><td>HD 85512</td><td>2017-04-01</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>C</td><td>32.3</td><td>1.04</td><td>2.4</td><td>—</td><td>1.06</td></tr><tr><td>HD 85512</td><td>2017-12-30</td><td>IRDIS</td><td>H23</td><td>60</td><td>48</td><td>B</td><td>32.8</td><td>0.46</td><td>6.5</td><td>86</td><td>1.06</td></tr><tr><td>HD 85512</td><td>2017-12-30</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>B</td><td>32.2</td><td>0.46</td><td>6.5</td><td>—</td><td>1.06</td></tr><tr><td>HD 85512</td><td>2019-11-25</td><td>IRDIS</td><td>K12</td><td>136</td><td>16</td><td>C</td><td>7.0</td><td>0.39</td><td>7.9</td><td>91</td><td>1.55</td></tr><tr><td>HD 85512</td><td>2019-11-25</td><td>IFS</td><td>YJH</td><td>34</td><td>64</td><td>C</td><td>6.5</td><td>0.38</td><td>7.7</td><td>—</td><td>1.56</td></tr><tr><td>HD 85512</td><td>2020-01-03</td><td>IRDIS</td><td>K12</td><td>102</td><td>32</td><td>B</td><td>78.4</td><td>0.74</td><td>12.6</td><td>93</td><td>1.13</td></tr><tr><td>HD 85512</td><td>2020-01-03</td><td>IFS</td><td>YJH</td><td>34</td><td>64</td><td>B</td><td>24.6</td><td>0.82</td><td>10.3</td><td>—</td><td>1.06</td></tr><tr><td>HD 99492</td><td>2018-02-03</td><td>IRDIS</td><td>H23</td><td>30</td><td>96</td><td>A</td><td>22.7</td><td>0.94</td><td>5.8</td><td>85</td><td>1.13</td></tr><tr><td>HD 99492</td><td>2018-02-03</td><td>IFS</td><td>YJ</td><td>30</td><td>96</td><td>A</td><td>22.9</td><td>0.92</td><td>6.3</td><td>—</td><td>1.13</td></tr><tr><td>HD 99492</td><td>2020-03-16</td><td>IRDIS</td><td>K12</td><td>24</td><td>96</td><td>B</td><td>17.5</td><td>0.80</td><td>4.8</td><td>87</td><td>1.13</td></tr><tr><td>HD 99492</td><td>2020-03-16</td><td>IFS</td><td>YJH</td><td>24</td><td>96</td><td>B</td><td>17.6</td><td>1.06</td><td>3.4</td><td>—</td><td>1.14</td></tr><tr><td>HD 102365</td><td>2018-04-07</td><td>IRDIS</td><td>H23</td><td>136</td><td>24</td><td>A</td><td>40.1</td><td>0.44</td><td>7.7</td><td>91</td><td>1.05</td></tr><tr><td>HD 102365</td><td>2018-04-07</td><td>IFS</td><td>YJ</td><td>135</td><td>24</td><td>A</td><td>40.9</td><td>0.46</td><td>7.1</td><td>—</td><td>1.05</td></tr><tr><td>61 Vir</td><td>2017-06-28</td><td>IRDIS</td><td>H23</td><td>208</td><td>16</td><td>A</td><td>76.1</td><td>0.83</td><td>2.6</td><td>87</td><td>1.01</td></tr><tr><td>61 Vir</td><td>2017-06-28</td><td>IFS</td><td>YJ</td><td>203</td><td>16</td><td>A</td><td>15.8</td><td>0.78</td><td>2.9</td><td>—</td><td>1.01</td></tr><tr><td>HD 136352</td><td>2017-07-14</td><td>IRDIS</td><td>H23</td><td>70</td><td>48</td><td>A</td><td>31.2</td><td>0.82</td><td>2.9</td><td>80</td><td>1.10</td></tr><tr><td>HD 136352</td><td>2017-07-14</td><td>IFS</td><td>YJ</td><td>68</td><td>48</td><td>A</td><td>30.8</td><td>0.88</td><td>2.8</td><td>—</td><td>1.10</td></tr><tr><td>HD 136352</td><td>2020-03-16</td><td>IRDIS</td><td>K12</td><td>84</td><td>24</td><td>A</td><td>19.3</td><td>0.65</td><td>6.1</td><td>91</td><td>1.09</td></tr><tr><td>HD 136352</td><td>2020-03-16</td><td>IFS</td><td>YJH</td><td>64</td><td>32</td><td>A</td><td>19.7</td><td>0.64</td><td>6.1</td><td>—</td><td>1.10</td></tr><tr><td>HD 154088</td><td>2017-06-21</td><td>IRDIS</td><td>H23</td><td>90</td><td>32</td><td>A</td><td>21.6</td><td>1.20</td><td>2.6</td><td>73</td><td>1.03</td></tr><tr><td>HD 154088</td><td>2017-06-21</td><td>IFS</td><td>YJ</td><td>90</td><td>32</td><td>A</td><td>22.1</td><td>1.20</td><td>2.4</td><td>—</td><td>1.03</td></tr><tr><td>HD 154088</td><td>2019-07-22</td><td>IRDIS</td><td>K12</td><td>56</td><td>32</td><td>C</td><td>86.6</td><td>0.50</td><td>3.4</td><td>80</td><td>1.00</td></tr><tr><td>HD 154088</td><td>2019-07-22</td><td>IFS</td><td>YJH</td><td>28</td><td>64</td><td>C</td><td>84.1</td><td>0.51</td><td>3.5</td><td>—</td><td>1.00</td></tr><tr><td>HD 154088</td><td>2021-07-04</td><td>IRDIS</td><td>K12</td><td>28</td><td>32</td><td>A</td><td>34.6</td><td>0.55</td><td>6.6</td><td>91</td><td>1.00</td></tr><tr><td>HD 154088</td><td>2021-07-04</td><td>IFS</td><td>YJH</td><td>14</td><td>64</td><td>A</td><td>34.6</td><td>0.55</td><td>6.6</td><td>—</td><td>1.00</td></tr><tr><td>HD 189567</td><td>2017-05-29</td><td>IRDIS</td><td>H23</td><td>368</td><td>8</td><td>A</td><td>18.2</td><td>0.90</td><td>2.5</td><td>83</td><td>1.37</td></tr><tr><td>HD 189567</td><td>2017-05-29</td><td>IFS</td><td>YJ</td><td>60</td><td>12</td><td>A</td><td>18.1</td><td>0.93</td><td>2.5</td><td>—</td><td>1.37</td></tr></tbody></table>
**Appendix E: Reduced observations**

Figures E.1–E.3 show the reduced images via SpeCal-cADI, SpeCal-TLOCI, ANDROMEDA ADI algorithms for all the IRDIS observations. In addition, Figs. E.4 and E.5 show the reduced images via SpeCal-PCA ASDI and ANDROMEDA ASDI algorithms for all the IFS observations.

<figure><img src="image_26.png" /><figcaption>**Fig. E.1.** Reduced images from SPHERE-IRDIS for the whole survey for SpeCal-cADI reductions. The factor in the bottom left hand corner of each figure indicates the number by which to multiply the color bar to have the corresponding contrast values.</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>**Fig. E.2.** Reduced images from SPHERE-IRDIS for the whole survey for SpeCal-TLOCI ADI reductions.</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>Fig. E.3. Reduced images from SPHERE-IRDIS for the whole survey for ANDROMEDA reductions.</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>Fig. E.4. Reduced images from SPHERE-IFS for the whole survey for SpeCal-PCA-ADSI reductions.</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>**Fig. E.5.** Reduced images from SPHERE-IFS for the whole survey for ANDROMEDA-ASDI reductions.</figcaption></figure>
# Appendix F: Companion candidates from ANDROMEDA and SpeCal processing

Figure F.1 reports the distribution of the detections for SPHERE-IRDIS observations with the ANDROMEDA-ADI or SpeCal-cADI processing, as well as the separations and contrasts of the detections. We can see that below 2", ANDROMEDA processing results in additional detections compared to SpeCal-cADI, which is expected (e.g., Cantalloube et al. 2015).

In addition, we note that concerning bright ($> 10^{-4}$ or $10^{-5}$) candidates, there is a bias between ANDROMEDA and SpeCal photometry: the same candidate can have a difference up to 0.3 mag depending on which processing is used to retrieve the photometry. This photometric bias correlates with the apparent magnitude of the candidate. The brighter is the detection, the larger is the bias. There is no visible correlation with the separation. In our observations, this effect is only visible in the H2 band, corresponding to observations with bright candidates. By investigating this effect on the known brown dwarf GJ 229 B for which the photometry is reported in the literature, we found that SpeCal-cADI (and Special-non-ADI) was consistent with the values from Nakajima et al. (1995) and Faherty et al. (2012), contrary to ANDROMEDA.

<figure><img src="image_31.png" /><figcaption>**Fig. F.1.** At the *top*, distribution of the separations of all the point-source detections from SPHERE-IRDIS in the H2-band (*on the left*) and the K1-band (*on the right*). At the *bottom*, contrasts and separations of all the point-source detections from SPHERE-IRDIS in the H2-band (*on the left*) and the K1-band (*on the right*). The post-processing algorithms used are SpeCal-cADI and ANDROMEDA-ADI.</figcaption></figure>

# Appendix G: Input parameters for Gaia and Hipparcos results via the GaiaPMEX tool

Table G.1 summarizes the parameters used for running the tool GaiaPMEX (Kiefer et al. (in prep.) for the systems GJ 832 and GJ 229, the only two that led to a positive detection from Gaia and HIPPARCOS data (see 5.3))
<table><caption>**Table G.1.** Parameters used with the GaiaPMEX tool for the systems GJ 229 and GJ 832.</caption><thead><tr><th>Parameter</th><th>Unit</th><th>GJ 229</th><th>GJ 832</th></tr></thead><tbody><tr><td colspan="4" style="text-align: center; font-weight: bold;">Aliases</td></tr><tr><td>HIP</td><td></td><td>29295</td><td>106440</td></tr><tr><td>Gaia DR3</td><td></td><td>2940856402123426176</td><td>6562924609150908416</td></tr><tr><td colspan="4" style="text-align: center; font-weight: bold;">Main parameters</td></tr><tr><td>M<sub>*</sub></td><td>M<sub>☉</sub></td><td>0.570</td><td>0.480</td></tr><tr><td>σ<sub>M*</sub></td><td>M<sub>☉</sub></td><td>0.049975713178077</td><td>0.0498015394994533</td></tr><tr><td>V</td><td></td><td>8.12</td><td>8.67</td></tr><tr><td>RA</td><td></td><td>06:10:34.4589</td><td>21:33:33.9004</td></tr><tr><td>DEC</td><td></td><td>-21:52:04.163</td><td>-49:00:45.468</td></tr><tr><td colspan="4" style="text-align: center; font-weight: bold;">Gaia parameters</td></tr><tr><td>ra</td><td>deg</td><td>92.644</td><td>323.391</td></tr><tr><td>ra_error</td><td>deg</td><td>0.008</td><td>0.018</td></tr><tr><td>dec</td><td>deg</td><td>-21.868</td><td>-49.013</td></tr><tr><td>dec_error</td><td>deg</td><td>0.014</td><td>0.014</td></tr><tr><td>pmra</td><td>mas yr<sup>-1</sup></td><td>-135.692</td><td>-45.917</td></tr><tr><td>pmra_error</td><td>mas yr<sup>-1</sup></td><td>0.011</td><td>0.023</td></tr><tr><td>pmdec</td><td>mas yr<sup>-1</sup></td><td>-719.178</td><td>-816.875</td></tr><tr><td>pmdec_error</td><td>mas yr<sup>-1</sup></td><td>0.017</td><td>0.018</td></tr><tr><td>parallax</td><td>mas</td><td>173.57</td><td>201.33</td></tr><tr><td>parallax_error</td><td>mas</td><td>0.02</td><td>0.02</td></tr><tr><td>phot_g_mean_mag</td><td></td><td>7.31</td><td>7.74</td></tr><tr><td>bp RP</td><td></td><td>2.074</td><td>2.240</td></tr><tr><td>astrometric_matched_transits</td><td></td><td>82</td><td>47</td></tr><tr><td>astrometric_n good obs_al</td><td></td><td>723</td><td>414</td></tr><tr><td>astrometric_params_solved</td><td></td><td>31</td><td>31</td></tr><tr><td>astrometric_excess.noise or AEN<sub>obs</sub></td><td>mas</td><td>0.123</td><td>0.160</td></tr><tr><td>ruwe or RUWE<sub>obs</sub></td><td></td><td>1.013</td><td>1.097</td></tr><tr><td colspan="4" style="text-align: center; font-weight: bold;">Hipparcos parameters</td></tr><tr><td>e<sub>RA</sub> cos DEC</td><td>mas</td><td>0.381</td><td>0.420</td></tr><tr><td>e<sub>DEC</sub></td><td>mas</td><td>0.670</td><td>0.600</td></tr><tr><td>σ<sub>pos</sub></td><td>mas</td><td>0.771</td><td>0.732</td></tr><tr><td colspan="4" style="text-align: center; font-weight: bold;">Kervella et al. (2022) parameters</td></tr><tr><td>pmRAH2EG3b</td><td>mas yr<sup>-1</sup></td><td>-136.406</td><td>-46.046</td></tr><tr><td>e_ppmRAH2EG3b</td><td>mas yr<sup>-1</sup></td><td>0.015</td><td>0.018</td></tr><tr><td>pmDEH2EG3b</td><td>mas yr<sup>-1</sup></td><td>-714.974</td><td>-816.289</td></tr><tr><td>e_ppmDEH2EG3b</td><td>mas yr<sup>-1</sup></td><td>0.019</td><td>0.020</td></tr><tr><td>PMaRAH2EG3b</td><td>mas yr<sup>-1</sup></td><td>0.712</td><td>0.140</td></tr><tr><td>e_PMaRAH2EG3b</td><td>mas yr<sup>-1</sup></td><td>0.018</td><td>0.029</td></tr><tr><td>PMaDEH2EG3b</td><td>mas yr<sup>-1</sup></td><td>-4.224</td><td>-0.547</td></tr><tr><td>e_PMaDEH2EG3b</td><td>mas yr<sup>-1</sup></td><td>0.025</td><td>0.027</td></tr><tr><td>||PMa|| (or PMa<sub>obs</sub>)</td><td>mas yr<sup>-1</sup></td><td>4.284</td><td>0.565</td></tr><tr><td>σ<sub>PMa,obs</sub></td><td>mas yr<sup>-1</sup></td><td>0.025</td><td>0.027</td></tr><tr><td colspan="4" style="text-align: center; font-weight: bold;">Noise parameters and simulations of single systems</td></tr><tr><td>σ<sub>AL</sub></td><td>mas</td><td>0.083</td><td>0.086</td></tr><tr><td>σ<sub>attitude</sub></td><td>mas</td><td>0.064</td><td>0.082</td></tr><tr><td>σ<sub>jitter</sub></td><td>mas</td><td>0.129</td><td>0.135</td></tr><tr><td>AEN<sub>simu</sub> as single</td><td>mas</td><td>0.123</td><td>0.124</td></tr><tr><td>σ<sub>AEN,simu,single</sub></td><td>mas</td><td>0.015</td><td>0.021</td></tr><tr><td>PMa<sub>simu</sub> as single</td><td>mas yr<sup>-1</sup></td><td>0.060</td><td>0.059</td></tr><tr><td>σ<sub>PMa,simu,single</sub></td><td>mas yr<sup>-1</sup></td><td>0.034</td><td>0.033</td></tr><tr><td>AEN<sub>obs</sub> significance</td><td></td><td>0.007</td><td>1.696</td></tr><tr><td>PMa<sub>obs</sub> significance</td><td></td><td>&gt;3.82</td><td>&gt;3.82</td></tr></tbody></table>
**Appendix H: Comparison of detection method sensitivity on our survey**

Detection methods of exoplanet suffer from observational biases. Combining different detection techniques enable to have a more global view on planetary systems (see Fig. H.1), even though observers are still blind to low-mass exoplanets at wide orbits (e.g., an exoplanet of 1 M⊕ planet orbiting at 20 au).

<figure><img src="image_32.png" /><figcaption>**Fig. H.1.** Comparison of the sensitivity of the direct imaging (DI, red), proper motion anomaly and *Gaia* astrometric excess noise (PMa+AEN, blue) and radial velocity (RV, purple) detections methods on our survey. We took the median of the detection probabilities at 10%, 50%, and 90% the M-stars (**left**) and the GK-stars (**right**).</figcaption></figure>

Figure H.2 shows sensitivity from high-contrast imaging SPHERE-IRDIS and SPHERE-IFS observations for each system of our sample (see Section 5.4). For a few mature systems, high-contrast imaging observations are sensitive to companions of ≲ 10 M<sub>Jup</sub> beyond a few astronomical units (e.g., GJ 433) or dozen of astronomical units (e.g., GJ 229, GJ 649, GJ 674, GJ 832).
<figure><img src="image_33.png" /><figcaption>**Fig. H.2.** Detection limits from direct imaging observations (SPHERE-IRDIS and SPHERE-IFS) for each system of the survey obtained with the MESS3 tool.</figcaption></figure>