<table><caption>Table C.4: Properties of the HAT-P-49 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5"><em>Stellar parameters</em></td></tr><tr><td>Spectral type</td><td></td><td>F3</td><td></td><td>Derived</td></tr><tr><td>Stellar temperature</td><td><i>T</i><sub>eff</sub></td><td>6820 ± 52</td><td>K</td><td>Bieryla et al. (2014)</td></tr><tr><td>Stellar radius</td><td><i>R</i><sub>★</sub></td><td>1.833<sup>+0.138</sup><sub>-0.076</sub></td><td><i>R</i><sub>☉</sub></td><td>Bieryla et al. (2014)</td></tr><tr><td>Stellar spin inclination</td><td><i>i</i><sub>★</sub></td><td>—</td><td>deg</td><td>—</td></tr><tr><td>Stellar equatorial period</td><td><i>P</i><sub>eq</sub></td><td>—</td><td>d</td><td>—</td></tr><tr><td>Stellar projected velocity</td><td><i>v</i><sub>eq</sub> sin <i>i</i><sub>★</sub></td><td>10.68<sup>+0.46</sup><sub>-0.47</sub></td><td>km s<sup>-1</sup></td><td>This work</td></tr><tr><td>Age</td><td><i>τ</i></td><td>1.5 ± 0.2</td><td>Gyr</td><td>Bieryla et al. (2014)</td></tr><tr><td>Limb-darkening coefficients</td><td><i>u</i><sub>1</sub><br><i>u</i><sub>2</sub></td><td>0.312<br>0.336</td><td></td><td>Exofast</td></tr><tr><td colspan="5"><em>Planet b parameters</em></td></tr><tr><td>Orbital period</td><td><i>P</i></td><td>2.6915539 ± 0.0000012</td><td>d</td><td>This work (STELLA)</td></tr><tr><td>Transit epoch</td><td><i>T</i><sub>0</sub></td><td>2456975.61736 ± 0.00050</td><td>BJD<sub>TDB</sub></td><td>This work (STELLA)</td></tr><tr><td>Eccentricity</td><td><i>e</i></td><td>0.0 (fixed)</td><td></td><td>Bieryla et al. (2014)</td></tr><tr><td>Argument of periastron</td><td><i>ω</i></td><td>90 (fixed)</td><td>deg</td><td>Bieryla et al. (2014)</td></tr><tr><td>Stellar reflex velocity</td><td><i>K</i></td><td>177.6 ± 16.0</td><td></td><td>This work</td></tr><tr><td>Scaled separation</td><td><i>a</i>/<i>R</i><sub>★</sub></td><td>5.13<sup>+0.19</sup><sub>-0.30</sub></td><td></td><td>Bieryla et al. (2014)</td></tr><tr><td>Orbital inclination</td><td><i>i</i></td><td>86.2 ± 1.7</td><td>deg</td><td>Bieryla et al. (2014)</td></tr><tr><td>Impact parameter</td><td><i>b</i></td><td>0.340<sup>+0.119</sup><sub>-0.141</sub></td><td></td><td>Bieryla et al. (2014)</td></tr><tr><td>Transit duration</td><td><i>T</i><sub>14</sub></td><td>4.1088 ± 0.0456</td><td>h</td><td>Bieryla et al. (2014)</td></tr><tr><td>Planet-to-star radius ratio</td><td><i>R</i><sub>p</sub>/<i>R</i><sub>★</sub></td><td>0.0792 ± 0.0019</td><td></td><td>Bieryla et al. (2014)</td></tr><tr><td>Projected spin-orbit angle</td><td><i>λ</i></td><td>-97.7 ± 1.8</td><td>deg</td><td>This work</td></tr></tbody></table>

<table><caption>Table C.5: Properties of the HD 89345 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5"><em>Stellar parameters</em></td></tr><tr><td>Spectral type</td><td></td><td>G5</td><td></td><td>Cannon &amp; Pickering (1993)</td></tr><tr><td>Stellar temperature</td><td><i>T</i><sub>eff</sub></td><td>5499 ± 73</td><td>K</td><td>Van Eylen et al. (2018)</td></tr><tr><td>Stellar radius</td><td><i>R</i><sub>★</sub></td><td>1.657<sup>+0.020</sup><sub>-0.004</sub></td><td><i>R</i><sub>☉</sub></td><td>Van Eylen et al. (2018)</td></tr><tr><td>Stellar spin inclination</td><td><i>i</i><sub>★</sub></td><td>&gt; 44<sup>†</sup></td><td>deg</td><td>Van Eylen et al. (2018)</td></tr><tr><td>Stellar equatorial period</td><td><i>P</i><sub>eq</sub></td><td>—</td><td>d</td><td>—</td></tr><tr><td>Stellar projected velocity</td><td><i>v</i><sub>eq</sub> sin <i>i</i><sub>★</sub></td><td>0.58 ± 0.28</td><td>km s<sup>-1</sup></td><td>This work</td></tr><tr><td>Age</td><td><i>τ</i></td><td>9.4<sup>+0.4</sup><sub>-1.3</sub></td><td>Gyr</td><td>Van Eylen et al. (2018)</td></tr><tr><td>Limb-darkening coefficients</td><td><i>u</i><sub>1</sub><br><i>u</i><sub>2</sub></td><td>0.535<br>0.215</td><td></td><td>Exofast</td></tr><tr><td colspan="5"><em>Planet b parameters</em></td></tr><tr><td>Orbital period</td><td><i>P</i></td><td>11.8144024 ± 0.0000066</td><td>d</td><td>This work (TESS + K2)</td></tr><tr><td>Transit epoch</td><td><i>T</i><sub>0</sub></td><td>2458740.81147 ± 0.00044</td><td>BJD<sub>TDB</sub></td><td>This work (TESS + K2)</td></tr><tr><td>Eccentricity</td><td><i>e</i></td><td>0.208 ± 0.039</td><td></td><td>This work</td></tr><tr><td>Argument of periastron</td><td><i>ω</i></td><td>21.7 ± 19.1</td><td></td><td>This work</td></tr><tr><td>Stellar reflex velocity</td><td><i>K</i></td><td>9.1 ± 0.5</td><td></td><td>This work</td></tr><tr><td>Scaled separation</td><td><i>a</i>/<i>R</i><sub>★</sub></td><td>13.625 ± 0.027</td><td></td><td>Van Eylen et al. (2018)</td></tr><tr><td>Orbital inclination</td><td><i>i</i></td><td>87.68 ± 0.10</td><td>deg</td><td>This work (TESS + K2)</td></tr><tr><td>Impact parameter</td><td><i>b</i></td><td>0.564 ± 0.017</td><td></td><td>This work (TESS + K2)</td></tr><tr><td>Transit duration</td><td><i>T</i><sub>14</sub></td><td>5.65 ± 0.02</td><td>h</td><td>This work (TESS + K2)</td></tr><tr><td>Planet-to-star radius ratio</td><td><i>R</i><sub>p</sub>/<i>R</i><sub>★</sub></td><td>0.03696 ± 0.00041</td><td></td><td>This work (TESS + K2)</td></tr><tr><td>Projected spin-orbit angle</td><td><i>λ</i></td><td>74.2<sup>+33.6</sup><sub>-32.5</sub></td><td>deg</td><td>This work</td></tr><tr><td>3D spin-orbit angle</td><td><i>ψ</i><sub>N</sub></td><td>78.7<sup>+22.5</sup><sub>-23.0</sub></td><td>deg</td><td>This work</td></tr><tr><td></td><td><i>ψ</i><sub>S</sub></td><td>81.6<sup>+22.2</sup><sub>-23.2</sub></td><td>deg</td><td></td></tr><tr><td></td><td><i>ψ</i></td><td>80.1<sup>+22.3</sup><sub>-23.1</sub></td><td>deg</td><td></td></tr></tbody></table>

Notes: † Instead of using this lower limit we reproduced the PDF on $i_{\star}$ from Van Eylen et al. (2018) to calculate the PDF on $\psi$ from our results.
<table><caption>Table C.6: Properties of the HD 106315 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5"><em>Stellar parameters</em></td></tr><tr><td>Spectral type</td><td></td><td>F5</td><td></td><td>Barros et al. (2017)</td></tr><tr><td>Stellar temperature</td><td>T<sub>eff</sub></td><td>6364 ± 87</td><td>K</td><td>Kosiarek et al. (2021)</td></tr><tr><td>Stellar radius</td><td>R<sub>★</sub></td><td>1.269 ± 0.024</td><td>R<sub>☉</sub></td><td>Kosiarek et al. (2021)</td></tr><tr><td>Stellar spin inclination</td><td>i<sub>★</sub></td><td>—</td><td>deg</td><td>—</td></tr><tr><td>Stellar equatorial period</td><td>P<sub>eq</sub></td><td>—</td><td>d</td><td>—</td></tr><tr><td>Stellar projected velocity</td><td>v<sub>eq</sub> sin i<sub>★</sub></td><td>9.66<sup>+0.64</sup><sub>-0.65</sub></td><td>km s<sup>-1</sup></td><td>This work</td></tr><tr><td>Age</td><td>τ</td><td>4.48 ± 0.96</td><td>Gyr</td><td>Barros et al. (2017)</td></tr><tr><td>Limb-darkening coefficients</td><td>u<sub>1</sub><br>u<sub>2</sub></td><td>0.340<br>0.316</td><td></td><td>Exofast</td></tr><tr><td colspan="5"><em>Planet b parameters</em></td></tr><tr><td>Orbital period</td><td>P</td><td>9.55287 ± 0.00021</td><td>d</td><td>Kosiarek et al. (2021)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2457586.5476 ± 0.0025</td><td>BJD<sub>TDB</sub></td><td>Kosiarek et al. (2021)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.0 (fixed)</td><td></td><td>Kosiarek et al. (2021)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>90 (fixed)</td><td>deg</td><td>Kosiarek et al. (2021)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>2.88<sup>+0.85</sup><sub>-0.84</sub></td><td>m s<sup>-1</sup></td><td>Kosiarek et al. (2021)</td></tr><tr><td colspan="5"><em>Planet c parameters</em></td></tr><tr><td>Orbital period</td><td>P</td><td>21.05652 ± 0.00012</td><td>d</td><td>Kosiarek et al. (2021)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2457569.01767 ± 0.00097</td><td>BJD<sub>TDB</sub></td><td>Kosiarek et al. (2021)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.0 (fixed)</td><td></td><td>Kosiarek et al. (2021)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>90 (fixed)</td><td>deg</td><td>Kosiarek et al. (2021)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>2.53 ± 0.79</td><td>m s<sup>-1</sup></td><td>Kosiarek et al. (2021)</td></tr><tr><td>Scaled separation</td><td>a/R<sub>★</sub></td><td>29.5<sup>+5.7†</sup><sub>-4.2</sub></td><td></td><td>Kosiarek et al. (2021)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>88.89<sup>+0.69†</sup><sub>-0.51</sub></td><td>deg</td><td>Kosiarek et al. (2021)</td></tr><tr><td>Impact parameter</td><td>b</td><td>0.688<sup>+0.044</sup><sub>-0.094</sub></td><td></td><td>Rodriguez et al. (2017)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>4.728<sup>+0.084</sup><sub>-0.065</sub></td><td>h</td><td>Rodriguez et al. (2017)</td></tr><tr><td>Planet-to-star radius ratio</td><td>R<sub>p</sub>/R<sub>★</sub></td><td>0.03481 ± 0.00099</td><td></td><td>Guilluy et al. (2021)</td></tr><tr><td>Projected spin-orbit angle</td><td>λ</td><td>-2.68<sup>+2.7</sup><sub>-2.6</sub></td><td>deg</td><td>This work</td></tr></tbody></table>

Notes: † We use the scaled separation and orbital inclination derived by Kosiarek et al. (2021) from Spitzer transits, as they provide a better match to the transit duration.

<table><caption>Table C.7: Properties of the K2-105 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5"><em>Stellar parameters</em></td></tr><tr><td>Spectral type</td><td></td><td>K1</td><td></td><td>Luo et al. (2018)</td></tr><tr><td>Stellar temperature</td><td>T<sub>eff</sub></td><td>5636<sup>+49</sup><sub>-52</sub></td><td></td><td>Castro-González et al. (2022)</td></tr><tr><td>Stellar radius</td><td>R<sub>★</sub></td><td>0.97 ± 0.01</td><td>R<sub>☉</sub></td><td>Castro-González et al. (2022)</td></tr><tr><td>Stellar spin inclination</td><td>i<sub>★</sub></td><td>—</td><td>deg</td><td>—</td></tr><tr><td>Stellar equatorial period</td><td>P<sub>eq</sub></td><td>—</td><td>d</td><td>—</td></tr><tr><td>Stellar projected velocity</td><td>v<sub>eq</sub> sin i<sub>★</sub></td><td>2.13<sup>+0.96</sup><sub>-0.92</sub></td><td>km s<sup>-1</sup></td><td>This work</td></tr><tr><td>Age</td><td>τ</td><td>> 0.6</td><td>Gyr</td><td>Narita et al. (2017)</td></tr><tr><td>Limb-darkening coefficients</td><td>u<sub>1</sub><br>u<sub>2</sub></td><td>0.338<br>0.186</td><td></td><td>Exofast</td></tr><tr><td colspan="5"><em>Planet b parameters</em></td></tr><tr><td>Orbital period</td><td>P</td><td>8.267043 ± 0.000015</td><td>d</td><td>This work (STELLA)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>8.2669897 ± 0.0000057</td><td>d</td><td>This work (TESS + K2)</td></tr><tr><td>Eccentricity</td><td>e</td><td>2457379.46827 ± 0.00114</td><td>BJD<sub>TDB</sub></td><td>This work (STELLA)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>2458363.23873<sup>+0.00069</sup><sub>-0.00063</sub></td><td>BJD<sub>TDB</sub></td><td>This work (TESS + K2)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>0</td><td></td><td>(fixed)</td></tr><tr><td>Impact parameter</td><td>b</td><td>90</td><td>deg</td><td>(fixed)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>9.4 ± 5.8</td><td>m s<sup>-1</sup></td><td>Narita et al. (2017)</td></tr><tr><td>Planet-to-star radius ratio</td><td>R<sub>p</sub>/R<sub>★</sub></td><td>17.39 ± 0.19</td><td></td><td>This work (TESS + K2)</td></tr><tr><td>Projected spin-orbit angle</td><td>λ</td><td>-81<sup>+50</sup><sub>-47</sub> †</td><td></td><td>This work</td></tr></tbody></table>

Notes: † We consider this measurement as marginal, as λ is not constrained at the 3σ level (see text)
<table><caption>Table C.8: Properties of the *Kepler*-25 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5"><em>Stellar parameters</em></td></tr><tr><td>Spectral type</td><td></td><td>F8</td><td></td><td>Derived</td></tr><tr><td>Stellar temperature</td><td>T<sub>eff</sub></td><td>6354 ± 27</td><td>K</td><td>Benomar et al. (2014)</td></tr><tr><td>Stellar radius</td><td>R<sub>★</sub></td><td>1.316<sup>+0.016</sup><sub>-0.015</sub></td><td>R<sub>☉</sub></td><td>Mills et al. (2019)</td></tr><tr><td>Stellar Mass</td><td>M<sub>★</sub></td><td>1.165<sup>+0.029</sup><sub>-0.027</sub></td><td>M<sub>☉</sub></td><td>Mills et al. (2019)</td></tr><tr><td>Stellar spin inclination</td><td>i<sub>★</sub></td><td>66.7<sup>+12</sup><sub>-7.4</sub><sup>†</sup></td><td>deg</td><td>Benomar et al. (2014)</td></tr><tr><td>Stellar equatorial period</td><td>P<sub>eq</sub></td><td>—</td><td>d</td><td>—</td></tr><tr><td>Stellar projected velocity</td><td>v<sub>eq</sub> sin i<sub>★</sub></td><td>8.89<sup>+0.59</sup><sub>-0.63</sub></td><td></td><td>This work</td></tr><tr><td>Limb-darkening coefficients</td><td>u<sub>1</sub><br>u<sub>2</sub></td><td>0.381<br>0.302</td><td></td><td>Exofast</td></tr><tr><td>Age</td><td>τ</td><td>2.75 ± 0.3</td><td>Gyr</td><td>Benomar et al. (2014)</td></tr><tr><td colspan="5"><em>Planet b parameters</em></td></tr><tr><td>Orbital period</td><td>P</td><td>6.2385347882 ± 0.0000001619</td><td>d</td><td>Battley et al. (2021)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2454954.7979391 ± 0.0002168</td><td>BJD<sub>TDB</sub></td><td>Battley et al. (2021)</td></tr><tr><td></td><td></td><td>2458648.00807<sup>+0.00057</sup><sub>-0.00051</sub></td><td>BJD<sub>TDB</sub></td><td>This work</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.0029<sup>+0.0023</sup><sub>-0.0017</sub></td><td></td><td>Mills et al. (2019)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>—</td><td>deg</td><td>—</td></tr><tr><td>Planetary mass</td><td>M<sub>p</sub></td><td>0.0275<sup>+0.0079</sup><sub>-0.0073</sub></td><td>M<sub>Jup</sub></td><td>Mills et al. (2019)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>87.173<sup>+0.083</sup><sub>-0.084</sub></td><td>deg</td><td>Mills et al. (2019)</td></tr><tr><td colspan="5"><em>Planet c parameters</em></td></tr><tr><td>Orbital period</td><td>P</td><td>12.720370495 ± 0.000001703</td><td>d</td><td>Battley et al. (2021)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2454960.6467450 ± 0.0001144</td><td>BJD<sub>TDB</sub></td><td>Battley et al. (2021)</td></tr><tr><td></td><td></td><td>2458649.55482<sup>+0.00028</sup><sub>-0.00026</sub></td><td>BJD<sub>TDB</sub></td><td>This work</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.0061<sup>+0.0049</sup><sub>-0.0041</sub></td><td></td><td>Mills et al. (2019)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>—</td><td>deg</td><td>—</td></tr><tr><td>Planetary mass</td><td>M<sub>p</sub></td><td>0.0479<sup>+0.0051</sup><sub>-0.0041</sub></td><td>M<sub>Jup</sub></td><td>Mills et al. (2019)</td></tr><tr><td>Scaled separation</td><td>a/R<sub>★</sub></td><td>18.336 ± 0.27</td><td></td><td>Mills et al. (2019)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>87.236<sup>+0.039</sup><sub>-0.042</sub></td><td>deg</td><td>Mills et al. (2019)</td></tr><tr><td>Impact parameter</td><td>b</td><td>0.8826 ± 0.0018</td><td></td><td>Benomar et al. (2014)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>2.862 ± 0.006</td><td>h</td><td>Benomar et al. (2014)</td></tr><tr><td>Planet-to-star radius ratio</td><td>R<sub>p</sub>/R<sub>★</sub></td><td>0.03637 ± 0.00012</td><td></td><td>Mills et al. (2019)</td></tr><tr><td>Projected spin-orbit angle</td><td>λ</td><td>-0.9<sup>+7.7</sup><sub>-6.4</sub></td><td>deg</td><td>This work</td></tr><tr><td>3D spin-orbit angle</td><td>ψ<sub>N</sub></td><td>21.4<sup>+8.9</sup><sub>-9.2</sub></td><td>deg</td><td>This work</td></tr><tr><td></td><td>ψ<sub>S</sub></td><td>26.8<sup>+9.5</sup><sub>-9.4</sub></td><td>deg</td><td></td></tr><tr><td></td><td>ψ</td><td>24.1<sup>+9.2</sup><sub>-9.3</sub></td><td>deg</td><td></td></tr><tr><td colspan="5"><em>Planet d parameters</em></td></tr><tr><td>Orbital period</td><td>P</td><td>122.4<sup>+0.80</sup><sub>-0.71</sub></td><td>d</td><td>Mills et al. (2019)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2455715<sup>+6.8</sup><sub>-6.2</sub></td><td>BJD<sub>TDB</sub></td><td>Mills et al. (2019)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.13<sup>+0.13</sup><sub>-0.09</sub></td><td></td><td>Mills et al. (2019)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>—</td><td>deg</td><td>—</td></tr><tr><td>Minimum planetary mass</td><td>M<sub>p</sub> sin i</td><td>0.226 ± 0.031</td><td>M<sub>Jup</sub></td><td>Mills et al. (2019)</td></tr></tbody></table>

Notes: For consistency with our framework we brought the orbital inclinations published by Mills et al. (2019) within 90-180° back to within 0-90°. Arguments of periastron were not derived by Mills et al. (2019), but are not required here as circular orbital models were used for the RM analysis. The stellar reflex motion induced by each planet was calculated using the stellar and planetary masses and orbital inclination. The scaled separation was derived by reconstructing PDFs for $P_c$, $R_★$, and $M_★$ from Mills et al. (2019) and using *Kepler's* third law. † We use the value derived from asteroseismology alone (Fig. 9 in Benomar et al. 2014).
<table><caption>Table C.9: Properties of the Kepler-63 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-style: italic;">Stellar parameters</td></tr><tr><td>Spectral type</td><td></td><td>G5</td><td></td><td>Frasca et al. (2016)</td></tr><tr><td>Stellar temperature</td><td>T<sub>eff</sub></td><td>5576 ± 50</td><td>K</td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Stellar radius</td><td>R<sub>⋆</sub></td><td>0.901<sup>+0.027</sup><sub>-0.022</sub></td><td>R<sub>☉</sub></td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Stellar spin inclination</td><td>i<sub>⋆</sub></td><td>138 ± 7 <sup>†</sup></td><td>deg</td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Stellar equatorial period</td><td>P<sub>eq</sub></td><td>5.401 ± 0.014</td><td>d</td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Stellar projected velocity</td><td>v<sub>eq</sub> sin i<sub>⋆</sub></td><td>7.47<sup>+2.6</sup><sub>-2.7</sub></td><td>km s<sup>-1</sup></td><td>This work</td></tr><tr><td>Age</td><td>τ</td><td>0.210 ± 0.045</td><td>Gyr</td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Limb-darkening coefficients</td><td>u<sub>1</sub><br>u<sub>2</sub></td><td>0.527<br>0.217</td><td></td><td>Exofast</td></tr><tr><td colspan="5" style="text-align: center; font-style: italic;">Planet b parameters</td></tr><tr><td>Orbital period</td><td>P</td><td>9.4341503479 ± 0.0000003339</td><td>d</td><td>Gajdoš et al. (2019)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2455010.84340000 ± 0.00002768</td><td>BJD<sub>TDB</sub></td><td>Gajdoš et al. (2019)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0 (fixed)<sup>††</sup></td><td></td><td>—</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>90 (fixed)<sup>††</sup></td><td>deg</td><td>—</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>40 ± 20<sup>††</sup></td><td>m s<sup>-1</sup></td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Scaled separation</td><td>a/R<sub>⋆</sub></td><td>19.12 ± 0.08</td><td></td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>87.806<sup>+0.018</sup><sub>-0.019</sub></td><td>deg</td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Impact parameter</td><td>b</td><td>0.732 ± 0.003</td><td></td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>2.903 ± 0.003</td><td>h</td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Planet-to-star radius ratio</td><td>R<sub>p</sub>/R<sub>⋆</sub></td><td>0.0622 ± 0.0010</td><td></td><td>Sanchis-Ojeda et al. (2013)</td></tr><tr><td>Projected spin-orbit angle</td><td>λ</td><td>-135<sup>+21.2</sup><sub>-26.8</sub></td><td>deg</td><td>This work</td></tr><tr><td>3D spin-orbit angle</td><td>ψ ≡ ψ<sub>S</sub></td><td>114.6<sup>+16.6</sup><sub>-12.5</sub><sup>†</sup></td><td>deg</td><td>This work</td></tr></tbody></table>

Notes: † The analysis from Sanchis-Ojeda et al. (2013) favors the configuration where the southern stellar pole is visible. †† The RV data from Sanchis-Ojeda et al. (2013) are too strongly affected by stellar activity to accurately constrain the orbital properties. The reflex velocity semi-amplitude we adopt comes from the RM effect and seems compatible with the apparent value from RVs. The orbit is fixed to circular, as Sanchis-Ojeda et al. (2013) set a $3\sigma$ upper limit of 0.45 on e.
<table><caption>Table C.10: Properties of the Kepler-68 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-style: italic;">Stellar parameters</td></tr><tr><td>Spectral type</td><td></td><td>G1</td><td></td><td>Grieves et al. (2018)</td></tr><tr><td>Stellar temperature</td><td>T<sub>eff</sub></td><td>5793 ± 74</td><td>K</td><td>Gilliland et al. (2013)</td></tr><tr><td>Stellar radius</td><td>R<sub>★</sub></td><td>1.243 ± 0.019</td><td>R<sub>☉</sub></td><td>Gilliland et al. (2013)</td></tr><tr><td>Stellar spin inclination</td><td>i<sub>★</sub></td><td>—</td><td>deg</td><td>—</td></tr><tr><td>Stellar equatorial period</td><td>P<sub>eq</sub></td><td>—</td><td>d</td><td>—</td></tr><tr><td>Stellar projected velocity</td><td>v<sub>eq</sub> sin i<sub>★</sub></td><td>0.5 ± 0.5</td><td>km s<sup>-1</sup></td><td>Gilliland et al. (2013)</td></tr><tr><td>Age</td><td>τ</td><td>6.3 ± 1.7</td><td>Gyr</td><td>Gilliland et al. (2013)</td></tr><tr><td>Limb-darkening coefficients</td><td>u<sub>1</sub><br>u<sub>2</sub></td><td>0.449<br>0.267</td><td></td><td>Exofast</td></tr><tr><td colspan="5" style="text-align: center; font-style: italic;">Planet b parameters</td></tr><tr><td>Orbital period</td><td>P</td><td>5.3987525913 ± 0.0000005231</td><td>d</td><td>Gajdoš et al. (2019)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2455006.85878000 ± 0.00007639</td><td>BJD<sub>TDB</sub></td><td>Gajdoš et al. (2019)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.0 (fixed)</td><td></td><td>Mills et al. (2019)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>90 (fixed)</td><td>deg</td><td>Mills et al. (2019)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>2.70<sup>+0.48</sup><sub>-0.46</sub></td><td>m s<sup>-1</sup></td><td>Mills et al. (2019)</td></tr><tr><td>Scaled separation</td><td>a/R<sub>★</sub></td><td>10.68 ± 0.14</td><td></td><td>Gilliland et al. (2013)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>87.60 ± 0.90</td><td>deg</td><td>Gilliland et al. (2013)</td></tr><tr><td>Impact parameter</td><td>b</td><td>0.45 ± 0.17</td><td></td><td>Gilliland et al. (2013)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>3.459 ± 0.009</td><td>h</td><td>Gilliland et al. (2013)</td></tr><tr><td>Planet-to-star radius ratio</td><td>R<sub>p</sub>/R<sub>★</sub></td><td>0.01700 ± 0.00046</td><td></td><td>Gilliland et al. (2013)</td></tr><tr><td>Projected spin-orbit angle</td><td>λ</td><td>Nondetection</td><td></td><td>This work</td></tr><tr><td colspan="5" style="text-align: center; font-style: italic;">Planet c parameters</td></tr><tr><td>Orbital period</td><td>P</td><td>9.60502738150 ± 0.0000132365</td><td>d</td><td>Gajdoš et al. (2019)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2454969.38207000 ± 0.00110495</td><td>BJD<sub>TDB</sub></td><td>Gajdoš et al. (2019)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.0 (fixed)</td><td></td><td>Mills et al. (2019)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>90 (fixed)</td><td>deg</td><td>Mills et al. (2019)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>0.59<sup>+0.50</sup><sub>-0.52</sub></td><td>m s<sup>-1</sup></td><td>Mills et al. (2019)</td></tr><tr><td colspan="5" style="text-align: center; font-style: italic;">Planet d parameters</td></tr><tr><td>Orbital period</td><td>P</td><td>634.6<sup>+4.1</sup><sub>-3.7</sub></td><td>d</td><td>Mills et al. (2019)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2455878 ± 11</td><td>BJD<sub>TDB</sub></td><td>Mills et al. (2019)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.112<sup>+0.035</sup><sub>-0.034</sub></td><td></td><td>Mills et al. (2019)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>-1.13<sup>+0.36</sup><sub>-0.45</sub></td><td>deg</td><td>Mills et al. (2019)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>17.75<sup>+0.50</sup><sub>-0.49</sub></td><td>m s<sup>-1</sup></td><td>Mills et al. (2019)</td></tr></tbody></table>
<table><caption>Table C.11: Properties of the WASP-47 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5"><strong>Stellar parameters</strong></td></tr><tr><td>Spectral type</td><td></td><td>G9</td><td></td><td>Hellier et al. (2012)</td></tr><tr><td>Stellar temperature</td><td>T<sub>eff</sub></td><td>5552 ± 75</td><td>K</td><td>Vanderburg et al. (2017)</td></tr><tr><td>Stellar mass</td><td>M<sub>★</sub></td><td>1.040 ± 0.031</td><td>M<sub>☉</sub></td><td>Vanderburg et al. (2017)</td></tr><tr><td>Stellar radius</td><td>R<sub>★</sub></td><td>1.137 ± 0.013</td><td>R<sub>☉</sub></td><td>Vanderburg et al. (2017)</td></tr><tr><td>Stellar spin inclination</td><td>i<sub>★</sub></td><td>69.8<sup>+11.0</sup><sub>-9.2</sub></td><td>deg</td><td>This work</td></tr><tr><td>Stellar equatorial period</td><td>P<sub>eq</sub></td><td>39.4<sup>+2.2</sup><sub>-4.5</sub></td><td>d</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Stellar projected velocity</td><td>v<sub>eq</sub> sin i<sub>★</sub></td><td>1.80<sup>+0.24</sup><sub>-0.16</sub></td><td>km s<sup>-1</sup></td><td>Sanchis-Ojeda et al. (2015)</td></tr><tr><td>Age</td><td>τ</td><td>6.5<sup>+2.6</sup><sub>-1.2</sub></td><td>Gyr</td><td>Almenara et al. (2016)</td></tr><tr><td>Limb-darkening coefficients</td><td>u<sub>1</sub></td><td>0.540</td><td></td><td>Exofast</td></tr><tr><td>u<sub>2</sub></td><td></td><td>0.209</td><td></td><td></td></tr><tr><td colspan="5"><strong>Planet b parameters</strong></td></tr><tr><td>Orbital period</td><td>P</td><td>4.1591492 ± 0.0000006</td><td>d</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2457007.932103 ± 0.000019</td><td>BJD<sub>TDB</sub></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0 (fixed)</td><td></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>90 (fixed)</td><td>deg</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>140.84 ± 0.40</td><td>m s<sup>-1</sup></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>88.98<sup>+0.20</sup><sub>-0.17</sub></td><td>deg</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Projected spin-orbit angle</td><td>λ</td><td>0 ± 24</td><td>deg</td><td>Sanchis-Ojeda et al. (2015)</td></tr><tr><td>3D spin-orbit angle</td><td>ψ<sub>N</sub></td><td>28.8<sup>+11.1</sup><sub>-13.3</sub></td><td>deg</td><td>This work</td></tr><tr><td>ψ<sub>S</sub></td><td></td><td>29.5<sup>+11.0</sup><sub>-13.3</sub></td><td>deg</td><td></td></tr><tr><td>ψ</td><td></td><td>29.2<sup>+11.1</sup><sub>-13.3</sub></td><td>deg</td><td></td></tr><tr><td colspan="5"><strong>Planet c parameters</strong></td></tr><tr><td>Orbital period</td><td>P</td><td>588.8 ± 2.0</td><td>d</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Inferior conjunction epoch</td><td>T<sub>0</sub></td><td>2457763.1 ± 4.3</td><td>BJD<sub>TDB</sub></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.295 ± 0.016</td><td></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>112.0 ± 4.3</td><td>deg</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>31.04 ± 0.40</td><td>m s<sup>-1</sup></td><td>Bryant & Bayliss (2022)</td></tr><tr><td colspan="5"><strong>Planet d parameters</strong></td></tr><tr><td>Orbital period</td><td>P</td><td>9.03052118 ± 0.00000753</td><td>d</td><td>This work</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2459426.5437 ± 0.0028<sup>†</sup></td><td>BJD<sub>TDB</sub></td><td>This work</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.01<sup>+0.011</sup><sub>-0.007</sub></td><td></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>16.5<sup>+84.2</sup><sub>-98.6</sub></td><td>deg</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>4.26 ± 0.37</td><td>m s<sup>-1</sup></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Scaled separation</td><td>a/R<sub>★</sub></td><td>16.34<sup>+0.08</sup><sub>-0.11</sub></td><td></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>89.55<sup>+0.30</sup><sub>-0.27</sub></td><td>deg</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Impact parameter</td><td>b</td><td>0.128<sup>+0.076</sup><sub>-0.085</sub></td><td></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>4.288 ± 0.039</td><td>h</td><td>Vanderburg et al. (2017)</td></tr><tr><td>Planet-to-star radius ratio</td><td>R<sub>p</sub>/R<sub>★</sub></td><td>0.02876 ± 0.00017</td><td></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Projected spin-orbit angle</td><td>Nondetection</td><td>deg</td><td>This work</td><td></td></tr><tr><td colspan="5"><strong>Planet e parameters</strong></td></tr><tr><td>Orbital period</td><td>P</td><td>0.7895933 ± 0.0000044</td><td>d</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2457011.34862 ± 0.00030</td><td>BJD<sub>TDB</sub></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0 (fixed)</td><td></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>90 (fixed)</td><td>deg</td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>4.55 ± 0.37</td><td>m s<sup>-1</sup></td><td>Bryant & Bayliss (2022)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>1.899 ± 0.013</td><td>h</td><td>Vanderburg et al. (2017)</td></tr></tbody></table>

<footnote>† We caution that WASP-47 d displays strong TTV with an amplitude of ~6 min. We report here the mid-transit time calculated with a TTV model at the specific epoch of our RM observations (see Sect. 5.11).</footnote>
<table><caption>Table C.12: Properties of the WASP-107 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-style: italic;">Stellar parameters</td></tr><tr><td>Spectral type</td><td></td><td>K6</td><td></td><td>Anderson et al. (2017)</td></tr><tr><td>Stellar temperature</td><td>T<sub>eff</sub></td><td>4425 ± 70</td><td>K</td><td>Piaulet et al. (2021)</td></tr><tr><td>Stellar radius</td><td>R<sub>⋆</sub></td><td>0.67 ± 0.02</td><td>R<sub>☉</sub></td><td>Piaulet et al. (2021)</td></tr><tr><td>Stellar spin inclination</td><td>i<sub>⋆</sub></td><td>15.1<sup>+2.1</sup><sub>-2.6</sub></td><td>deg</td><td>This work</td></tr><tr><td>Stellar equatorial period</td><td>P<sub>eq</sub></td><td>17.1 ± 1.0</td><td>d</td><td>Anderson et al. (2017)</td></tr><tr><td>Stellar projected velocity</td><td>v<sub>eq</sub> sin i<sub>⋆</sub></td><td>0.507<sup>+0.072</sup><sub>-0.086</sub></td><td>km s<sup>-1</sup></td><td>This work</td></tr><tr><td>Age</td><td>τ</td><td>3.4 ± 0.7</td><td>Gyr</td><td>Piaulet et al. (2021)</td></tr><tr><td>Limb-darkening coefficients</td><td>u<sub>1</sub><br>u<sub>2</sub></td><td>0.771<br>0.023</td><td></td><td>Exofast</td></tr><tr><td colspan="5" style="text-align: center; font-style: italic;">Planet b parameters</td></tr><tr><td>Orbital period</td><td>P</td><td>5.7214742 ± 0.0000043</td><td>d</td><td>Dai &amp; Winn (2017)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2457584.329897 ± 0.000032</td><td>BJD<sub>TDB</sub></td><td>Dai &amp; Winn (2017)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.0 (fixed)</td><td></td><td>Allart et al. (2019)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>90 (fixed)</td><td>deg</td><td>Allart et al. (2019)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>14.1 ± 0.8</td><td>m s<sup>-1</sup></td><td>Piaulet et al. (2021)</td></tr><tr><td>Scaled separation</td><td>a/R<sub>⋆</sub></td><td>18.02 ± 0.27</td><td></td><td>Allart et al. (2019)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>89.560 ± 0.078</td><td></td><td>Močnik et al. (2017)</td></tr><tr><td>Impact parameter</td><td>b</td><td>0.139 ± 0.024</td><td></td><td>Močnik et al. (2017)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>2.7528 ± 0.0072</td><td>h</td><td>Anderson et al. (2017)</td></tr><tr><td>Planet-to-star radius ratio</td><td>R<sub>p</sub>/R<sub>⋆</sub></td><td>0.142988 ± 0.00012</td><td></td><td>Spake et al. (2018)</td></tr><tr><td>Projected spin-orbit angle</td><td>λ</td><td>-158.0<sup>+15.2</sup><sub>-18.5</sub></td><td>deg</td><td>This work</td></tr><tr><td rowspan="3">3D spin-orbit angle</td><td>ψ<sub>N</sub></td><td>103.0<sup>+1.7</sup><sub>-1.8</sub></td><td>deg</td><td>This work</td></tr><tr><td>ψ<sub>S</sub></td><td>103.9<sup>+1.7</sup><sub>-1.8</sub></td><td>deg</td><td></td></tr><tr><td>ψ</td><td>103.5<sup>+1.7</sup><sub>-1.8</sub></td><td>deg</td><td></td></tr><tr><td colspan="5" style="text-align: center; font-style: italic;">Planet c parameters</td></tr><tr><td>Orbital period</td><td>P</td><td>1088<sup>+15</sup><sub>-16</sub></td><td>d</td><td>Piaulet et al. (2021)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2458520<sup>+60</sup><sub>-70</sub></td><td>BJD<sub>TDB</sub></td><td>Piaulet et al. (2021)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.28 ± 0.07</td><td></td><td>Piaulet et al. (2021)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>-120<sup>+30</sup><sub>-20</sub></td><td>deg</td><td>Piaulet et al. (2021)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>9.6<sup>+1.1</sup><sub>-1.0</sub></td><td>m s<sup>-1</sup></td><td>Piaulet et al. (2021)</td></tr></tbody></table>
<table><caption>Table C.13: Properties of the WASP-156 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-style: italic;">Stellar parameters</td></tr><tr><td>Spectral type</td><td></td><td>K3</td><td></td><td>Demangeon et al. (2018)</td></tr><tr><td>Stellar temperature</td><td>T<sub>eff</sub></td><td>4910 ± 61</td><td>K</td><td>Demangeon et al. (2018)</td></tr><tr><td>Stellar radius</td><td>R<sub>⋆</sub></td><td>0.76 ± 0.03</td><td>R<sub>☉</sub></td><td>Demangeon et al. (2018)</td></tr><tr><td>Stellar mass</td><td>M<sub>⋆</sub></td><td>0.842 ± 0.052</td><td>M<sub>☉</sub></td><td>Demangeon et al. (2018)</td></tr><tr><td>Stellar spin inclination</td><td>i<sub>⋆</sub></td><td>—</td><td>deg</td><td>—</td></tr><tr><td>Stellar equatorial period</td><td>P<sub>eq</sub></td><td>—</td><td>d</td><td>—</td></tr><tr><td>Stellar projected velocity</td><td>v<sub>eq</sub> sin i<sub>⋆</sub></td><td>3.17<sup>+0.73</sup><sub>-0.84</sub></td><td>km s<sup>-1</sup></td><td>This work</td></tr><tr><td>Age</td><td>τ</td><td>6.4 ± 4.0</td><td>Gyr</td><td>Demangeon et al. (2018)</td></tr><tr><td>Limb-darkening coefficients</td><td>u<sub>1</sub></td><td>0.693</td><td></td><td>Exofast</td></tr><tr><td></td><td>u<sub>2</sub></td><td>0.092</td><td></td><td></td></tr><tr><td colspan="5" style="text-align: center; font-style: italic;">Planet b parameters</td></tr><tr><td>Orbital period</td><td>P</td><td>3.8361672 ± 0.0000019</td><td>d</td><td>This work (STELLA)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2458644.30467 ± 0.00045</td><td>BJD<sub>TDB</sub></td><td>This work (STELLA)</td></tr><tr><td>Eccentricity</td><td>e</td><td>&lt; 0.007</td><td></td><td>Demangeon et al. (2018)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>—</td><td>deg</td><td>Demangeon et al. (2018)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>19 ± 1</td><td>m s<sup>-1</sup></td><td>Demangeon et al. (2018)</td></tr><tr><td>Scaled separation</td><td>a/R<sub>⋆</sub></td><td>12.748<sup>+0.025</sup><sub>-0.027</sub></td><td></td><td>Saha & Sengupta (2021)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>88.902<sup>+0.033</sup><sub>-0.028</sub></td><td></td><td>Saha & Sengupta (2021)</td></tr><tr><td>Impact parameter</td><td>b</td><td>0.2442<sup>+0.0061</sup><sub>-0.0073</sub></td><td></td><td>Saha & Sengupta (2021)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>2.3926<sup>+0.0049</sup><sub>-0.0055</sub></td><td></td><td>Saha & Sengupta (2021)</td></tr><tr><td>Planet-to-star radius ratio</td><td>R<sub>p</sub>/R<sub>⋆</sub></td><td>0.0685<sup>+0.0012</sup><sub>-0.0008</sub><br>0.067654<sup>+0.000082</sup><sub>-0.000060</sub></td><td></td><td>Demangeon et al. (2018)<br>Saha & Sengupta (2021)</td></tr><tr><td>Projected spin-orbit angle</td><td>λ</td><td>105.7<sup>+14.0</sup><sub>-14.4</sub></td><td>deg</td><td>This work</td></tr></tbody></table>
<table><caption>Table C.14: Properties of the WASP-166 system</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Unit</th><th>Origin</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-style: italic;">Stellar parameters</td></tr><tr><td>Spectral type</td><td></td><td>F9</td><td></td><td>Hellier et al. (2019)</td></tr><tr><td>Stellar temperature</td><td>T<sub>eff</sub></td><td>6050 ± 50</td><td>K</td><td>Hellier et al. (2019)</td></tr><tr><td>Stellar radius</td><td>R<sub>⋆</sub></td><td>1.22 ± 0.06</td><td>R<sub>☉</sub></td><td>Hellier et al. (2019)</td></tr><tr><td>Stellar spin inclination</td><td>i<sub>⋆</sub></td><td>87.9<sup>+22.9</sup><sub>-19.3</sub></td><td>deg</td><td>This work</td></tr><tr><td>Stellar equatorial period</td><td>P<sub>eq</sub></td><td>12.3 ± 1.9</td><td>d</td><td>Hellier et al. (2019)</td></tr><tr><td>Stellar projected velocity</td><td>v<sub>eq</sub> sin i<sub>⋆</sub></td><td>5.4 ± 0.14</td><td>km s<sup>-1</sup></td><td>This work</td></tr><tr><td>Age</td><td>τ</td><td>2.1 ± 0.9</td><td>Gyr</td><td>Hellier et al. (2019)</td></tr><tr><td>Limb-darkening coefficients</td><td>u<sub>1</sub></td><td>0.416</td><td></td><td>Exofast</td></tr><tr><td>u<sub>2</sub></td><td></td><td>0.287</td><td></td><td></td></tr><tr><td colspan="5" style="text-align: center; font-style: italic;">Planet b parameters</td></tr><tr><td>Orbital period</td><td>P</td><td>5.4435402<sup>+0.0000027</sup><sub>-0.0000030</sub></td><td>d</td><td>Bryant et al. (2020)</td></tr><tr><td>Transit epoch</td><td>T<sub>0</sub></td><td>2458540.739389<sup>+0.000721</sup><sub>-0.000670</sub></td><td>BJD<sub>TDB</sub></td><td>Bryant et al. (2020)</td></tr><tr><td>Eccentricity</td><td>e</td><td>0.0 (fixed)</td><td></td><td>Hellier et al. (2019)</td></tr><tr><td>Argument of periastron</td><td>ω</td><td>—</td><td>deg</td><td>Hellier et al. (2019)</td></tr><tr><td>Stellar reflex velocity</td><td>K</td><td>10.4 ± 0.4</td><td>m s<sup>-1</sup></td><td>Hellier et al. (2019)</td></tr><tr><td>Scaled separation</td><td>a/R<sub>⋆</sub></td><td>11.14<sup>+0.42</sup><sub>-0.50</sub></td><td></td><td>Bryant et al. (2020)</td></tr><tr><td>Orbital inclination</td><td>i</td><td>87.95<sup>+0.62</sup><sub>-0.59</sub></td><td>deg</td><td>Bryant et al. (2020)</td></tr><tr><td>Impact parameter</td><td>b</td><td>0.398<sup>+0.093</sup><sub>-0.111</sub></td><td></td><td>Bryant et al. (2020)</td></tr><tr><td>Transit duration</td><td>T<sub>14</sub></td><td>3.600 ± 0.024</td><td>h</td><td>Hellier et al. (2019)</td></tr><tr><td>Planet-to-star radius ratio</td><td>R<sub>p</sub>/R<sub>⋆</sub></td><td>0.0515 ± 0.0011</td><td></td><td>Bryant et al. (2020)</td></tr><tr><td>Projected spin-orbit angle</td><td>λ</td><td>-0.7 ± 1.6</td><td>deg</td><td>This work</td></tr><tr><td>3D spin-orbit angle</td><td>ψ<sup>†</sup></td><td>&lt;22.0 (1σ)</td><td>deg</td><td>This work</td></tr><tr><td></td><td></td><td>&lt;56.2 (3σ)</td><td></td><td></td></tr></tbody></table>

<footnote>† WASP-166 is seen edge-on with λ ~0°, so that ψ<sub>N</sub> ≡ ψ<sub>S</sub></footnote>
Appendix D: Residual CCF maps

<figure><img src="image_15.png" /><figcaption>Fig. D.1: Residual maps between the master-out and individual CCF<sub>DI</sub> (outside of transit) and between the CCF<sub>intr</sub> and their best-fit RMR model (during transit). Transit contacts are shown as white dashed lines. Values are colored as a function of the residual flux and plotted as a function of RV in the star rest frame (in abscissa) and orbital phase (in ordinate). The black dashed line shows the stellar surface RV model from the RMR best fit.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. D.1: Continued</figcaption></figure>