stars\

For simplicity, we require habitable zones to receive a constant bolometric stellar flux regardless of spectral type. Thus, we only need to calculate the projected separations once; we can scale the habitable zone with stellar luminosity to maintain a constant bolometric stellar flux. For each star on the target list, we scaled the projected separations according to $$s_{{\rm p},i} = s_{\rm p} \sqrt{\frac{L_{\star,i}}{L_{\sun}}} \left(\frac{1\, \rm{pc}}{d_i}\right),$$ where $s_{{\rm p},i}$ is the projected separation of a single synthetic exoEarth from the $i^{\rm th}$ star, $L_{\star,i}$ is the stellar luminosity of the $i^{\rm th}$ star, $L_{\sun}$ is the solar luminosity, and $d_i$ is the distance to the $i^{\rm th}$ star. The flux ratio of the planet and star also changes with spectral type. For each star on the target list, we scaled the planet to star flux ratio according to $$\Delta {\rm mag}_{{\rm p},i} = \Delta {\rm mag}_{\rm p} + 2.5 \log{\frac{L_{\star,i}}{L_{\sun}}},$$ where $\Delta \rm{mag}_{{\rm p},i}$ is the magnitude flux ratio of a single synthetic exoEarth for the $i^{\rm th}$ star. Completeness $C_i(\Delta {\rm mag_{obs}}, \rm{IWA}, \rm{OWA})$ for the $i^{\rm th}$ star is then calculated as the fraction of synthetic exoEarths with ${\rm IWA} < s_{{\rm p},i} < {\rm OWA}$ and $\Delta 