Theoretical Reflectance Spectra of Earth-Like Planets through Their Evolutions: Impact of Clouds on the Detectability of Oxygen, Water, and Methane with Future Direct Imaging Missions

In the near-future, atmospheric characterization of Earth-like planets in the habitable zone will become possible via reflectance spectroscopy with future telescopes such as the proposed LUVOIR and HabEx missions. While previous studies have considered the effect of clouds on the reflectance spectra of Earth-like planets, the molecular detectability considering a wide range of cloud properties has not been previously explored in detail. In this study, we explore the effect of cloud altitude and coverage on the reflectance spectra of Earth-like planets at different geological epochs and examine the detectability of $mathrm{O_2}$, $mathrm{H_2O}$, and $mathrm{CH_4}$ with test parameters for the future mission concept, LUVOIR, using a coronagraph noise simulator previously designed for WFIRST-AFTA. Considering an Earth-like planet located at 5 pc away, we have found that for the proposed LUVOIR telescope, the detection of the $mathrm{O_2}$ A-band feature (0.76 $mathrm{mu}$m) will take approximately 100, 30, and 10 hours for the majority of the cloud parameter space modeled for the atmospheres with 10%, 50%, and 100% of modern Earth O$_2$ abundances, respectively. Especially, for {the case of $gtrsim 50$%} of modern Earth O$_2$ abundance, the feature will be detectable with integration time $lesssim 10$ hours as long as there are lower altitude ($lesssim 8$ km) clouds with a global coverage of $gtrsim 20%$. For the 1% of modern Earth $mathrm{O_2}$ abundance case, however, it will take more than 100 hours for all the cloud parameters we modeled.