Characterization of the Atmospheres of Terrestrial Exoplanets

Abstract

Context: Over 5,000 exoplanets have been discovered to date, yet our knowledge of their atmospheres is still quite limited, and we have not yet identified any truly habitable exoplanets. It is the high time to characterize the atmospheres of Earth-like planets, especially as we enter an era of ambitious, big missions such as the Roman Space Telescope, the Thirty Meter Telescope, HabEx, the Extremely Large Telescope, and the Habitable Worlds Observatory (HWO). These groundbreaking missions are poised to significantly enhance our understanding and bring us closer to discovering potentially habitable worlds. Aim: Our goal is to characterize the atmospheres of terrestrial exoplanets by calculating their reflected spectra, transmission spectra, and polarization phase curves. For the reflection spectra, we considered both present and prebiotic Earth-like exoplanets orbiting stars of F, G, K, and M spectral types, as well as nine known terrestrial exoplanets. The transmission spectra are modeled for present and prebiotic Earth-like exoplanets using the Beer-Bouguer-Lambert’s law and a general law of multiple scattering, which accounts for diffused radiation. We also model the polarization phase curves of terrestrial exoplanets orbiting Sun-like stars. Various planetary surface types were considered, including water worlds, present and prebiotic Earth-like surfaces, and different sky conditions, such as clear and cloudy atmospheres. Additionally, we modeled atmospheres with increased greenhouse gas abundances. Methodology: The reflected spectra and geometric albedo is computed by solving the equation applicable for multiple scattering radiative transfer problem. The atmospheric abundance is assumed to be analogous to that of the present Earth-like exoplanets. The Temperature - Pressure profiles for the known exoplanets are derived using hydrostatic equilibrium and the energy balance equation. The transmission spectra is calculated using Beer-Bouguer-Lambert’s law as well as using multiple scattering radiative transfer equation. We numerically solve the 3D vector radiative transfer equations to calculate the phase curves of albedo and disk-integrated polarization by using appropriate scattering phase matrices and integrating the local Stokes vectors over the illuminated part of the planetary disks along the line of sight. Results: Firstly, we present the reflected spectra and the geometric albedo for the present and prebiotic Earth-like exoplanets orbiting around F, G, K and M spectral types of stars and also for the nine known terrestrial exoplanets. We note the effect of the globally averaged surface albedo, clouds and the greenhouse gases abundance on the reflectivity. Secondly, we present the transmission spectra for Earth-like exoplanets, both with and without diffused scattering. We see the effect of the clouds on the transmission spectra and note the absorption lines of the bio-molecules present in the planetary atmospheres. Our models demonstrate that the effect of the diffusely transmitted radiation can be significant, especially in the atmospheres with clouds. Thirdly, we explore the effects of the Bond surface albedo on the polarization and albedo phase curves. The surface features of such planets are known to significantly dictate the nature of these observational quantities. We also determine the effect of the inclination angle and the clouds for two different wavebands i.e. visible and infrared. Our findings indicate that the clouds serve as an indicator for the polarization due to scattering for the terrestrial exoplanets. More information can be extracted through the synergistic observations of spectra and phase curves. Additionally, the degeneracy among the estimated parameters of terrestrial exoplanets can be reduced by characterizing the atmospheres through various methods like, reflection spectra, transmission spectra and polarization phase curves. Consequently, our models will be instrumental in guiding future observations and enhancing the precision of exoplanetary atmospheric characterization.