Impact of atmospheric refraction: How deeply can we probe exo-Earth's atmospheres during primary eclipse observations?

Most models used to predict or fit exoplanet transmission spectra do not include all the effects of atmospheric refraction. Namely, the angular size of the star with respect to the planet can limit the lowest altitude, or highest density and pressure, probed during primary eclipses as no rays passing below this critical altitude can reach the observer. We discuss this geometrical effect of refraction for all exoplanets and tabulate the critical altitude, density, and pressure for an exoplanet identical to Earth with a 1 bar N2/O2 atmosphere as a function of both the incident stellar flux (Venus, Earth, and Mars-like) at the top of the atmosphere and the spectral type (O5-M9) of the host star. We show that such a habitable exo-Earth can be probed to a surface pressure of 1 bar only around the coolest stars. We present 0.4-5.0 μm model transmission spectra of Earth's atmosphere viewed as a transiting exoplanet, and show how atmospheric refraction modifies the transmission spectrum depending on the spectral type of the host star. We demonstrate that refraction is another phenomenon that can potentially explain flat transmission spectra over some spectral regions.