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Atmospheric refraction affects to various degrees exoplanet transit, lunareclipse, as well as stellar occultation observations. Exoplanet retrievalalgorithms often use analytical expressions for the column abundance along aray traversing the atmosphere as well as for the deflection of that ray, whichare first order approximations valid for low densities in a sphericallysymmetric homogeneous isothermal atmosphere. We derive new analytical formulaefor both of these quantities, which are valid for higher densities, and usethem to refine and validate a new ray tracing algorithm which can be used forarbitrary atmospheric temperature-pressure profiles. We illustrate with simpleisothermal atmospheric profiles the consequences of our model for differentplanets: temperate Earth-like and Jovian-like planets, as well as HD189733b,and GJ1214b. We find that, for both hot exoplanets, our treatment of refractiondoes not make much of a difference to pressures as high as 10 atmosphere, butthat it is important to consider the variation of gravity with altitude forGJ1214b. However, we find that the temperate atmospheres have an apparent scaleheight significantly smaller than their actual density scale height atdensities larger than 1 amagat, thus increasing the difficulty of detectingspectral features originating in these regions. These denser atmosphericregions form a refractive boundary layer where column abundances and raydeflection increases dramatically with decreasing impact parameter. Thisrefractive boundary layer mimics a surface, and none of the techniquesmentioned above can probe atmospheric regions denser than about 4 amagat onthese temperate planets.

Refraction in planetary atmospheres: improved analytical expressions and comparison with a new ray-tracing algorithm