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

2015/06/04 by Yan Betremieux, Yan Bétremieux, Lisa Kaltenegger · 2 citations
Physics and Astronomy · #Astro and Planetary Science #Astronomy #Astrophysics #Astrophysics and Star Formation Studies #Atmosphere (unit) #Atmospheric models #Atmospheric refraction #Atmospheric sciences #Computational physics #Exoplanet #Jovian #Lapse rate #Meteorology #Optics #Physics #Planet #Ray tracing (physics) #Refraction #Stellar, planetary, and galactic studies #astro-ph.EP

paper · pdf · doi:10.1093/mnras/stv1078

published as Betremieux & Kaltenegger (2015), MNRAS, 451, 1268 · 16 pages, 15 figures, 4 tables, Accepted for publication in MNRAS

openalex publication_date 2015/06/04 · arxiv created 2017/03/21 · arxiv updated 2017/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Atmospheric refraction affects to various degrees exoplanet transit, lunar eclipse, as well as stellar occultation observations. Exoplanet retrieval algorithms often use analytical expressions for the column abundance along a ray traversing the atmosphere as well as for the deflection of that ray, which are first-order approximations valid for low densities in a spherically symmetric homogeneous isothermal atmosphere. We derive new analytical formulae for both of these quantities, which are valid for higher densities, and use them to refine and validate a new ray-tracing algorithm which can be used for arbitrary atmospheric temperature–pressure profiles. We illustrate with simple isothermal atmospheric profiles the consequences of our model for different planets: temperate Earth-like and Jovian-like planets, as well as HD 189733b, and GJ1214b. We find that, for both hot exoplanets, our treatment of refraction does not make much of a difference to pressures as high as 10 atm, but that it is important to consider the variation of gravity with altitude for GJ1214b. However, we find that the temperate atmospheres have an apparent scaleheight significantly smaller than their actual density scaleheight at densities larger than 1 amagat, thus increasing the difficulty of detecting spectral features originating in these regions. These denser atmospheric regions form a refractive boundary layer where column abundances and ray deflection increases dramatically with decreasing impact parameter. This refractive boundary layer mimics a surface, and none of the techniques mentioned above can probe atmospheric regions denser than about 4 amagat on these temperate planets.

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