Refraction of Line and Continuum Light in Exoplanet Atmospheres

Exoplanet transit spectra are calculated including the effect of atmospheric opacity and refractive lightbending. While previous studies considered the case of continuum light, here the effect of an atomic resonance line is included. The model assumes a clear atmosphere and includes H and He, which contribute static polarizability and Rayleigh scattering, as well as the Na D doublet, which contributes dynamic polarizability and a resonant cross section. The image locations and magnifications are found using the lens equation. The model including lightbending is compared to the standard model in which the light travels on straight lines. It is found that near the line center, where the polarizability is large, bending angles are nevertheless small since the optical depth tau = 1 trajectory is at such a high altitude where the particle density is low. Moving away from the line center, the Na D resonance dominates the opacity over similar to 400 angstrom, and over most of this wavelength range the polarizability is dominated by hydrogen and helium and is nearly wavelength-independent. However, the density of the tau = 1 trajectory is wavelength-dependent, and hence the bending angle increases strongly away from the line center. The wavelength-dependent flux deviation between the straight-line and lightbending models occurs at the level of Delta F lambda /F 0 similar to 10-5 for a planet at orbital separation a = 10 R circle dot.