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Disentangling degenerate solutions from primary transit and secondary eclipse spectroscopy of exoplanets

Infrared transmission and emission spectroscopy of exoplanets, recorded from primary transit and secondary eclipse measurements, indicate the presence of the most abundant carbon and oxygen molecular species (H2O, CH4, CO, and CO2) in a few exoplanets. However, efforts to constrain the molecular abundances to within several orders of magnitude are thwarted by the broad range of degenerate solutions that fit the data. Here we explore, with radiative transfer models and analytical approximations, the nature of the degenerate solution sets resulting from the sparse measurements of "hot Jupiter" exoplanets. As demonstrated with simple analytical expressions, primary transit measurements probe roughly 4 atmospheric scale heights at each wavelength band. Derived mixing ratios from these data are highly sensitive to errors in the radius in planet (at a reference pressure), which are approximately a few percent. For example, an uncertainty of 1% in the radius of a 1000 K and H2-based exoplanet with Jupiter's radius and mass, causes an uncertainty of a factor of ~100-10000 in the derived gas mixing ratios. The degree of sensitivity depends on how the line strength increases with the optical depth (i.e. the curve of growth) and the atmospheric scale height. Temperature degeneracies in the solutions of the primary transit data, which manifest their effects through scale height and absorption coefficients, are smaller. We argue that these challenges can be partially surmounted by a combination of selected wavelength sampling of optical and IR measurements and, when possible, the joint analysis of transit and secondary eclipse data of exoplanets.