We present a retrieval method based on Bayesian analysis to infer the atmospheric compositions and surface or cloud-top pressures from transmission spectra of exoplanets with general compositions. In this study, we identify what can unambiguously be determined about the atmospheres of exoplanets from their transmission spectra by applying the retrieval method to synthetic observations of the super-Earth GJ 1214b. Our approach to infer constraints on atmospheric parameters is to compute their joint and marginal posterior probability distributions using the MCMC technique in a parallel tempering scheme. A new atmospheric parameterization is introduced that is applicable to general atmospheres in which the main constituent is not known a priori and clouds may be present. Our main finding is that a unique constraint of the mixing ratios of the absorbers and up to two spectrally inactive gases (such as N2 and primordial H2+He) is possible if the observations are sufficient to quantify both (1) the broadband transit depths in at least one absorption feature for each absorber and (2) the slope and strength of the molecular Rayleigh scattering signature. The surface or cloud-top pressure can be quantified if a surface or cloud deck is present. The mean molecular mass can be constrained from the Rayleigh slope or the shapes of absorption features, thus enabling to distinguish between cloudy hydrogen-rich atmospheres and high mean molecular mass atmospheres. We conclude, however, that without the signature of Rayleigh scattering--even with robustly detected infrared absorption features--there is no reliable way to tell if the absorber is the main constituent of the atmosphere or just a minor species with a mixing ratio of <0.1%. The retrieval method leads us to a conceptual picture of which details in transmission spectra are essential for unique characterizations of well-mixed atmospheres.
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