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.Comment: 23 pages, 13 figures, accepted at ApJ, submitted to ApJ on Nov 4,
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