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The computation of transmission spectra is a central ingredient in the studyof exoplanetary atmospheres. First, we revisit the theory of transmissionspectra, unifying ideas from several workers in the literature. Transmissionspectra lack an absolute normalization due to the a priori unknown value of areference transit radius, which is tied to an unknown reference pressure. Weshow that there is a degeneracy between the uncertainty in the transit radius,the assumed value of the reference pressure (typically set to 10 bar) and theinferred value of the water abundance when interpreting a WFC3 transmissionspectrum. Second, we show that the transmission spectra of isothermalatmospheres are nearly isobaric. We validate the isothermal, isobaricanalytical formula for the transmission spectrum against full numericalcalculations and show that the typical errors are ~0.1% (~10 ppm) within theWFC3 range of wavelengths for temperatures of 1500 K (or higher). Third, wegeneralize the previous expression for the transit radius to include a smalltemperature gradient. Finally, we analyze the measured WFC3 transmissionspectrum of WASP-12b and demonstrate that we obtain consistent results with theretrieval approach of Kreidberg et al. (2015) if the reference transit radiusand reference pressure are fixed to assumed values. The unknown functionalrelationship between the reference transit radius and reference pressureimplies that it is the product of the water abundance and reference pressurethat is being retrieved from the data, and not just the water abundance alone.This degeneracy leads to a limitation on how accurately we may extractmolecular abundances from transmission spectra using WFC3 data alone. Finally,we compare our study to that of Griffith (2014) and discuss why the degeneracywas missed in previous retrieval studies. [abridged]

The theory of transmission spectra revisited: a semi-analytical method for interpreting WFC3 data and an unresolved challenge