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Several transiting super-Earths are expected to be discovered in the comingfew years. While tools to model the interior structure of transiting planetsexist, inferences about the composition are fraught with ambiguities. Wepresent a framework to quantify how much we can robustly infer aboutsuper-Earth and Neptune-size exoplanet interiors from radius and massmeasurements. We introduce quaternary diagrams to illustrate the range ofpossible interior compositions for planets with four layers (iron core,silicate mantles, water layers, and H/He envelopes). We apply our model toCoRoT-7b, GJ 436b, and HAT-P-11b. Interpretation of planets with H/He envelopesis limited by the model uncertainty in the interior temperature, while forCoRoT-7b observational uncertainties dominate. We further find that our planetinterior model sharpens the observational constraints on CoRoT-7b's mass andradius, assuming the planet does not contain significant amounts of water orgas. We show that the strength of the limits that can be placed on asuper-Earth's composition depends on the planet's density; for similarobservational uncertainties, high-density super-Mercuries allow the tightestcomposition constraints. Finally, we describe how techniques from Bayesianstatistics can be used to take into account in a formal way the combinedcontributions of both theoretical and observational uncertainties toambiguities in a planet's interior composition. On the whole, with only a massand radius measurement an exact interior composition cannot be inferred for anexoplanet because the problem is highly underconstrained. Detailed quantitativeranges of plausible compositions, however, can be found.

A Framework for Quantifying the Degeneracies of Exoplanet Interior Compositions