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We present an open-source retrieval code named HELIOS-Retrieval (hereafterHELIOS-R), designed to obtain chemical abundances and temperature-pressureprofiles from inverting the measured spectra of exoplanetary atmospheres. Inthe current implementation, we use an exact solution of the radiative transferequation, in the pure absorption limit, in our forward model, which allows usto analytically integrate over all of the outgoing rays (instead of performingGaussian quadrature). Two chemistry models are considered: unconstrainedchemistry (where the mixing ratios are treated as free parameters) andequilibrium chemistry (enforced via analytical formulae, where only theelemental abundances are free parameters). The nested sampling algorithm allowsus to formally implement Occam's Razor based on a comparison of the Bayesianevidence between models. We perform a retrieval analysis on the measuredspectra of the HR 8799b, c, d and e directly imaged exoplanets. Chemicalequilibrium is disfavored by the Bayesian evidence for HR 8799b, c and d. Wefind supersolar C/O, C/H and O/H values for the outer HR 8799b and cexoplanets, while the inner HR 8799d and e exoplanets have substellar C/O,substellar C/H and superstellar O/H values. If these retrieved properties arerepresentative of the bulk compositions of the exoplanets, then they areinconsistent with formation via gravitational instability (without late-timeaccretion) and consistent with a core accretion scenario in which late-timeaccretion of ices occurred differently for the inner and outer exoplanets. ForHR 8799e, we find that spectroscopy in the K band is crucial for constrainingC/O and C/H. HELIOS-R is publicly available as part of the Exoclimes SimulationPlatform (ESP; www.exoclime.org).

the astronomical journal

HELIOS-Retrieval: An Open-source, Nested Sampling Atmospheric Retrieval  Code, Application to the HR 8799 Exoplanets and Inferred Constraints for  Planet Formation