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

Abstract

We present an open-source retrieval code named HELIOS-RETRIEVAL, designed to obtain chemical abundances and temperature-pressure profiles from inverting the measured spectra of exoplanetary atmospheres. We use an exact solution of the radiative transfer equation, in the pure absorption limit, in our forward model, which allows us to analytically integrate over all of the outgoing rays. Two chemistry models are considered: unconstrained chemistry and equilibrium chemistry (enforced via analytical formulae). The nested sampling algorithm allows us to formally implement Occam's Razor based on a comparison of the Bayesian evidence between models. We perform a retrieval analysis on the measured spectra of the four HR 8799 directly imaged exoplanets. Chemical equilibrium is disfavored for HR 8799b and c. We find supersolar C/H and O/H values for the outer HR 8799b and c exoplanets, while the inner HR 8799d and e exoplanets have a range of C/H and O/H values. The C/O values range from being superstellar for HR 8799b to being consistent with stellar for HR 8799c and being substellar for HR8799d and e. If these retrieved properties are representative of the bulk compositions of the exoplanets, then they are inconsistent with formation via gravitational instability (without late-time accretion) and consistent with a core accretion scenario in which late-time accretion of ices occurred differently for the inner and outer exoplanets. For HR 8799e, we find that spectroscopy in the K band is crucial for constraining C/O and C/H. HELIOS-RETRIEVAL is publicly available as part of the Exoclimes Simulation Platform (ESP; www.exoclime.org).

Equilibrium chemistry down to 100 K

“…We do this because in fast spectral retrieval models (e.g. Lavie et al 2017), the influence of these metals on the concentration of molecules like H 2 O and CO 2 is often neglected, i.e. (C/O) eff ≈ C/O is assumed.…”

Wind of change: retrieving exoplanet atmospheric winds from high-resolution spectroscopy

“…The basics of these concepts are introduced in Trotta (2008); Skilling (2006). A full description of the approach taken here can be found in Lavie et al (2017). For similar applications and examples see Benneke & Seager (2013); Waldmann et al (2015); Line et al (2016).…”

“…To begin, N live points are randomly selected from the parameter space under the constrain of our prior, where N parameters form an N-dimensional parameter space. For this first set of points, the likelihood values are calculated and in each step, the algorithm discards the point with the lowest likelihood and adds a new one until convergence is reached (see Skilling (2006); Lavie et al (2017)). Taking into account the independent Gaussian errors of our spectral observations, we calculate the likelihood as a Gaussian function (Equation 3 in (Benneke & Seager 2013 (Feroz & Hobson 2008;Feroz et al 2009Feroz et al , 2013.…”

Probabilistic Detection of Spectral Line Components

“…We use the popular MultiNest (Feroz & Hobson 2008;Feroz et al 2009) implementation of nested sampling through the PyMultiNest (Buchner et al 2014) Python inter-face. This has been widely used in the past to perform model selection for astrophysical spectra (e.g., Bernardi et al 2016;Feldmeier-Krause et al 2017;Lavie et al 2017;Baronchelli et al 2018). The likelihood function was sampled through a wrapper to pyspeckit, specifically designed to perform nested sampling of spectral cubes 1 .…”