HELIOS-Retrieval: An Open-source, Nested Sampling Atmospheric Retrieval Code, Application to the HR 8799 Exoplanets and Inferred Constraints for Planet Formation
Baptiste Lavie, João M. Mendonça, Christoph Mordasini, Matej Malik, Mickaël Bonnefoy, Brice-Olivier Demory, Maria Oreshenko, Simon L. Grimm, David Ehrenreich, Kevin Heng
We present an open-source retrieval code named HELIOS-Retrieval (hereafter HELIOS-R), designed to obtain chemical abundances and temperature-pressure profiles from inverting the measured spectra of exoplanetary atmospheres. In the current implementation, 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 (instead of performing Gaussian quadrature). Two chemistry models are considered: unconstrained chemistry (where the mixing ratios are treated as free parameters) and equilibrium chemistry (enforced via analytical formulae, where only the elemental abundances are free parameters). 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 HR 8799b, c, d and e directly imaged exoplanets. Chemical equilibrium is disfavored by the Bayesian evidence for HR 8799b, c and d. We find supersolar C/O, C/H and O/H values for the outer HR 8799b and c exoplanets, while the inner HR 8799d and e exoplanets have substellar C/O, substellar C/H and superstellar O/H values. 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-R is publicly available as part of the Exoclimes Simulation Platform (ESP; www.exoclime.org).
We present the open-source radiative transfer code named HELIOS, which is constructed for studying exoplanetary atmospheres. In its initial version, the model atmospheres of HELIOS are one-dimensional and plane-parallel, and the equation of radiative transfer is solved in the two-stream approximation with non-isotropic scattering. A small set of the main infrared absorbers is employed, computed with the opacity calculator HELIOS-K and combined using a correlated-$k$ approximation. The molecular abundances originate from validated analytical formulae for equilibrium chemistry. We compare HELIOS…
We present new methodological features and physical ingredients included in the 1D radiative transfer code HELIOS, improving the hemispheric two-stream formalism. We conduct a thorough intercomparison survey with several established forward models, including COOLTLUSTY, PHOENIX, and find satisfactory consistency with their results. Then, we explore the impact of (i) different groups of opacity sources, (ii) a stellar path length adjustment, and (iii) a scattering correction on self-consistently calculated atmospheric temperatures and planetary emission spectra. First, we observe that temperatu…
Computing and using opacities is a key part of modeling and interpreting data of exoplanetary atmospheres. Since the underlying spectroscopic line lists are constantly expanding and currently include up to ~ 10^10 - 10^11 transition lines, the opacity calculator codes need to become more powerful. Here we present major upgrades to the HELIOS-K GPU-accelerated opacity calculator and describe the necessary steps to process large line lists within a reasonable amount of time. Besides performance improvements, we include more capabilities and present a toolbox for handling different atomic and mol…
Here we present juliet, a versatile tool for the analysis of transits, radial-velocities, or both. juliet is built over many available tools for the modelling of transits, radial-velocities and stochastic processes (here modelled as Gaussian Processes; GPs) in order to deliver a tool/wrapper which can be used for the analysis of transit photometry and radial-velocity measurements from multiple instruments at the same time, using nested sampling algorithms which allows it to not only perform a thorough sampling of the parameter space, but also to perform model comparison via bayesian evidences.…
We present an improved, hybrid CPU-GPU atmospheric retrieval code, Helios-r2, which is applicable to medium-resolution emission spectra of brown dwarfs, in preparation for precision atmospheric spectroscopy in the era of the James Webb Space Telescope. The model is available as open-source code on the Exoclimes Simulation Platform. We subject Helios-r2 to a battery of tests of varying difficulty. The simplest test involves a mock retrieval on a forward model generated using the same radiative transfer technique, the same implementation of opacities, and the same chemistry model. The least triv…
Spectroscopy of exoplanetary atmospheres has become a well established method for the characterisation of extrasolar planets. We here present a novel inverse retrieval code for exoplanetary atmospheres. TauRex (Tau Retrieval for Exoplanets) is a line-by-line radiative transfer fully Bayesian retrieval framework. TauRex includes the following features: 1) the optimised use of molecular line-lists from the Exomol project; 2) an unbiased atmospheric composition prior selection, through custom built pattern recognition software; 3) the use of two independent algorithms to fully sample the Bayesian…
We present EOS, a procedure for determining the Outgoing Longwave Radiation (OLR) and top-of-atmosphere (TOA) albedo for a wide range of conditions expected to be present in the atmospheres of rocky planets with temperate conditions. EOS is based on HELIOS and HELIOS-K, which are novel and publicly available atmospheric radiative transfer (RT) codes optimized for fast calculations with GPU processors. These codes were originally developed for the study of giant planets. In this paper we present an adaptation for applications to terrestrial-type, habitable planets, adding specific physical reci…
We present a new method for performing atmospheric retrieval on ground-based, high-resolution data of exoplanets. Our method combines cross-correlation functions with a random forest, a supervised machine learning technique, to overcome challenges associated with high-resolution data. A series of cross-correlation functions are concatenated to give a "CCF-sequence" for each model atmosphere, which reduces the dimensionality by a factor of ~100. The random forest, trained on our grid of ~65,000 models, provides a likelihood-free method of retrieval. The pre-computed grid spans 31 values of both…
We present an ultrafast opacity calculator that we name HELIOS-K. It takes a line list as an input, computes the shape of each spectral line and provides an option for grouping an enormous number of lines into a manageable number of bins. We implement a combination of Algorithm 916 and Gauss-Hermite quadrature to compute the Voigt profile, write the code in CUDA and optimise the computation for graphics processing units (GPUs). We restate the theory of the k-distribution method and use it to reduce $\sim 10^5$ to $10^8$ lines to $\sim 10$ to $10^4$ wavenumber bins, which may then be used for r…
Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡普坦天文研究所）；Netherlands Space Research Institute (SRON)（荷兰空间研究所（SRON））；Centre for Exoplanet Science, University of Edinburgh（爱丁堡大学系外行星科学中心）；School of GeoSciences, University of Edinburgh（爱丁堡大学地球科学学院）
Exoplanet observations are currently analysed with Bayesian retrieval techniques. Due to the computational load of the models used, a compromise is needed between model complexity and computing time. Analysis of data from future facilities, will need more complex models which will increase the computational load of retrievals, prompting the search for a faster approach for interpreting exoplanet observations. Our goal is to compare machine learning retrievals of exoplanet transmission spectra with nested sampling, and understand if machine learning can be as reliable as Bayesian retrievals for…
One of the principal bottlenecks to atmosphere characterisation in the era of all-sky surveys is the availability of fast, autonomous and robust atmospheric retrieval methods. We present a new approach using unsupervised machine learning to generate informed priors for retrieval of exoplanetary atmosphere parameters from transmission spectra. We use principal component analysis (PCA) to efficiently compress the information content of a library of transmission spectra forward models generated using the PLATON package. We then apply a $k$-means clustering algorithm in PCA space to segregate the …
With more than 4,300 confirmed exoplanets and counting, the next milestone in exoplanet research is to determine which of these newly found worlds could harbor life. Coronal Mass Ejections (CMEs), spawn by magnetically active, superflare-triggering dwarf stars, pose a direct threat to the habitability of terrestrial exoplanets as they can deprive them from their atmospheres. Here we develop a readily implementable atmosphere sustainability constraint for terrestrial exoplanets orbiting active dwarfs, relying on the magnetospheric compression caused by CME impacts. Our constraint focuses on a s…
Inferring the number of planets $N$ in an exoplanetary system from radial velocity (RV) data is a challenging task. Recently, it has become clear that RV data can contain periodic signals due to stellar activity, which can be difficult to distinguish from planetary signals. However, even doing the inference under a given set of simplifying assumptions (e.g. no stellar activity) can be difficult. It is common for the posterior distribution for the planet parameters, such as orbital periods, to be multimodal and to have other awkward features. In addition, when $N$ is unknown, the marginal likel…
The use of machine learning is becoming ubiquitous in astronomy, but remains rare in the study of the atmospheres of exoplanets. Given the spectrum of an exoplanetary atmosphere, a multi-parameter space is swept through in real time to find the best-fit model. Known as atmospheric retrieval, it is a technique that originates from the Earth and planetary sciences. Such methods are very time-consuming and by necessity there is a compromise between physical and chemical realism versus computational feasibility. Machine learning has previously been used to determine which molecules to include in t…
Thermal emission spectra of exoplanets provide constraints on the chemical compositions, pressure-temperature (P-T) profiles, and energy transport in exoplanetary atmospheres. Accurate inferences of these properties rely on the robustness of the atmospheric retrieval methods employed. While extant retrieval codes have provided significant constraints on molecular abundances and temperature profiles in several exoplanetary atmospheres, the constraints on their deviations from thermal and chemical equilibria have yet to be fully explored. Our present work is a step in this direction. We report H…
We investigate the prospects for the capture of the proposed Planet 9 from other stars in the Sun's birth cluster. Any capture scenario must satisfy three conditions: the encounter must be more distant than ~150 au to avoid perturbing the Kuiper belt; the other star must have a wide-orbit planet (a>~100au); the planet must be captured onto an appropriate orbit to sculpt the orbital distribution of wide-orbit Solar System bodies. Here we use N-body simulations to show that these criteria may be simultaneously satisfied. In a few percent of slow close encounters in a cluster, bodies are captured…
It is suggested that the distribution of orbital eccentricities for extrasolar planets is well-described by the Beta distribution. Several properties of the Beta distribution make it a powerful tool for this purpose. For example, the Beta distribution can reproduce a diverse range of probability density functions (PDFs) using just two shape parameters (a and b). We argue that this makes it ideal for serving as a parametric model in Bayesian comparative population analysis. The Beta distribution is also uniquely defined over the interval zero to unity, meaning that it can serve as a proper prio…
The transiting "hot Saturn" HD 149026b, which has the highest mean density of any confirmed planet in the Neptune-Jupiter mass range, has challenged theories of planet formation since its discovery in 2005. Previous investigations could not explain the origin of the planet's 45-110 Earth-mass solid core without invoking catastrophes such as gas giant collisions or heavy planetesimal bombardment launched by neighboring planets. Here we show that HD 149026b's large core can be successfully explained by the standard core accretion theory of planet formation. The keys to our reconstruction of HD 1…
Searching for Molecular Signatures in 14 Transiting Exoplanets with SPIRou
Centro de Astrobiología (CAB), CSIC-INTA（天体生物学中心）；LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台）；Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, CNRS UMR 5277（图卢兹大学）；McGill University（麦吉尔大学）；Université de Montréal（蒙特利尔大学）
Pyrat Bay 2.0: an Upgraded Framework for Exoplanet Atmosphere Modeling in the JWST Era
Space Research Institute, Austrian Academy of Sciences（奥地利科学院空间研究所）；INAF – Osservatorio Astrofisico di Torino（意大利国家天体物理研究所都灵天文台）；Department of Physics, New York University Abu Dhabi（阿布扎比纽约大学物理系）；Center for Astrophysics and Space Science (CASS), New York University Abu Dhabi（阿布扎比纽约大学天体物理学与空间科学中心）；Instituto de Astrofísica de Andalucía - CSIC（安达卢西亚天体物理研究所-西班牙国家研究委员会）
Pyrat Bay 2.0框架新增chemcat等功能，经代码验证后用于气态巨行星大气研究，发现JWST数据可准确恢复大气垂直丰度变化，忽略该变化会导致丰度约束偏差。
Medium-resolution integral-field spectrographs (IFS) coupled with adaptive-optics such as Keck/OSIRIS, VLT/MUSE, or SINFONI are appearing as a new avenue for enhancing the detection and characterization capabilities of young, gas giant exoplanets at large heliocentric distances (>5 au). We analyzed K-band VLT/SINFONI medium-resolution (R_lambda~5577) observations of the young giant exoplanet HIP 65426 b. Our dedicated IFS data analysis toolkit (TExTRIS) optimized the cube building, star registration, and allowed for the extraction of the planet spectrum. A Bayesian inference with the nested sa…
Exoplanet characterization is one of the main foci of current exoplanetary science. For super-Earths and sub-Neptunes, we mostly rely on mass and radius measurements, which allow to derive the body's mean density and give a rough estimate of the planet's bulk composition. However, the determination of planetary interiors is a very challenging task. In addition to the uncertainty in the observed fundamental parameters, theoretical models are limited due to the degeneracy in determining the planetary composition. We aim to study several aspects that affect internal characterization of super-Eart…
Observations of the Earth's exosphere have unveiled an extended envelope of hydrogen reaching further than 10 Earth radii composed of atoms orbiting around the Earth. This large envelope increases significantly the opacity of the Earth to Lyman-alpha (Lya) photons coming from the Sun, to the point of making feasible the detection of the Earth's transit signature from 1.35 pc if pointing with an 8~meter primary mirror space telescope through a clean line of sight (NH < 1e17 cm-2), as we show. In this work, we evaluate the potential detectability of Earth analogues orbiting around nearby M-type …
Flow Matching for Atmospheric Retrieval of Exoplanets: Where Reliability meets Adaptive Noise Levels
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；ETH Zurich（苏黎世联邦理工学院）；ELLIS Institute Tübingen（埃利斯研究所蒂宾根分支）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（阿尔伯特·爱因斯坦研究所））
The construction and implementation of atmospheric model grids is a popular tool in exoplanet characterisation. These typically vary a number of parameters linearly, containing one model for every combination of parameter values. Here we investigate alternative methods of sampling parameters, including random sampling and Latin hypercube (LH) sampling, and how these compare to linearly sampled grids. We use a random forest to analyse the performance of these grids for two different models, as well as investigate the information content of the particular model grid from Goyal et al. 2019. We al…
Atmospheric retrieval of exoplanets from spectroscopic observations requires an extensive exploration of a highly degenerate and high-dimensional parameter space to accurately constrain atmospheric parameters. Retrieval methods commonly conduct Bayesian parameter estimation and statistical inference using sampling algorithms such as Markov Chain Monte Carlo (MCMC) or Nested Sampling. Recently several attempts have been made to use machine learning algorithms either to complement or replace fully Bayesian methods. While much progress has been made, these approaches are still at times unable to …
NAUTILUS: boosting Bayesian importance nested sampling with deep learning
Kavli Institute for Particle Astrophysics and Cosmology（卡夫利粒子天体物理与宇宙学研究所）；Stanford University（斯坦福大学）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；University of Michigan（密歇根大学）；Leinweber Center for Theoretical Physics（莱因韦伯理论物理中心）
Context. The atmosphere of exoplanets has been studied extensively in recent years, using numerical models to retrieve chemical composition, dynamical circulation or temperature from data. One of the best observational probes in transmission is the sodium doublet, due to its large cross section. However, modelling the shape of the planetary sodium lines has proven to be challenging. Models with different assumptions regarding the atmosphere have been employed to fit the lines in the literature, yet statistically sound direct comparisons of different models are needed to paint a clear picture. …
Machine Learning and Deep Learning for Exoplanet Detection and Atmospheric Characterization with JWST and the Upcoming Ariel Mission
Department of Industrial Physics, Enugu State University of Science and Technology（恩古州科技大学工业物理系）；Department of Physics, Dennis Osadebay University（德尼斯·奥萨德贝大学物理系）
University of Oxford（牛津大学）；University of Central Florida（中佛罗里达大学）；King’s College London（伦敦国王学院）；Luxembourg Institute of Science and Technology（卢森堡科学技术研究院）；University of Pittsburgh（匹兹堡大学）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；University of Bern（伯尔尼大学）；Blue Marble Space Institute of Science（蓝大理石空间科学研究所）
Machine learning is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using machine learning algorithms for atmospheric retrieval by implementing a random forest to perform retrievals in seconds that are consistent with the traditional, computationally-expensive nested-sampling retrieval method. We expand upon their approach by presenting a new machine learning model, \texttt{plan-net}, based on an ensemble of Bayesian neural networks that yields more accurate inferences than …
Estimating Orbital Parameters of Direct Imaging Exoplanet Using Neural Network
Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（引力波实验中心、国家微重力实验室、力学研究所、中国科学院）；Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences (UCAS), Beijing（太极引力波宇宙实验室（北京/杭州）、中国科学院大学（UCAS））；National Space Science Center, Chinese Academy of Sciences（国家空间科学中心、中国科学院）；School of Physics, Peking University（北京大学物理学院）；Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences（上海光学精密机械研究所、中国科学院）
Temperate terrestrial exoplanets are likely common objects, but their discovery and characterization is very challenging. Concepts for optimized space missions to overcome these challenges are being studied. The LIFE initiative focuses on the development of a space-based mid-infrared (MIR) nulling interferometer probing the thermal emission of a large sample of exoplanets. We derive first estimates for the signal-to-noise (S/N), spectral resolution (R), and wavelength requirements for LIFE. Using an Earth-twin exoplanet as reference case, we quantify how well planetary/atmospheric properties c…
Coupled atmospHere Interior modeL Intercomparison (CHILI) Protocol Version 1.0: A CUISINES Intercomparison Project of Magma Ocean Models
Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡佩因天文研究所）；Department of Earth & Planetary Sciences, Stanford University（斯坦福大学地球与行星科学系）；Department of Earth and Space Sciences / Astrobiology Program, University of Washington（华盛顿大学地球与空间科学系/天体生物学项目）；Leiden Observatory（莱顿天文台）；SRON Netherlands Institute for Space Research（荷兰空间研究研究所）；School of Physics, University of Bristol（布里斯托尔大学物理学院）；Department of Earth Sciences, Freie Universität Berlin（柏林自由大学地球科学系）；Harvard Paulson School of Engineering and Applied Sciences（哈佛保罗森工程与应用科学学院）；Department of Physics, McGill University（麦吉尔大学物理系）
Bayesian Analysis for Remote Biosignature Identification on exoEarths (BARBIE) I: Using Grid-Based Nested Sampling in Coronagraphy Observation Simulations for H2O
EMPEROR I. Exoplanet MCMC parallel tempering for RV orbit retrieval
Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias, Universidad Diego Portales（迪亚斯·波萨莱斯大学工程与科学学院天体物理研究所）；Centro de Astrofísica y Tecnologías Afines (CATA)（天体物理学及相关技术中心）
$\texttt{Exoformer}$: Accelerating Bayesian atmospheric retrievals with transformer neural networks
Università degli Studi di Padova（帕多瓦大学）；INAF, Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；Centro di Ateneo di Studi e Attività Spaziali “G. Colombo” – Università degli Studi di Padova（帕多瓦大学“G.科洛姆博”太空研究与活动中心）
Improving exoplanet mass characterisation with Bayesian model selection using the Learned Harmonic Mean Estimator
Mullard Space Science Laboratory, Department of Space & Climate Physics, University College London（伦敦大学学院穆拉德空间科学实验室空间与气候物理系）；Department of Statistical Science, University College London（伦敦大学学院统计科学系）
The field of exoplanetary science is making rapid progress both in statistical studies of exoplanet properties as well as in individual characterization. As space missions provide an emerging picture of formation and evolution of exoplanetary systems, the search for habitable worlds becomes one of the fundamental issues to address. To tackle such a complex challenge, we need to specify the conditions favorable for the origin, development and sustainment of life as we know it. This requires the understanding of global (astrospheric) and local (atmospheric, surface and internal) environments of …
ThousandWorlds: A benchmark for climate emulation of potentially habitable exoplanets
University of Cambridge（剑桥大学）；University of Oxford（牛津大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）；University of Bristol（布里斯托大学）；Purdue University（普渡大学）；University of Exeter（埃克塞特大学）
Transiting exoplanets in multi-planet systems exhibit non-Keplerian orbits as a result of the gravitational influence from companions which can cause the times and durations of transits to vary. The amplitude and periodicity of the transit time variations (TTV) are characteristic of the perturbing planet's mass and orbit. The objects of interest (TOI) from the Transiting Exoplanet Survey Satellite (TESS) are analyzed in a uniform way to search for TTVs with sectors 1-3 of data. Due to the volume of targets in the TESS candidate list, artificial intelligence is used to expedite the search for p…
The strong, nearly wavelength-independent absorption cross section of aerosols produces featureless exoplanet transmission spectra, limiting our ability to characterize their atmospheres. Here we show that even in the presence of featureless spectra, we can still characterize certain atmospheric properties. Specifically, we constrain the upper and lower pressure boundaries of aerosol layers, and present plausible composition candidates. We study the case of the bloated Saturn-mass planet WASP-49b, where near-infrared observations reveal a flat transmission spectrum between 0.7 and 1.0 {\micron…
Atmospheric characterization of HIP 67522 b with VLT/CRIRES+. VLT/CRIRES+ suggests a heavier planet and hints at deuterium fractionation
Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, CNRS UMR 5277（天体物理学与行星学研究所，图卢兹大学）；Department of Physics, University of Oxford（牛津大学物理系）；LIRA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎天文台，巴黎文理研究大学）；Laboratoire Lagrange, Observatoire de la Côte d’Azur, CNRS, Université Côte d’Azur（蔚蓝海岸大学拉格朗日实验室）；Centro de Astrobiología (CAB), CSIC-INTA（西班牙国家航空航天技术研究所/西班牙国家科学研究委员会天体生物学中心）；Center for Astrophysics | Harvard & Smithsonian（哈佛史密森尼天体物理中心）
In this work we study the effect of disequilibrium processes on mixing ratio profiles of neutral species and on the simulated spectra of a hot Jupiter exoplanet that orbits stars of different spectral types. We also address the impact of stellar activity that should be present to a different degree in all stars with convective envelopes. We used the VULCAN chemical kinetic code to compute number densities of species. The temperature-pressure profile of the atmosphere was computed with the HELIOS code. We also utilized the $τ$-ReX forward model to predict the spectra of planets in primary and s…
The work presented here attempts at answering the question: how do we decide when a given adetection is a planet or just residual noise in exoplanet direct imaging data? To this end we present a method implemented within a Bayesian framework: (1) to unify 'source detection', and, 'source characterization' into one single rigorous mathematical framework; (2) to enable an adequate hypothesis testing given the S/N of the data; (3) to enhance the detectability of planets faint signal in the presence of instrumental and background noise and to optimize the characterization of the planet. As a proof…
The ESO SupJup Survey XI. Atmospheric properties of six isolated M- and L-type dwarfs with CRIRES+
California Institute of Technology（加州理工学院）；University of Warwick（华威大学）；Max-Planck-Institut für Astronomie（马克斯·普朗克天文学研究所）；Trinity College Dublin, University of Dublin（都柏林大学三一学院）；Leiden Observatory, Leiden University（莱顿大学莱顿天文台）
