154 research outputs found
Analytical Models of Exoplanetary Atmospheres. VI. Full Solutions for Improved Two-stream Radiative Transfer, Including Direct Stellar Beam
No full textTwo-stream radiative transfer is used frequently in Earth, planetary, and exoplanetary sciences due to its simplicity and ease of implementation. However, a longstanding limitation of the two-stream approximation is its inaccuracy in the presence of medium-sized or large aerosols. This limitation was lifted by the discovery of the improved two-stream technique, where the accuracy of the scattering greenhouse effect is matched to that of multi-stream calculations by construction. In this study, we derive the full solutions for improved two-stream radiative transfer, following its introduction by Heng & Kitzmann, and include contributions from the direct stellar beam. The generalization of the original two-stream flux solutions comes in the form of a correction factor, traditionally set to unity, which is the ratio of a pair of first Eddington coefficients. We derive an analytical expression for this correction factor and also provide a simple fitting function for its ease of use by other workers. We prove that the direct stellar beam is associated with a second Eddington coefficient that is on the order of unity. Setting this second Eddington coefficient to 2/3 and 1/√3 reproduces the Eddington and quadrature closures, respectively, associated with the direct beam. We use our improved two-stream solutions for the fluxes to derive two-stream source function solutions for both the intensity and fluxes
The THOR + HELIOS general circulation model: multiwavelength radiative transfer with accurate scattering by clouds/hazes
No full textGeneral circulation models (GCMs) provide context for interpreting multiwavelength, multiphase data of the atmospheres of tidally locked exoplanets. In the current study, the non-hydrostatic THOR GCM is coupled with the HELIOS radiative transfer solver for the first time, supported by an equilibrium chemistry solver (FastChem), opacity calculator (HELIOS-K), and Mie scattering code (LX-MIE). To accurately treat the scattering of radiation by medium-sized to large aerosols/condensates, improved two-stream radiative transfer is implemented within a GCM for the first time. Multiple scattering is implemented using a Thomas algorithm formulation of the two-stream flux solutions, which decreases the computational time by about 2 orders of magnitude compared to the iterative method used in past versions of HELIOS. As a case study, we present four GCMs of the hot Jupiter WASP-43b, where we compare the temperature, velocity, entropy, and streamfunction, as well as the synthetic spectra and phase curves, of runs using regular versus improved two-stream radiative transfer and isothermal versus non-isothermal layers. While the global climate is qualitatively robust, the synthetic spectra and phase curves are sensitive to these details. A THOR + HELIOS WASP-43b GCM (horizontal resolution of about 4 deg on the sphere and with 40 radial points) with multiwavelength radiative transfer (30 k-table bins) running for 3000 Earth days (864 000 time-steps) takes about 19–26 d to complete depending on the type of GP
Revisiting the Scattering Greenhouse Effect of CO2 Ice Clouds
No full textCarbon dioxide ice clouds are thought to play an important role for cold terrestrial planets with thick CO2 dominated atmospheres. Various previous studies showed that a scattering greenhouse effect by carbon dioxide ice clouds could result in a massive warming of the planetary surface. However, all of these studies only employed simplified two-stream radiative transfer schemes to describe the anisotropic scattering. Using accurate radiative transfer models with a general discrete ordinate method, this study revisits this important effect and shows that the positive climatic impact of carbon dioxide clouds was strongly overestimated in the past. The revised scattering greenhouse effect can have important implications for the early Mars, but also for planets like the early Earth or the position of the outer boundary of the habitable zone
Self-luminous and irradiated exoplanetary atmospheres explored with HELIOS
No full textWe present new methodological features and physical ingredients included in the one-dimensional radiative transfer code HELIOS, improving the hemispheric two-stream formalism. We conduct a thorough intercomparison survey with several established forward models, including COOLTLUSTY and 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 temperature–pressure (T–P) profiles are very sensitive to the opacities included, with metal oxides, hydrides, and alkali atoms (and ionized hydrogen) playing an important role in the absorption of shortwave radiation (in very hot surroundings). Moreover, if these species are sufficiently abundant, they are likely to induce nonmonotonic T–P profiles. Second, without the stellar path length adjustment, the incoming stellar flux is significantly underestimated for zenith angles above 80°, which somewhat affects the upper atmospheric temperatures and the planetary emission. Third, the scattering correction improves the accuracy of the computation of the reflected stellar light by ~10%. We use HELIOS to calculate a grid of cloud-free atmospheres in radiative–convective equilibrium for self-luminous planets for a range of effective temperatures, surface gravities, metallicities, and C/O ratios to be used by planetary evolution studies. Furthermore, we calculate dayside temperatures and secondary eclipse spectra for a sample of exoplanets for varying chemistry and heat redistribution. These results may be used to make predictions on the feasibility of atmospheric characterizations with future observations
The theory of transmission spectra revisited: a semi-analytical method for interpreting WFC3 data and an unresolved challenge
No full textThe computation of transmission spectra is a central ingredient in the study of exoplanetary atmospheres. First, we revisit the theory of transmission spectra, unifying ideas from several workers in the literature. Transmission spectra lack an absolute normalization due to the a priori unknown value of a reference transit radius, which is tied to an unknown reference pressure. We show 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 the inferred value of the water abundance when interpreting a WFC3 transmission spectrum. Second, we show that the transmission spectra of isothermal atmospheres are nearly isobaric. We validate the isothermal, isobaric analytical formula for the transmission spectrum against full numerical calculations and show that the typical errors are ~0.1% (~10 ppm) within the WFC3 range of wavelengths for temperatures of 1500 K (or higher). Third, we generalize the previous expression for the transit radius to include a small temperature gradient. Finally, we analyze the measured WFC3 transmission spectrum of WASP-12b and demonstrate that we obtain consistent results with the retrieval approach of Kreidberg et al. (2015) if the reference transit radius and reference pressure are fixed to assumed values. The unknown functional relationship between the reference transit radius and reference pressure implies that it is the product of the water abundance and reference pressure that is being retrieved from the data, and not just the water abundance alone. This degeneracy leads to a limitation on how accurately we may extract molecular abundances from transmission spectra using WFC3 data alone. Finally, we compare our study to that of Griffith (2014) and discuss why the degeneracy was missed in previous retrieval studies
Optical properties of potential condensates in exoplanetary atmospheres
No full textThe prevalence of clouds in currently observable exoplanetary atmospheres motivates the compilation and calculation of their optical properties. First, we present a new open-source Mie scattering code known as LX-MIE, which is able to consider large-size parameters (~10⁷) using a single computational treatment. We validate LX-MIE against the classical MIEVO code as well as previous studies. Secondly, we embark on an expanded survey of the published literature for both the real and imaginary components of the refractive indices of 32 condensate species. As much as possible, we rely on experimental measurements of the refractive indices and resort to obtaining the real from the imaginary component (or vice versa), via the Kramers–Kronig relation, only in the absence of data. We use these refractive indices as input for LX-MIE to compute the absorption, scattering and extinction efficiencies of all 32 condensate species. Finally, we use a three-parameter function to provide convenient fits to the shape of the extinction efficiency curve. We show that the errors associated with these simple fits in the Wide Field Camera 3 (WFC3), J, H, and K wavebands are ~10 per cent. These fits allow for the extinction cross-section or opacity of the condensate species to be easily included in retrieval analyses of transmission spectra. We discuss prospects for future experimental work. The compilation of the optical constants and LX-MIE is publicly available as part of the open-source Exoclime Simulation Platform (http://www.exoclime.org)
HELIOS: A new open-source radiative transfer code
No full textI present the new open-source code HELIOS, developed to accurately describe radiative transfer in a wide variety of irradiated atmospheres. We employ a one-dimensional multi-wavelength two-stream approach with scattering. Written in Cuda C++, HELIOS uses the GPU’s potential of massive parallelization and is able to compute the TP-profile of an atmosphere in radiative equilibrium and the subsequent emission spectrum in a few minutes on a single computer (for 60 layers and 1000 wavelength bins).The required molecular opacities are obtained with the recently published code HELIOS-K [1], which calculates the line shapes from an input line list and resamples the numerous line-by-line data into a manageable k-distribution format. Based on simple equilibrium chemistry theory [2] we combine the k-distribution functions of the molecules H2O, CO2, CO & CH4 to generate a k-table, which we then employ in HELIOS.I present our results of the following: (i) Various numerical tests, e.g. isothermal vs. non-isothermal treatment of layers. (ii) Comparison of iteratively determined TP-profiles with their analytical parametric prescriptions [3] and of the corresponding spectra. (iii) Benchmarks of TP-profiles & spectra for various elemental abundances. (iv) Benchmarks of averaged TP-profiles & spectra for the exoplanets GJ1214b, HD189733b & HD209458b. (v) Comparison with secondary eclipse data for HD189733b, XO-1b & Corot-2b.HELIOS is being developed, together with the dynamical core THOR and the chemistry solver VULCAN, in the group of Kevin Heng at the University of Bern as part of the Exoclimes Simulation Platform (ESP) [4], which is an open-source project aimed to provide community tools to model exoplanetary atmospheres.-----------------------------[1] Grimm & Heng 2015, ArXiv, 1503.03806[2] Heng, Lyons & Tsai, Arxiv, 1506.05501Heng & Lyons, ArXiv, 1507.01944[3] e.g. Heng, Mendonca & Lee, 2014, ApJS, 215, 4H[4] exoclime.net ..
Analytical Models of Exoplanetary Atmospheres. IV. Improved Two-stream Radiative Transfer for the Treatment of Aerosols
No full textWe present a novel generalization of the two-stream method of radiative transfer, which allows for the accurate treatment of radiative transfer in the presence of strong infrared scattering by aerosols. We prove that this generalization involves only a simple modification of the coupling coefficients and transmission functions in the hemispheric two-stream method. This modification originates from allowing the ratio of the first Eddington coefficients to depart from unity. At the heart of the method is the fact that this ratio may be computed once and for all over the entire range of values of the single-scattering albedo and scattering asymmetry factor. We benchmark our improved two-stream method by calculating the fraction of flux reflected by a single atmospheric layer (the reflectivity) and comparing these calculations to those performed using a 32-stream discrete-ordinates method. We further compare our improved two-stream method to the two-stream source function (16 streams) and delta-Eddington methods, demonstrating that it is often more accurate at the order-of-magnitude level. Finally, we illustrate its accuracy using a toy model of the early Martian atmosphere hosting a cloud layer composed of carbon-dioxide ice particles. The simplicity of implementation and accuracy of our improved two-stream method renders it suitable for implementation in three-dimensional general circulation models. In other words, our improved two-stream method has the ease of implementation of a standard two-stream method, but the accuracy of a 32-stream method
Toward Consistent Modeling of Atmospheric Chemistry and Dynamics in Exoplanets: Validation and Generalization of the Chemical Relaxation Method
No full textMotivated by the work of Cooper & Showman, we revisit the chemical relaxation method, which seeks to enhance the computational efficiency of chemical kinetics calculations by replacing the chemical network with a handful of independent source/sink terms. Chemical relaxation solves the evolution of the system and can treat disequilibrium chemistry, as the source/sink terms are driven toward chemical equilibrium on a prescribed chemical timescale, but it has surprisingly never been validated. First, we generalize the treatment by forgoing the use of a single chemical timescale, instead developing a pathway analysis tool that allows us to identify the rate-limiting reaction as a function of temperature and pressure. For the interconversion between methane and carbon monoxide, and between ammonia and molecular nitrogen, we identify the key rate-limiting reactions for conditions relevant to currently characterizable exo-atmospheres (500-3000 K, 0.1 mbar to 1 kbar). Second, we extend chemical relaxation to include carbon dioxide and water. Third, we examine the role of metallicity and the carbon-to-oxygen ratio in chemical relaxation. Fourth, we apply our pathway analysis tool to diagnose the differences between our chemical network and that of Moses and Venot. Finally, we validate the chemical relaxation method against full chemical kinetics calculations in one dimension. For WASP-18b-, HD 189733b-, and GJ 1214-b-like atmospheres, we show that chemical relaxation is mostly accurate to within an order of magnitude, a factor of 2, and similar to 10%, respectively. The level of accuracy attained allows for the chemical relaxation method to be included in three-dimensional general circulation models
Closed-form ab initio solutions of geometric albedos and reflected light phase curves of exoplanets
No full textStudying the albedos of the planets and moons of the Solar System dates back at least a century1,2,3,4. Of particular interest is the relationship between the albedo measured at superior conjunction, known as the ‘geometric albedo’, and the albedo considered over all orbital phase angles, known as the ‘spherical albedo’2,5,6. Determining the relationship between the geometric and spherical albedos usually involves complex numerical calculations7,8,9,10,11, and closed-form solutions are restricted to simple reflection laws12,13. Here we report the discovery of closed-form solutions for the geometric albedo and integral phase function, which apply to any law of reflection that only depends on the scattering angle. The shape of a reflected light phase curve, quantified by the integral phase function, and the secondary eclipse depth, quantified by the geometric albedo, may now be self-consistently inverted to retrieve globally averaged physical parameters. Fully Bayesian phase-curve inversions for reflectance maps and simultaneous light-curve detrending may now be performed due to the efficiency of computation. Demonstrating these innovations for the hot Jupiter Kepler-7b, we infer a geometric albedo of 0.25+0.01−0.02, a phase integral of 1.77 ± 0.07, a spherical albedo of 0.44+0.02−0.03 and a scattering asymmetry factor of 0.07+0.12−0.11
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