Optical properties of potential condensates in exoplanetary atmospheres

The 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 ($\sim 10^7$) using a single computational treatment. We validate LX-MIE against the classical MIEV0 code as well as previous studies. Second, 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 $\sim 10\%$. 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 are publicly available as part of the open-source Exoclime Simulation Platform (http://www.exoclime.org).Comment: accepted version; 15 pages, 5 figures, 3 table

The theory of transmission spectra revisited: a semi-analytical method for interpreting WFC3 data and an unresolved challenge

The 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. [abridged]Comment: Accepted by MNRAS. 11 pages, 7 figures, 2 table

Analytical Models of Exoplanetary Atmospheres. IV. Improved Two-stream Radiative Transfer for the Treatment of Aerosols

We 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.Comment: Accepted by ApJS. 7 pages, 5 figure

Revisiting the Scattering Greenhouse Effect of CO2 Ice Clouds

Carbon 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

Linking the evolution of terrestrial interiors and an early outgassed atmosphere to astrophysical observations

A terrestrial planet is molten during formation and may remain so if subject to intense insolation or tidal forces. Observations continue to favour the detection and characterisation of hot planets, potentially with large outgassed atmospheres. We aim to determine the radius of hot Earth-like planets with large outgassed atmospheres and explore differences between molten and solid silicate planets and their influence on the mass-radius relationship and transmission and emission spectra. An interior-atmosphere model, combined with static structure calculations, tracks the evolving radius of a rocky mantle that is outgassing CO$_2$ and H$_2$O. Synthetic emission and transmission spectra are generated for CO$_2$ and H$_2$O dominated atmospheres. Atmospheres dominated by CO$_2$ suppress the outgassing of H$_2$O to a greater extent than previously realised, as previous studies have applied an erroneous relationship between volatile mass and partial pressure. We therefore predict more H$_2$O can be retained by the interior during the later stages of magma ocean crystallisation. Furthermore, formation of a lid at the surface can tie outgassing of H$_2$O to the efficiency of heat transport through the lid, rather than the atmosphere's radiative timescale. Contraction of the mantle as it solidifies gives $\sim5\%$ radius decrease, which can partly be offset by addition of a relatively light species to the atmosphere. We conclude that a molten silicate mantle can increase the radius of a terrestrial planet by around $5\%$ compared to its solid counterpart, or equivalently account for a $13\%$ decrease in bulk density. An outgassing atmosphere can perturb the total radius according to its speciation. Atmospheres of terrestrial planets around M-stars that are dominated by CO$_2$ or H$_2$O can be distinguished by observing facilities with extended wavelength coverage (e.g., JWST).Comment: 19 pages, published in A&A, abstract shortene

On the climatic impact of CO2 ice particles in atmospheres of terrestrial exoplanets

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Clouds play a significant role for the energy budget in planetary atmospheres. They can scatter incident stellar radiation back to space, effectively cooling the surface of terrestrial planets. On the other hand, they may contribute to the atmospheric greenhouse effect by trapping outgoing thermal radiation. For exoplanets near the outer boundary of the habitable zone, condensation of CO2 can occur due to the low atmospheric temperatures. These CO2 ice clouds may play an important role for the surface temperature and, therefore, for the question of habitability of those planets. However, the optical properties of CO2 ice crystals differ significantly from those of water droplets or water ice particles. Except for a small number of strong absorption bands, they are almost transparent with respect to absorption. Instead, they are highly effective scatterers at long and short wavelengths. Therefore, the climatic effect of a CO2 ice cloud will depend on how much incident stellar radiation is scattered to space in comparison to the amount of thermal radiation scattered back towards the planetary surface. This contribution aims at the potential greenhouse effect of CO2 ice particles. Their scattering and absorption properties are calculated for assumed particle size distributions with different effective radii and particle densities. An accurate radiative transfer model is used to determine the atmospheric radiation field affected by such CO2 particles. These results are compared to less detailed radiative transfer schemes employed in previous studies

A ground-based NUV secondary eclipse observation of KELT-9b

KELT-9b is a recently discovered exoplanet with a 1.49 d orbit around a B9.5/A0-type star. The unparalleled levels of UV irradiation it receives from its host star put KELT-9b in its own unique class of ultra-hot Jupiters, with an equilibrium temperature > 4000 K. The high quantities of dissociated hydrogen and atomic metals present in the dayside atmosphere of KELT-9b bear more resemblance to a K-type star than a gas giant. We present a single observation of KELT-9b during its secondary eclipse, taken with the Wide Field Camera on the Isaac Newton Telescope (INT). This observation was taken in the U-band, a window particularly sensitive to Rayleigh scattering. We do not detect a secondary eclipse signal, but our 3$\sigma$ upper limit of 181 ppm on the depth allows us to constrain the dayside temperature of KELT-9b at pressures of ~30 mbar to 4995 K (3$\sigma$). Although we can place an observational constraint of $A_g<$ 0.14, our models suggest that the actual value is considerably lower than this due to H$^-$ opacity. This places KELT-9b squarely in the albedo regime populated by its cooler cousins, almost all of which reflect very small components of the light incident on their daysides. This work demonstrates the ability of ground-based 2m-class telescopes like the INT to perform secondary eclipse studies in the NUV, which have previously only been conducted from space-based facilities.Comment: Accepted in ApJL. 7 pages, 3 figure

FastChem Cond: Equilibrium chemistry with condensation and rainout for cool planetary and stellar environments

Cool astrophysical objects, such as (exo)planets, brown dwarfs, or asymptotic giant branch stars, can be strongly affected by condensation. Condensation does not only directly affect the chemical composition of the gas phase by removing elements but the condensed material also influences other chemical and physical processes in these object. This includes, for example, the formation of clouds in planetary atmospheres and brown dwarfs or the dust-driven winds of evolved stars. In this study we introduce FastChem Cond, a new version of the FastChem equilibrium chemistry code that adds a treatment of equilibrium condensation. Determining the equilibrium composition under the impact of condensation is complicated by the fact that the number of condensates that can exist in equilibrium with the gas phase is limited by a phase rule. However, this phase rule does not directly provide information on which condensates are stable. As a major advantage of FastChem Cond is able to automatically select the set stable condensates satisfying the phase rule. Besides the normal equilibrium condensation, FastChem Cond can also be used with the rainout approximation that is commonly employed in atmospheres of brown dwarfs or (exo)planets. FastChem Cond is available as open-source code, released under the GPLv3 licence. In addition to the C++ code, FastChem Cond also offers a Python interface. Together with the code update we also add about 290 liquid and solid condensate species to FastChem.Comment: submitted to MNRAS, code available at https://github.com/exoclime/FastChe