High Resolution Transmission Spectroscopy as a Diagnostic for Jovian Exoplanet Atmospheres: Constraints from Theoretical Models

We present high resolution transmission spectra of giant planet atmospheres from a coupled 3-D atmospheric dynamics and transmission spectrum model that includes Doppler shifts which arise from winds and planetary motion. We model jovian planets covering more than two orders of magnitude in incident flux, corresponding to planets with 0.9 to 55 day orbital periods around solar-type stars. The results of our 3-D dynamical models reveal certain aspects of high resolution transmission spectra that are not present in simple 1-D models. We find that the hottest planets experience strong substellar to anti-stellar (SSAS) winds, resulting in transmission spectra with net blue shifts of up to 3 km s−1, whereas less irradiated planets show almost no net Doppler shifts. Compared to 1-D models, peak line strengths are significantly reduced for the hottest atmospheres owing to Doppler broadening from a combination of rotation (which is faster for close-in planets under the assumption of tidal locking) and atmospheric winds. Finally, high resolution transmission spectra may be useful in studying the atmospheres of exoplanets with optically thick clouds since line cores for very strong transitions should remain optically thick to very high altitude. High resolution transmission spectra are an excellent observational test for the validity of 3-D atmospheric dynamics models, because they provide a direct probe of wind structures and heat circulation. Ground-based exoplanet spectroscopy is currently on the verge of being able to verify some of our modeling predictions, most notably the dependence of SSAS winds on insolation. We caution that interpretation of high resolution transmission spectra based on 1-D atmospheric models may be inadequate, as 3-D atmospheric motions can produce a noticeable effect on the absorption signatures.

Impact of volcanic stratospheric aerosols on diurnal temperature range in Europe over the past 200 years: Observations versus model simulations

We analyze the impact of stratospheric volcanic aerosols on the diurnal temperature range (DTR) over Europe using long-term subdaily station records. We compare the results with a 28-member ensemble of European Centre/Hamburg version 5.4 (ECHAM5.4) general circulation model simulations. Eight stratospheric volcanic eruptions during the instrumental period are investigated. Seasonal all- and clear-sky DTR anomalies are compared with contemporary (approximately 20 year) reference periods. Clear sky is used to eliminate cloud effects and better estimate the signal from the direct radiative forcing of the volcanic aerosols. We do not find a consistent effect of stratospheric aerosols on all-sky DTR. For clear skies, we find average DTR anomalies of −0.08°C (−0.13°C) in the observations (in the model), with the largest effect in the second winter after the eruption. Although the clear-sky DTR anomalies from different stations, volcanic eruptions, and seasons show heterogeneous signals in terms of order of magnitude and sign, the significantly negative DTR anomalies (e.g., after the Tambora eruption) are qualitatively consistent with other studies. Referencing with clear-sky DTR anomalies to the radiative forcing from stratospheric volcanic eruptions, we find the resulting sensitivity to be of the same order of magnitude as previously published estimates for tropospheric aerosols during the so-called “global dimming” period (i.e., 1950s to 1980s). Analyzing cloud cover changes after volcanic eruptions reveals an increase in clear-sky days in both data sets. Quantifying the impact of stratospheric volcanic eruptions on clear-sky DTR over Europe provides valuable information for the study of the radiative effect of stratospheric aerosols and for geo-engineering purposes.

ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. I. ATMOSPHERIC DYNAMICS VIA THE SHALLOW WATER SYSTEM

Within the context of exoplanetary atmospheres, we present a comprehensive linear analysis of forced, damped, magnetized shallow water systems, exploring the effects of dimensionality, geometry (Cartesian, pseudo-spherical, and spherical), rotation, magnetic tension, and hydrodynamic and magnetic sources of friction. Across a broad range of conditions, we find that the key governing equation for atmospheres and quantum harmonic oscillators are identical, even when forcing (stellar irradiation), sources of friction (molecular viscosity, Rayleigh drag, and magnetic drag), and magnetic tension are included. The global atmospheric structure is largely controlled by a single key parameter that involves the Rossby and Prandtl numbers. This near-universality breaks down when either molecular viscosity or magnetic drag acts non-uniformly across latitude or a poloidal magnetic field is present, suggesting that these effects will introduce qualitative changes to the familiar chevron-shaped feature witnessed in simulations of atmospheric circulation. We also find that hydrodynamic and magnetic sources of friction have dissimilar phase signatures and affect the flow in fundamentally different ways, implying that using Rayleigh drag to mimic magnetic drag is inaccurate. We exhaustively lay down the theoretical formalism (dispersion relations, governing equations, and time-dependent wave solutions) for a broad suite of models. In all situations, we derive the steady state of an atmosphere, which is relevant to interpreting infrared phase and eclipse maps of exoplanetary atmospheres. We elucidate a pinching effect that confines the atmospheric structure to be near the equator. Our suite of analytical models may be used to develop decisively physical intuition and as a reference point for three-dimensional magnetohydrodynamic simulations of atmospheric circulation.

Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-Stream Approximation

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.

UNDERSTANDING TRENDS ASSOCIATED WITH CLOUDS IN IRRADIATED EXOPLANETS

Unlike previously explored relationships between the properties of hot Jovian atmospheres, the geometric albedo and the incident stellar flux do not exhibit a clear correlation, as revealed by our re-analysis of Q0-Q14 Kepler data. If the albedo is primarily associated with the presence of clouds in these irradiated atmospheres, a holistic modeling approach needs to relate the following properties: the strength of stellar irradiation (and hence the strength and depth of atmospheric circulation), the geometric albedo (which controls both the fraction of starlight absorbed and the pressure level at which it is predominantly absorbed), and the properties of the embedded cloud particles (which determine the albedo). The anticipated diversity in cloud properties renders any correlation between the geometric albedo and the stellar flux weak and characterized by considerable scatter. In the limit of vertically uniform populations of scatterers and absorbers, we use an analytical model and scaling relations to relate the temperature-pressure profile of an irradiated atmosphere and the photon deposition layer and to estimate whether a cloud particle will be lofted by atmospheric circulation. We derive an analytical formula for computing the albedo spectrum in terms of the cloud properties, which we compare to the measured albedo spectrum of HD 189733b by Evans et al. Furthermore, we show that whether an optical phase curve is flat or sinusoidal depends on whether the particles are small or large as defined by the Knudsen number. This may be an explanation for why Kepler-7b exhibits evidence for the longitudinal variation in abundance of condensates, while Kepler-12b shows no evidence for the presence of condensates despite the incident stellar flux being similar for both exoplanets. We include an "observer's cookbook" for deciphering various scenarios associated with the optical phase curve, the peak offset of the infrared phase curve, and the geometric albedo.

THE EFFECTS OF IRRADIATION ON HOT JOVIAN ATMOSPHERES: HEAT REDISTRIBUTION AND ENERGY DISSIPATION

Hot Jupiters, due to the proximity to their parent stars, are subjected to a strong irradiating flux that governs their radiative and dynamical properties. We compute a suite of three-dimensional circulation models with dual-band radiative transfer, exploring a relevant range of irradiation temperatures, both with and without temperature inversions. We find that, for irradiation temperatures T irr lsim 2000 K, heat redistribution is very efficient, producing comparable dayside and nightside fluxes. For T irr ≈ 2200-2400 K, the redistribution starts to break down, resulting in a high day-night flux contrast. Our simulations indicate that the efficiency of redistribution is primarily governed by the ratio of advective to radiative timescales. Models with temperature inversions display a higher day-night contrast due to the deposition of starlight at higher altitudes, but we find this opacity-driven effect to be secondary compared to the effects of irradiation. The hotspot offset from the substellar point is large when insolation is weak and redistribution is efficient, and decreases as redistribution breaks down. The atmospheric flow can be potentially subjected to the Kelvin-Helmholtz instability (as indicated by the Richardson number) only in the uppermost layers, with a depth that penetrates down to pressures of a few millibars at most. Shocks penetrate deeper, down to several bars in the hottest model. Ohmic dissipation generally occurs down to deeper levels than shock dissipation (to tens of bars), but the penetration depth varies with the atmospheric opacity. The total dissipated Ohmic power increases steeply with the strength of the irradiating flux and the dissipation depth recedes into the atmosphere, favoring radius inflation in the most irradiated objects. A survey of the existing data, as well as the inferences made from them, reveals that our results are broadly consistent with the observational trends.

From stellar nebula to planets: The refractory components

Context. To date, calculations of planet formation have mainly focused on dynamics, and only a few have considered the chemical composition of refractory elements and compounds in the planetary bodies. While many studies have been concentrating on the chemical composition of volatile compounds (such as H2O, CO, CO2) incorporated in planets, only a few have considered the refractory materials as well, although they are of great importance for the formation of rocky planets. Aims. We computed the abundance of refractory elements in planetary bodies formed in stellar systems with a solar chemical composition by combining models of chemical composition and planet formation. We also considered the formation of refractory organic compounds, which have been ignored in previous studies on this topic. Methods. We used the commercial software package HSC Chemistry to compute the condensation sequence and chemical composition of refractory minerals incorporated into planets. The problem of refractory organic material is approached with two distinct model calculations: the first considers that the fraction of atoms used in the formation of organic compounds is removed from the system (i.e., organic compounds are formed in the gas phase and are non-reactive); and the second assumes that organic compounds are formed by the reaction between different compounds that had previously condensed from the gas phase. Results. Results show that refractory material represents more than 50 wt % of the mass of solids accreted by the simulated planets with up to 30 wt % of the total mass composed of refractory organic compounds. Carbide and silicate abundances are consistent with C/O and Mg/Si elemental ratios of 0.5 and 1.02 for the Sun. Less than 1 wt % of carbides are present in the planets, and pyroxene and olivine are formed in similar quantities. The model predicts planets that are similar in composition to those of the solar system. Starting from a common initial nebula composition, it also shows that a wide variety of chemically different planets can form, which means that the differences in planetary compositions are due to differences in the planetary formation process. Conclusions. We show that a model in which refractory organic material is absent from the system is more compatible with observations. The use of a planet formation model is essential to form a wide diversity of planets in a consistent way.

From planetesimals to planets: volatile molecules

Context. Solar and extrasolar planets are the subject of numerous studies aiming to determine their chemical composition and internal structure. In the case of extrasolar planets, the composition is important as it partly governs their potential habitability. Moreover, observational determination of chemical composition of planetary atmospheres are becoming available, especially for transiting planets. Aims. The present works aims at determining the chemical composition of planets formed in stellar systems of solar chemical composition. The main objective of this work is to provide valuable theoretical data for models of planet formation and evolution, and future interpretation of chemical composition of solar and extrasolar planets. Methods. We have developed a model that computes the composition of ices in planets in different stellar systems with the use of models of ice and planetary formation. Results. We provide the chemical composition, ice/rock mass ratio and C:O molar ratio for planets in stellar systems of solar chemical composition. From an initial homogeneous composition of the nebula, we produce a wide variety of planetary chemical compositions as a function of the mass of the disk and distance to the star. The volatile species incorporated in planets are mainly composed of H2O, CO, CO2, CH3OH, and NH3. Icy or ocean planets have systematically higher values of molecular abundances compared to giant and rocky planets. Gas giant planets are depleted in highly volatile molecules such as CH4, CO, and N2 compared to icy or ocean planets. The ice/rock mass ratio in icy or ocean and gas giant planets is, respectively, equal at maximum to 1.01 ± 0.33 and 0.8 ± 0.5, and is different from the usual assumptions made in planet formation models, which suggested this ratio to be 2–3. The C:O molar ratio in the atmosphere of gas giant planets is depleted by at least 30% compared to solar value.

From stellar nebula to planetesimals

Context. Solar and extrasolar comets and extrasolar planets are the subject of numerous studies in order to determine their chemical composition and internal structure. In the case of planetesimals, their compositions are important as they govern in part the composition of future planets. Aims. The present works aims at determining the chemical composition of icy planetesimals, believed to be similar to present day comets, formed in stellar systems of solar chemical composition. The main objective of this work is to provide valuable theoretical data on chemical composition for models of planetesimals and comets, and models of planet formation and evolution. Methods. We have developed a model that calculates the composition of ices formed during the cooling of the stellar nebula. Coupled with a model of refractory element formation, it allows us to determine the chemical composition and mass ratio of ices to rocks in icy planetesimals throughout in the protoplanetary disc. Results. We provide relationships for ice line positions (for different volatile species) in the disc, and chemical compositions and mass ratios of ice relative to rock for icy planetesimals in stellar systems of solar chemical composition. From an initial homogeneous composition of the nebula, a wide variety of chemical compositions of planetesimals were produced as a function of the mass of the disc and distance to the star. Ices incorporated in planetesimals are mainly composed of H2O, CO, CO2, CH3OH, and NH3. The ice/rock mass ratio is equal to 1 ± 0.5 in icy planetesimals following assumptions. This last value is in good agreement with observations of solar system comets, but remains lower than usual assumptions made in planet formation models, taking this ratio to be of 2–3.

Gas composition of the main volatile elements in protoplanetary discs and its implication for planet formation

Context. Direct observations of gaseous exoplanets reveal that their gas envelope has a higher C/O ratio than that of the host star (e.g., Wasp 12-b). This has been explained by considering that the gas phase of the disc could be inhomogeneous, exceeding the stellar C/O ratio in regions where these planets formed; but few studies have considered the drift of the gas and planet migration. Aims. We aim to derive the gas composition in planets through planet formation to evaluate if the formation of giant planets with an enriched C/O ratio is possible. The study focusses on the effects of different processes on the C/O ratio, such as the disc evolution, the drift of gas, and planet migration. Methods. We used our previous models for computing the chemical composition, together with a planet formation model, to which we added the composition and drift of the gas phase of the disc, which is composed of the main volatile species H2O, CO, CO2, NH3, N2, CH3OH, CH4, and H2S, H2 and He. The study focusses on the region where ice lines are present and influence the C/O ratio of the planets. Results. Modelling shows that the condensation of volatile species as a function of radial distance allows for C/O enrichment in specific parts of the protoplanetary disc of up to four times the solar value. This leads to the formation of planets that can be enriched in C/O in their envelope up to three times the solar value. Planet migration, gas phase evolution and disc irradiation enables the evolution of the initial C/O ratio that decreases in the outer part of the disc and increases in the inner part of the disc. The total C/O ratio of the planets is governed by the contribution of ices accreted, suggesting that high C/O ratios measured in planetary atmospheres are indicative of a lack of exchange of material between the core of a planet and its envelope or an observational bias. It also suggests that the observed C/O ratio is not representative of the total C/O ratio of the planet.

Constraining planet structure from stellar chemistry: the cases of CoRoT-7, Kepler-10, and Kepler-93

Aims. We explore the possibility that the stellar relative abundances of different species can be used to constrain the bulk abundances of known transiting rocky planets. Methods. We use high resolution spectra to derive stellar parameters and chemical abundances for Fe, Si, Mg, O, and C in three stars hosting low mass, rocky planets: CoRoT-7, Kepler-10, and Kepler-93. These planets follow the same line along the mass-radius diagram, pointing toward a similar composition. The derived abundance ratios are compared with the solar values. With a simple stoichiometric model, we estimate the iron mass fraction in each planet, assuming stellar composition. Results. We show that in all cases, the iron mass fraction inferred from the mass-radius relationship seems to be in good agreement with the iron abundance derived from the host star's photospheric composition. Conclusions. The results suggest that stellar abundances can be used to add constraints on the composition of orbiting rocky planets.