Clouds in the atmospheres of extrasolar planets. IV. On the scattering greenhouse effect of CO2 ice particles: Numerical radiative transfer studies

Owing to their wavelengths dependent absorption and scattering properties, clouds have a strong impact on the climate of planetary atmospheres. Especially, the potential greenhouse effect of CO2 ice clouds in the atmospheres of terrestrial extrasolar planets is of particular interest because it might influence the position and thus the extension of the outer boundary of the classic habitable zone around main sequence stars. We study the radiative effects of CO2 ice particles obtained by different numerical treatments to solve the radiative transfer equation. The comparison between the results of a high-order discrete ordinate method and simpler two-stream approaches reveals large deviations in terms of a potential scattering efficiency of the greenhouse effect. The two-stream methods overestimate the transmitted and reflected radiation, thereby yielding a higher scattering greenhouse effect. For the particular case of a cool M-type dwarf the CO2 ice particles show no strong effective scattering greenhouse effect by using the high-order discrete ordinate method, whereas a positive net greenhouse effect was found in case of the two-stream radiative transfer schemes. As a result, previous studies on the effects of CO2 ice clouds using two-stream approximations overrated the atmospheric warming caused by the scattering greenhouse effect. Consequently, the scattering greenhouse effect of CO2 ice particles seems to be less effective than previously estimated. In general, higher order radiative transfer methods are necessary to describe the effects of CO2 ice clouds accurately as indicated by our numerical radiative transfer studies.Comment: accepted for publication in A&

Comparative accuracy of the Albedo, transmission and absorption for selected radiative transfer approximations

Illustrations of both the relative and absolute accuracy of eight different radiative transfer approximations as a function of optical thickness, solar zenith angle and single scattering albedo are given. Computational results for the plane albedo, total transmission and fractional absorption were obtained for plane-parallel atmospheres composed of cloud particles. These computations, which were obtained using the doubling method, are compared with comparable results obtained using selected radiative transfer approximations. Comparisons were made between asymptotic theory for thick layers and the following widely used two stream approximations: Coakley-Chylek's models 1 and 2, Meador-Weaver, Eddington, delta-Eddington, PIFM and delta-discrete ordinates

An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing

An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted

Calculation of flow of a radiating gas in a shock layer

Flow calculation of radiating gas in shock layers over blunt bodie

Radiative Transfer for Exoplanet Atmospheres

Remote sensing of the atmospheres of distant worlds motivates a firm understanding of radiative transfer. In this review, we provide a pedagogical cookbook that describes the principal ingredients needed to perform a radiative transfer calculation and predict the spectrum of an exoplanet atmosphere, including solving the radiative transfer equation, calculating opacities (and chemistry), iterating for radiative equilibrium (or not), and adapting the output of the calculations to the astronomical observations. A review of the state of the art is performed, focusing on selected milestone papers. Outstanding issues, including the need to understand aerosols or clouds and elucidating the assumptions and caveats behind inversion methods, are discussed. A checklist is provided to assist referees/reviewers in their scrutiny of works involving radiative transfer. A table summarizing the methodology employed by past studies is provided.Comment: 7 pages, no figures, 1 table. Filled in missing information in references, main text unchange

Radiative diffusivity factors in cirrus and stratocumulus clouds: Application to two-stream models

A diffusion-like description of radiative transfer in clouds and the free atmosphere is often used. The two stream model is probably the best known example of such a description. The main idea behind the approach is that only the first few moments of radiance are needed to describe the radiative field correctly. Integration smooths details of the angular distribution of specific intensity and it is assumed that the closure parameters of the theory (diffusivity factors) are only weakly dependent on the distribution. The diffusivity factors are investigated using the results obtained from both Stratocumulus and Cirrus phases of FIRE experiment. A new theoretical framework is described in which two (upwards and downwards) diffusivity factors are used and a detailed multistream model is used to provide further insight about both the diffusivity factors and their dependence on scattering properties of clouds

2D non-LTE Modeling for Axi-symmetric Winds. II. A Short Characteristic Solution for Radiative Transfer in Rotating Winds

We present a new radiative transfer code for axi-symmetric stellar atmospheres and compare test results against 1D and 2D models with and without velocity fields. The code uses the short characteristic method with modifications to handle axi-symmetric and non-monotonic 3D wind velocities, and allows for distributed calculations. The formal solution along a characteristic is evaluated with a resolution that is proportional to the velocity gradient along the characteristic. This allows us to accurately map the variation of the opacities and emissivities as a function of frequency and spatial coordinates, but avoids unnecessary work in low velocity regions. We represent a characteristic with an impact-parameter vector p (a vector that is normal to the plane containing the characteristic and the origin) rather than the traditional unit vector in the direction of the ray. The code calculates the incoming intensities for the characteristics by a single latitudinal interpolation without any further interpolation in the radiation angles. Using this representation also provides a venue for distributed calculations since the radiative transfer can be done independently for each p.Comment: 18 pages, 12 figures, accepted for publication in A&

Evolution of Ohmically Heated Hot Jupiters

We present calculations of thermal evolution of Hot Jupiters with various masses and effective temperatures under Ohmic dissipation. The resulting evolutionary sequences show a clear tendency towards inflated radii for effective temperatures that give rise to significant ionization of alkali metals in the atmosphere, compatible with the trend of the data. The degree of inflation shows that Ohmic dissipation, along with the likely variability in heavy element content can account for all of the currently detected radius anomalies. Furthermore, we find that in absence of a massive core, low-mass hot Jupiters can over-flow their Roche-lobes and evaporate on Gyr time-scales, possibly leaving behind small rocky cores.Comment: Accepted to The Astrophysical Journal (2011) 735-2, 9 pages, 8 figures, updated figures 2-

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.Comment: Accepted by ApJS. 23 pages, 11 figures, 3 tables, 158 equations. No change from previous version except for title (to match ApJS convention