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.

Optical and scintillation properties of CsBa2I5:Eu2+

The scintillation and luminescence properties of pure CsBa2I5 and CsBa2I5 doped with 0.5% Eu and 5% Eu were studied between 78 K and 600 K. Single crystals were grown by the vertical Bridgman method from the melt. CsBa2I5:5% Eu showed a light yield of 80,000 photons/MeV, an energy resolution of 2.3% for the 662 key full absorption peak, and an excellent proportional response. Two broad emission bands centered at 400 nm and 600 nm were observed in the radioluminescence spectrum of pure CsBa2I5. The Eu2+ 5d-4f emission band was observed at 430 nm. The radiative lifetime of the Eu2+ excited state was determined as 350 ns. With increasing temperature and Eu concentration the Eu2+ emission shifts to longer wavelengths and its decay time lengthens as a result of self-absorption of the Eu2+ emission. Multiple thermoluminescence glow peaks and a sharp decrease of the light yield at temperatures below 200 K were observed and related to the presence of the charge carrier traps in CsBa2I5:Eu.

A new, fast and flexible radiative transfer method for Venus general circulation models

We present a new radiation scheme for the Oxford Planetary Unified Model System for Venus, suitable for the solar and thermal bands. This new and fast radiative parameterization uses a different approach in the two main radiative wavelength bands: solar radiation (0.1-5.5 mu m) and thermal radiation (1.7-260 mu m). The solar radiation calculation is based on the delta-Eddington approximation (two-stream-type) with an adding layer method. For the thermal radiation case, a code based on an absorptivity/emissivity formulation is used. The new radiative transfer formulation implemented is intended to be computationally light, to allow its incorporation in 3D global circulation models, but still allowing for the calculation of the effect of atmospheric conditions on radiative fluxes. This will allow us to investigate the dynamical-radiative-microphysical feedbacks. The model flexibility can be also used to explore the uncertainties in the Venus atmosphere such as the optical properties in the deep atmosphere or cloud amount. The results of radiative cooling and heating rates and the global-mean radiative-convective equilibrium temperature profiles for different atmospheric conditions are presented and discussed. This new scheme works in an atmospheric column and can be easily implemented in 3D Venus global circulation models. (C) 2014 Elsevier Ltd. All rights reserved.