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Title: ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION

Abstract

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 underdetermined 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 tomore » 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 in both the optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing, and incoming fluxes in the convective regime.« less

Authors:
; ;  [1]
  1. University of Bern, Center for Space and Habitability, Sidlerstrasse 5, CH-3012 Bern (Switzerland)
Publication Date:
OSTI Identifier:
22340142
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal, Supplement Series; Journal Volume: 215; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALBEDO; ENERGY CONSERVATION; GENERAL CIRCULATION MODELS; GREENHOUSE EFFECT; INFRARED RADIATION; IRRADIATION; MATHEMATICAL SOLUTIONS; OPACITY; PHOTONS; PHOTOSPHERE; RADIANT HEAT TRANSFER; SCATTERING; VISIBLE RADIATION

Citation Formats

Heng, Kevin, Mendonça, João M., and Lee, Jae-Min, E-mail: kevin.heng@csh.unibe.ch, E-mail: joao.mendonca@csh.unibe.ch, E-mail: lee@physik.uzh.ch. ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION. United States: N. p., 2014. Web. doi:10.1088/0067-0049/215/1/4.
Heng, Kevin, Mendonça, João M., & Lee, Jae-Min, E-mail: kevin.heng@csh.unibe.ch, E-mail: joao.mendonca@csh.unibe.ch, E-mail: lee@physik.uzh.ch. ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION. United States. doi:10.1088/0067-0049/215/1/4.
Heng, Kevin, Mendonça, João M., and Lee, Jae-Min, E-mail: kevin.heng@csh.unibe.ch, E-mail: joao.mendonca@csh.unibe.ch, E-mail: lee@physik.uzh.ch. 2014. "ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION". United States. doi:10.1088/0067-0049/215/1/4.
@article{osti_22340142,
title = {ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION},
author = {Heng, Kevin and Mendonça, João M. and Lee, Jae-Min, E-mail: kevin.heng@csh.unibe.ch, E-mail: joao.mendonca@csh.unibe.ch, E-mail: lee@physik.uzh.ch},
abstractNote = {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 underdetermined 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 in both the optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing, and incoming fluxes in the convective regime.},
doi = {10.1088/0067-0049/215/1/4},
journal = {Astrophysical Journal, Supplement Series},
number = 1,
volume = 215,
place = {United States},
year = 2014,
month =
}
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