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

Heng, Kevin; Do Carmo Fialho Mendonça, João Manuel; Lee, Jea-min (2014). Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-Stream Approximation. Astrophysical journal - supplement series, 215(1), p. 4. Institute of Physics Publishing IOP 10.1088/0067-0049/215/1/4

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

10 Strategic Research Centers > Center for Space and Habitability (CSH)

UniBE Contributor:

Heng, Kevin and Do Carmo Fialho Mendonça, João Manuel

Subjects:

500 Science > 520 Astronomy
500 Science > 530 Physics

ISSN:

0067-0049

Publisher:

Institute of Physics Publishing IOP

Language:

English

Submitter:

Danielle Zemp

Date Deposited:

30 Oct 2014 09:24

Last Modified:

28 Jun 2016 16:53

Publisher DOI:

10.1088/0067-0049/215/1/4

ArXiv ID:

1405.0026

BORIS DOI:

10.7892/boris.59276

URI:

https://boris.unibe.ch/id/eprint/59276

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