Radiative transfer in disk geometry: Emergent intensity from cool gray disks

One of the quantities usually required when solving the equation of radiative transfer is the intensity of radiation emerging from the surface of the medium under consideration. For multi-dimensional situations however, the methods presented to date have been numerical, and these first calculate the so-called source function Sv (r, Ω) as a function of position r, angle Ω and frequency v. This is generally the most difficult part of the exercise since an integro-difierential equation must be solved. The emergent intensity is then determined by solving a relatively simple first order differential equation by any of the well known numerical integration schemes. However, if the emergent intensity is required at a large number of angles, frequencies, and positions on the surface of the medium, and this is usually the case, the amount of computing needed may be considerable.

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Exact and unique solution of a transport equation in a semi-infinite medium by Laplace transform and Wiener-Hopf technique

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.35.2004.192 ◽

2004 ◽

Vol 35 (4) ◽

pp. 347-350

Author(s):

Z. Islam ◽

A. Mukherjee ◽

S. Karanjai

Keyword(s):

Radiative Transfer ◽

Laplace Transform ◽

Transport Equation ◽

Unique Solution ◽

Optical Depth ◽

Axial Symmetry ◽

Diffuse Reflection ◽

Infinite Medium ◽

Plane Parallel ◽

Emergent Intensity

The equation of radiative transfer in non-conservative case for diffuse reflection in a plane-parallel semi-infinite atmosphere with axial symmetry has been solved by Laplace transform and Wiener-Hopf technique. We have determined the emergent intensity in terms of Chandrasekhar's H-function and the intensity at any optical depth by inversion.

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Frequency Redistribution Effects in the Formation of Lyman α in Prominences and Their Influence on the Ratio of Hα to Lα

International Astronomical Union Colloquium ◽

10.1017/s0252921100065210 ◽

1979 ◽

Vol 44 ◽

pp. 53-55

Author(s):

R.W. Milkey ◽

J.N. Heasley ◽

E.J. Schmahl ◽

O. Engvold

Keyword(s):

Line Profile ◽

Large Fraction ◽

Partial Frequency ◽

Frequency Redistribution ◽

Partial Frequency Redistribution ◽

Emergent Intensity

The effect of partial frequency redistribution in the formation of Lyman α in the chromosphere has been discussed by Milkey and Mihalas (1973) and others, and it has been shown that in this case the coherency of scattering in the wings of the line substantially influences the line profile. Although there are non-negligible sources for La photons within a prominence, a large fraction of the emergent line photons are due to scattering of photons incident on the surface of the prominence so that one expects that in a prominence the frequency redistribution processes will play an important role in determining the emergent intensity.

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