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Astron. Astrophys. 358, L33-L36 (2000)

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2. The line transfer equations

In order to model the individual line of a particular molecule one needs to solve the Non-LTE line transfer equations. The two level atom line transfer equation in the plane parallel stratified medium can be written as (Mihalas 1978)

[EQUATION]

where µ is the cosine of the angle made by the ray to the normal. The total absorption coefficient [FORMULA] where [FORMULA] is the frequency integrated line absorption coefficient, [FORMULA], [FORMULA] is the absorption coefficient for the continuum and [FORMULA] is the line profile function. The source function is given by

[EQUATION]

where [FORMULA] is the continuum source function which is set equal to the Planck function [FORMULA] and the line source function [FORMULA] is written as

[EQUATION]

where [FORMULA] is the probability per scattering that the photon is destroyed by collisional de-excitation and is given by (Mihalas 1978) [FORMULA] [FORMULA] is the rate of collisional de-excitation and [FORMULA] is the rate of spontaneous emission. R is the redistribution function defined according to a hybrid model prescription by Rees & Saliba (1982) and is given by [FORMULA] where [FORMULA] is the phase function and [FORMULA] is the angle-averaged frequency redistribution function for isotropic scattering.

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© European Southern Observatory (ESO) 2000

Online publication: June 8, 2000
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