Based on lecture at http://www.mrao.cam.ac.uk/~kjbg1/lectures/

Chapter 2 : The Transfer of Radiation

When we observe astronomical source, along the eye path cloud matter may absorb the radiation , scatter or emit further radiation.

Absorption

Particle number density n, cross section of one particle is $\sigma_\nu$ ,  beam of area dA propagates a distance ds into the cloud , the totla absorbing cross section is $\sigma_\nu n ds$ ,   $I_\nu$ is 单色辐射强度。

$d I_\nu = - I_\nu n \sigma_\nu ds \equiv - \alpha_\nu I_\nu ds$

$\alpha_\nu = n \sigma_\nu$ is absorption coefficient, defined as the fractional loss of intensity per unit length, with dimensions m^-1. It follows that the PHOTON MEAN FREE PATH $l_\nu = 1/ \alpha_\nu$

Emission

Two ways of an excited atom return to ground state:

ii) stimulated into emission by the presence of electromagnetic radiation

Crossing a length ds a beam's specific intensity is increased by spontaneous emission by

Define the optical depth tau_nu

Example

The Radiative Transfer Equation