The Interstellar Medium

1 Introduction 2 Interstellar Extinction 3 Interstellar Gas 4 Interstellar Molecules 5 Formation of Protostars 6 Planetary Nebulae 7 Supernova Remnants 8 Hot Corona of the Milky Way 9 Cosmic Rays and the Interstellar Magnetic Field 10 Examples Appendix: Radiative Transfer

Radiative Transfer

Here we will study the interaction of light with matter. We will not employ quantum mechanics, but will use emission and absorption coefficients to describe the interactions.
Let's first give a simple mathematical description of radiation.

Radiation Field

Describing blackbody radiation is fairly easy because it is homogeneous (uniform in space) isotropic (meaning it is similar in all directions, there are no preferred directions) in a container. We simply need the eneergy density \(u_\nu\) associated with the frequancy \(\nu\) and use Planck's law: $$u_\nu = \frac{8\pi h}{c^3}\frac{\nu^3}{e^{\frac{h\nu}{k_B T}}-1}$$

However, radiation is not isotropic in general. For example, the light entering a room from a window has a direction. This is non-isotropic.
For such situations, we need to define a non-isotropic radiation field.
Consider a small area \(dA\) at some point in space. Let radiation of energy \(dE_\nu d\nu\) be passing through this area in time \(dt\).
This light comes from the direction \(\theta\) from a solid angle of \(d\Omega\) and lying in the frequency range \(\nu\) to \(\nu+d\nu\)