In astrophysical contexts one often encounters very hot and strongly radiating shock fronts. The following picture gives a cross section through such a shock front in the case of a forming star.

The horizontal axis is the cross section through this shock front in linear scales, the distance from left to right being 800,000 km. The upper left figure shows the luminosity of the shock front in units of solar luminosities, ie this shock front is producing 55 times as much luminosity as the sun. The upper right picture shows the material temperature, as opposed to the radiation temperature just below. Through the shock front the material temperature is rising from about 3000 to 7000 degrees Kelvin.

The material temperature increase is due to the strong viscous energy input through the shock front seen in the middle figure on the left. The radiation temperature, the middle figure on the right has, in contrast to the material temperature, no increase through the shock front at all. This is because the material temperature increase is on such a small scale that the photons cannot react to it, ie the mean free path of photons is larger than the 'shock thickness' (actually, the shock adjusts to such a thickness that this is the case). The optical depth, seen on the lower right figure, measures how many mean free photon paths there are between the outer boundary on the right and the point under consideration. The density increase through the shock and immediately after leads to the sharp increase in optical depth to the left.

Due to the radiation, this shock front is isothermal in the sense that the material temperature before and after the shock front are the same. This is why this shock front is called a radiation shock front.

More details on these shocks can be found in:

Balluch, M., 1991:"Structure and stability of steady protostellar accretion flows. I. The flow structure". Astronomy and Astrophysics, 243, 168-186.

Balluch, M., 1991:"Structure and stability of steady protostellar accretion flows. II. Linear stability analysis". Astronomy and Astrophysics, 243, 187-204.

Balluch, M., 1991:"Structure and stability of steady protostellar accretion flows. III. Non-linear instabilities". Astronomy and Astrophysics, 243, 205-218.

Such radiation shocks, for example, or other sources of luminosity, send their light out into space. Often, as in the case of forming stars, these light sources are surrounded by extended clouds of dust and ice particles, or simply gas of some kind. The light passes through these enveloping media and get transformed before they enter space and eventually arrive in our telescopes on Earth. In the case of the radiation shock of a forming star, such a spectrum looks like:

The amount of energy per wavelength is plotted against the wavelength of the light. Such a spectrum gives us clues on how the enveloping matter of the light source is structured (in this case one can see contributions of dust particles and ice-coated dust particles, as well as absorption features of different elements), but also on the light source itself. More information on calculating such spectra can be found in

Balluch, M., 1987:"Energietransport durch Strahlung in protostellaren Huellen''. Diploma Thesis in Astronomy, University of Vienna, Austria.