Lecture #9a-- radiative cooling with metals



1) The dominant radiative cooling process in most astrophysical plasmas at intermediate temperatures (say 1000 to 10,000,000 K) is when free electrons collide with ions containing bound electron, excite the bound electrons, who then de-excite and emit line radiation that escapes the system. (At lower temperatures, collisional excitation by molecules dominates, and at higher temperatures, brehmstrahlung and inverse Compton scattering dominate). A particular version of this cooling appears in the absence of ionizing radiation (so not in HII regions), where collisions with free electrons also control the ionization stage of the gas. This type of cooling depends trivially on the free electron density (it is proportional to it, if considered to be a per-particle cooling, due to the collision rate dependence), so the only nontrivial dependence is on the electron temperature. The electron temperature controls the fraction of free electrons with the necessary energy to excite the transitions, and it also controls the ionization state of those ions. So we can define a "radiative cooling function", depending on T, for these situations, as shown here.
2) The key feature of this cooling function is that it rises with temperature if T is not too high (below about 200,000 K), as there are more and more free electrons with the few-eV energies needed to excite the main transitions. But as you crest over 200,000 K, you begin to strip most ions (except iron) of all their bound electrons, and the cooling turns over and decreases with temperature. This region of falling cooling as T rises is thermally unstable unless the heating also falls with T, because otherwise higher (or lower) T leads to less (or more) cooling and yet higher (or lower) T. As a result, we rarely find gas in equilibrium between 200,000 K and 1,000,000 K, it is a transitional state (called the "transition region" in the Sun) where the gas is always on its way to higher or lower T, depending on its history. Something similar happens when molecular cooling kicks in at much lower temperatures around 10-100 K, not shown in this cooling curve.