Lecture #10a-- Heating, cooling, and ionization in the dark ISM


1) We have talked a lot about HII regions where ionization is maintained by a bright UV source (a hot star). But there are warm and hot regions of the ISM where ionization of hydrogen and metals is maintained by collisions with thermal electrons, such as in regions that have been shocked, or low density regions heated by cosmic rays or thermal conduction. The heating may be maintained, so that a quasi-equilibrium obtains, or it might be in a cooling environment where only the ionization has reached statistical equilibrium with the current prevailing electron temperature.
2) Line optical depth and "optically" vs. "effectively" thin gas-- If the radiative cooling is in lines, then the line radiation must not be re-thermalized or it can't count as cooling. One way to assure no rethermalization is if the photons escape in a single flight (optically thin gas). But they can also escape eventually, after many scatterings (effectively thin) as long as they are never rethermalized. Generally, that means as long as the photons are never "destroyed" by a collisional de-excitation of the transition. That can be a rare event if the electron density is low and radiative downward rates are much higher than collisional downward rates. Thus the radiative cooling function will hold not just for optically thin lines, but also for effectively thin lines.

3) Collisional Ionization and the "coronal approximation"-- This is the ionization approximation that goes into the "radiative cooling function". The assumption is that ionization is by collisions with free electrons, and recombination is radiative (but that's collisions with free electrons too, in a way). Since both ionization and recombination rates are proportional to free electron density, the resulting degree of ionization depends only on temperature, allowing it to be used in a temperature-dependent cooling law.