The meaning of "diffuse" interstellar matter is imprecise and has changed over time. In its original sense it meant any gaseous matter outside the immediate environment of a star, but this has narrowed over time to imply gas that is easily penetrated by the galactic optical/UV radiation field. This is gas for which, locally, the attenuation of incoming radiation is not much greater than that for 1 magnitude of optical extinction. Diffuse gas is sometimes seen in isolation but it is also seen in directions having very high total extinction, for instance near the Galactic equator in the inner Galaxy. The outskirts of dark and molecular cloud complexes are diffuse gas.

Diffuse clouds on the other hand are intended to be discrete neutral gas parcels having modest attenuation of the radiation field, for instance a classical Spitzer H I cloud or the gas producing optical absorption lines toward nearby stars. Such things exist quite widely but are seldom imaged, as only their shadows (absorption lines) are apparent, complicating their definition. In any case, a discussion of diffuse gas is not entirely the same as a discussion of diffuse clouds.

In terms of the components of the ISM, diffuse gas is present as CNM (cold neutral medium) at temperatures below a few hundred Kelvin, WNM (warm neutral medium) and WIM (warm ionized medium) at 8000 K, and HIM (hot intercloud medium) at 10^6K. All of these are in rough thermal pressure equilibrium at p/k ~ 3000K/cc with volume filling factors ranging from a few percent for CNM to perhaps 20% for HIM+WNM, and 80-100% for HIM. Of course this interpretation, based on theoretical models of an ISM driven by supernovae explosions but traceable to Spitzer (1956), is an oversimplification that ignores molecular gas and molecular clouds even when they bear most of the mass.

This talk will concentrate on the colder, denser CNM bearing most of the atomic mass. It dominates the ISM in the outer Galaxy and carries about half the gas locally. The presence of this gas in observations follows from noting that its hydrogen is mostly atomic with H2 as a minority constituent, ~1/3 of the total on average near the Sun. C+ is the dominant form of gas-phase carbon with neutral carbon and CO each having perhaps a few percent of the total. Despite this, CO emission and some molecular absorption can be quite strong, giving the false impression of observing denser, more opaque material. H3+ is wildly over-abundant, with implications for the cosmic-ray flux.

To explain this it is necessary to consider the mechanisms of heating (mostly the photoelectric effect on small grains); cooling (CII and OI fine-structure transitions); ionization of carbon and metals (by photons) and hydrogen (cosmic-rays); atomic-ion recombination (radiative and assisted by small grains); formation of H2 (grain catalysis) and CO formation (recombination of HCO+); along with the thermal, chemical and ionization balance. I'll survey this all with a nod to understanding the diffuse molecular gas.