Can anyone point me in the direction of some resources - or know themselves - regarding the density distribution of the ISM? So far googling has turned up very little.
I realise there will be nuances relating to 'lumpiness' or turbulence, but any information on a general density distribution or a model based on different components would be greatly helpful.
Due to distinct plateaus in the cooling function of interstellar gas, densities and temperatures do not in general take any conceivable value, but are instead divided into certain phases. Because these phases are roughly (but definitely not always) in pressure equilibrium, in general the product of the temperature $T$ and density $n$ is constant. That is, the colder a phase is, the denser it gets (and vice versa).
I think the first to recognize this fact was Field et al. (1969), who considered two phases, a warm ($T\sim10^4\,\mathrm{K}$) and a cold ($T\sim10^2\,\mathrm{K}$) phase in the Milky Way.
McKee & Ostriker (1977) extended this with a third, hot ($T\sim10^6\,\mathrm{K}$) phase, created by supernova remnants. They also divided the warm phase into a neutral and an ionized phase.
In addition to this, there is an even denser phase that is so cold that molecules can form.
This leaves us with five phases, dubbed the molecular medium (MM), the cold neutral medium (CNM), the warm neutral medium (WNM), the warm ionized medium (WIM), and the hot ionized medium (HIM).
Although first based on the Milky Way, the interstellar medium of high-redshift galaxies seems to follow similar patterns. A very good review of the properties of these phases is given by Ferrière (2001). Her Table 1 gives the densities and temperatures. With additional information about the ionized fraction $x_\mathrm{HII}$ and the total volume filling factor FF of the gas from Brinks (1990), Caselli et al. (1998), Wolfire et al. (2003), Mihalas & Binney (1981), and Jenkins (2013), you have the following table:
Note that the above values are only approximate!
See also this answer to see the more or less universal cooling function that causes the different phases.
