Nereid said:
Would it be OK everyone if we do some exploring, and assume some conditions? I'm interested to get some OOM answers.
I'll do my best. Before we get into specifics, it's worth mentioning a few standard numbers. A professor in this department is writing a book on the subject, so I'll take these from his class notes. There are several "phases" of the ISM:
Coronal Gas: T\gtrsim 3\times 10^5 K, n \simeq 0.003~cm^{-3}, f \simeq 0.4
HII: T\simeq 10^4~K, n \simeq 0.3 - 10^4~cm^{-3}, f \simeq 0.1
HI Warm: T\simeq 6000~K, n_H \simeq 0.3~cm^{-3}, f \simeq 0.5
HI Cool: T\simeq 100~K, n_H \simeq 20~cm^{-3}, f \simeq 0.02
Diffuse H
2: T\simeq 60~K, n_H \simeq 20 - 100~cm^{-3}, f \simeq 0.01
Dense H
2: T\simeq 10 - 100~K, n_H \simeq 100 - 10^6~cm^{-3}, f \simeq 0.0005
where f is the fraction of the volume of the galaxy composed of that phase. We'll need these numbers to calculate some of the relevant timescales. Also, it's worth just reviewing the big picture for a moment.
Except for the dense H
2, most of the ISM is in approximate pressure balance (you can check for yourself by multiplying the temperatures and densities). Why is the H
2 not in pressure balance? Because it's contained in self-gravitating clouds in which a pressure gradient is required for support.
What about the filling factors? Well, the numbers above would indicate that the majority of the volume is made up of HI and coronal gas, while the majority of the mass is in a combination of HI and molecular gas. It would make sense that the molecular gas isn't a large fraction of the volume, being so dense.
Anyway, one of the most important questions when we're talking about equilibrium is the time it takes to reach a Maxwellian velocity distribution. In absence of this, you can't say much of anything about the gas, so we hope that the timescales are short (enough). It turns out that the timescale for electrons to thermalize from scattering off protons is:
t_s = \frac{3.8 \times 10^5 sec}{ln \Lambda}(\frac{T}{10^4 K})^{3/2}(\frac{cm^{-3}}{n_p})
The term with the natural log is called the "Coulomb logarithm" and is calculated based on the Debye length in the ISM. ln\Lambda typically has values of order 20-30, meaning that most of the electrons in the ISM will thermalize in less than a year. Even the longest timescale (~100 years for the coronal gas) is much shorter than the timescales on which conditions in the ISM typically change.
That's only for the electrons, however. If photoionization is the primary heating mechanism, then in order to thermalize the protons, you have to exchange energy from the electrons. This happens during scattering and the timescale is given roughly by:
t_{s,p}=\frac{m_p}{m_e}t_{s,e}
This will make the timescale longer by about a factor of a thousand, maximizing at about 10
5 years for coronal gas. Even that is less than the typical timescale for dynamical change in the ISM, so most of the gas we see should be in an approximately Maxwellian distribution.
I know I didn't answer all of your questions directly and there's a lot more, but let's just start there. Does this answer any of your questions? What else would you like to know?