What's the nature of intraction between hydrogen atoms in the interstellar medium? Interstellar densities are about 1 atom/cm$^3$. Do these atoms even move? If they do, why do they move? What would be their average speed? (Free expansion)
 A: The interstellar medium (ISM) has many components that vary in densities (see the table in the link to the ISM Wiki page). For the regions with densities in the $n_\text{ISM}\sim10^0\text{ cm}^{-3}$ range, the temperatures vary from between $(50,\,10^4)\text{ K}$. Using simple Boltzmann statistics, the mean thermal velocities of particles in the ISM could be
$$
v_\text{ISM}=\sqrt{\frac{3k_BT}{\mu}}\simeq(3,\,80)\text{ km/s}
$$
which seems pretty high, but recall that the solar system is moving at about 250 km/s around the galaxy.
ISM gas can also be pushed by astrophysical shock waves and pulled by gravitational collapse, both of which will cause motion in less-constant manners (depends on parameters of the shockwave or collapse). Further, if there are disordered magnetic fields in the ISM, the ISM can also be affected by these fields.
A: They move, at first because they once moved :-) . How do you stop them ?
Anyway the interstellar is not always cold, and it is even ultra hot at places. One of the reason is UVs travelling through, and thus bringing kinetics energy to atoms.
