Gas halo of our Milky Way Galaxy

The scale height of gas in a disk (if it were in equilibrium) is roughly $kT/mg$, where $T$ is the temperature, $g$ is the gravitational field, $m$ the mean mass of agas particle, and $k$ the Boltzmann constant.

If we assume most of the mass is in a thin disk, then Gauss's law for gravitation tells us that that $g = 2pi G sigma$, where $sigma$ is the mass per unit area in the disk. According to Rix & Bovy, $sigma simeq 70 M_{odot}$ pc$^{-2}$ at the location of the Sun (http://arxiv.org/abs/1309.0809).

If we assume hydrogen gas, then the effective particle mass is that of a proton, and this means the gas scale height is
$$H = 4300 left(frac{T}{10^6 K}right) pc$$

Thus gas hotter than a million degrees will have a very substantial scale height and is not expected to be confined to the Milky Way disk.

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