<p>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.</p>

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

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

<p>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.</p>

CC BY-SA 3.0
2015-11-26T11:24:32.933Z
Thank you for you considred response Rob. I have some further questions. If cooling is not achieve quickly, will this then mean that the gas collapse will eventually stop because of the increasing pressure force due to the thermal energy of the gas? I'm thinking that this could then be sustained if there is some input of energy in which the gas is heated to a temperature comparable to the virial temperature of the halo to sustain the pressure force...?
MichaelJRoberts
CC BY-SA 3.0
2015-11-26T12:09:05.900Z
@MichaelJRoberts Yes, hydrostatic equilibrium is a very crude approximation. There are energy inputs - shockwaves from supernovae for example. Also, the gas is not very dense and the cooling times will be long and cooling is less efficient once temperature exceed a million degrees. If I've done my sums right, for gas densities of $10^{-4}$ per cc and $T=2\times10^{6}$ K, the gas takes billions of years to cool, even without energy input.
ProfRob
CC BY-SA 3.0
2015-11-26T07:32:53.413Z
2015-11-26T07:32:53.413Z
ProfRob
<p>This question relates to a diffuse hot gas halo of our Milky Galaxy. I've read that there is a hot diffuse halo of gas surrounding our Galaxy (NED, Caltech)</p>

<p>I was wondering why such a halo can exist? Why doesn't it collapse to a disk shape? Is it because the gas itself is still hot and so remains largely unaffected by the Galaxy potential?</p>

<gas>
Gas halo of our Milky Way Galaxy
MichaelJRoberts
# Gas halo of our Milky Way Galaxy

(Asked by: username_0 on 2015-11-26)

This question relates to a diffuse hot gas halo of our Milky Galaxy. I've read that there is a hot diffuse halo of gas surrounding our Galaxy (NED, Caltech)

I was wondering why such a halo can exist? Why doesn't it collapse to a disk shape? Is it because the gas itself is still hot and so remains largely unaffected by the Galaxy potential?

**Tags:** gas

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## 1 answers

### Answer by username_1 on 2015-11-26. Score: 9 | Accepted answer

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 $g = 2\pi G \sigma$, 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.

> **Comments:**
> **username_0**: Thank you for you considred response Rob. I have some further questions. If cooling is not achieve quickly, will this then mean that the gas collapse will eventually stop because of the increasing pressure force due to the thermal energy of the gas? I'm thinking that this could then be sustained if there is some input of energy in which the gas is heated to a temperature comparable to the virial temperature of the halo to sustain the pressure force...?  
> **username_1**: @MichaelJRoberts Yes, hydrostatic equilibrium is a very crude approximation. There are energy inputs - shockwaves from supernovae for example. Also, the gas is not very dense and the cooling times will be long and cooling is less efficient once temperature exceed a million degrees. If I've done my sums right, for gas densities of $10^{-4}$ per cc and $T=2\times10^{6}$ K, the gas takes billions of years to cool, even without energy input.  

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