# Would the >100 km "knee" in Earth's atmosphere still be where MFP exceeded scale height if it were pure Ne or Ar?

There is currently one answer to How many solar system bodies have "knees" in their atmospheres? that points out that somewhere above roughly 100 km turbulent mixing drops off (thus the name turbopause) and that's the reason that the exponential rate of density fall off with altitude drops off so much, not that the average mass of atmospheric particles change from N2/O2 to monatomic oxygen with half the mass (and double the scale height).

I think the point there is that scale height is no longer a meaningful concept at this density. This comment on a different "knee" question says:

Let's never mind the fact that in these altitude ranges, it makes more sense to talk about atmospheric density than it does atmospheric pressure, as the mean free path of gas atoms and molecules is so long that the continuum assumption breaks down.

Going significantly above 100 km the mean free path (MFP) of atoms becomes kilometers and then tens of kilometers!

So a pure noble gas atmosphere makes for a good Gedankenexperiment since there is no change of particle mass at some altitude.

Question: I'm still trying to understand the actual origin of the "knee" in Earth's atmosphere that happens beyond 100 km. If Earth's atmosphere were made of pure neon or argon instead of mostly diatomic gases, would it still have a knee somewhere around there, where the mean free path exceeded the scale height?

• Earth's atmospheric continuum breaks down in the Exosphere at 1000km, not at 100km. There is nothing exotic about a change in density scale height. Realistic atmospheres or density structures inside of gas giants have non-constant scale heights. Strictly speaking, only a perfectly isothermal atmosphere has a constant scale height everywhere, otherwise it is $H=H(r)$. Commented Feb 5, 2021 at 16:29

There are a lot of phenomena at play here.

First of all, you already mentioned there's a factor of changing atmospheric composition. This one is easiest to understand. Consider a very simplistic model where your atmosphere have no turbulent mixing, there are just 2 type of gases and temperature of that gas is constant everywhere. Then you can model each gas with a simple model where gas density decays exponentially with height (but with different scale parameters) and these gases do not influence each other. Therefore at any given height this simplistic atmosphere can be modeled as a sum of densities of your two gases at this height

Now consider that one gas is 10x heavier (in terms of molecular weight) than other and it takes 90% of atmosphere at ground level. Let's play with our toy model in Python

import numpy as np
import matplotlib.pyplot as plt

h = np.linspace(0, 5, 100)
gas1 = 0.9 * np.exp(h * -10)
gas2 = 0.1 * np.exp(-h)
rho = gas1 + gas2
proportion = 100 * (gas1 / (gas1 + gas2))

plt.subplot(121)
plt.semilogy(h, rho)
plt.grid()
plt.title("Density")
plt.subplot(122)
plt.plot(h, proportion)
plt.grid()
plt.title("Proportion of gas 1 (%)")
plt.show()


You can see a clear knee in this model and change in atmospheric composition that starts at 90% heavy gas but quickly gets to 100% of light gas at high enough altitude. Once composition changes sufficiently, so does the slope of density chart. As you can see we did not needed anything here to get a knee except for 2 gases with sufficiently different density.

Now, the real atmosphere is of course a lot more complicated. One factor is a turbulent mixing of gases below certain height. This mixing makes atmosphere to act like it was a single gas with some "average" molecular weight rather than sum of non-interacting gases. In practice this means that "heavy" gas goes higher than it would in a simplistic model without turbulent mixing. But turbulent mixing is driven by heat (mostly heat of of Earth surface) and amount of available energy limit it in how high it can go. So at some altitude there's a transition between atmosphere dominated by turbulent mixing and atmosphere dominated by gas diffusion. This makes change in atmospheric composition and therefore "knee" more pronounced because turbulent mixing produces different mix at high altitude than diffusion.

Now, so far we were talking about atmosphere with constant temperature. This is unrealistic, temperature of real atmosphere changes considerably with a height. We get a lot of energy from Sun and some of it comes in form of UV and even X-ray light with highly energetic photons. Atmospheric gases absorb such photons well but this process goes only for highest layers of atmosphere because photons are absorbed before they can pass deep enough. A net result is a sharp and very strong increase of atmosphere temperature at high enough altitude. Furthermore, absorption of some of those energetic photons result in dissociation of molecules like O2 into simpler monoatomic gases. Both those processes (dissociation and high temperature) greatly reduce gas density and make it essentially "much lighter" for purposes of scale height. This means that even if you take pure noble gas atmosphere, rapid change in temperature will still produce two layers in it, "cold" layer of gas below some altitude and "hot" outer layer of gas that will behave differently. However it will be less pronounced than in earth-like atmosphere.

To sum things up:

1. Atmosphere naturally separates in layers of different gases above certain altitude
2. Lighter gases replace heavier ones because they have bigger scale height and their density decreases slower than density of heavier gases
3. Solar light naturally produces outer layer of gas in atmosphere that behaves like it's very "light" and therefore have large scale height, very different from gas of lower levels

All these factors tend to produce "knee". However in case of Earth, I'd bet that main factor is the solar light.

You can still get an atmosphere without a knee, but you'll need to move your planet away from any sources of light and make sure that its atmosphere is composed from gases with similar density. A distant gas giant with pure hydrogen atmosphere maybe?

• +n! This is a very thoughtful and informative answer, thank you for addressing several different aspects of the problem and describing how they interact! I've numbered your closing points so that we can discuss them directly. I wonder if point #2 applies mostly above the altitudes where mixing keeps them uniform (described in point #1)? Should point #2 begin "Above that altitude..."?
– uhoh
Commented Feb 6, 2021 at 2:06
• Well, I wrote that "even if you take pure noble gas atmosphere, rapid change in temperature will still produce two layers in it, "cold" layer of gas below some altitude and "hot" outer layer of gas that will behave differently". But that applies only to planet that receive enough sun light, so you might get or not get a knee depending on how far the planet is located from its star. Commented Feb 8, 2021 at 16:07
• Oh sorry, I missed that sentence, looks great!
– uhoh
Commented Feb 8, 2021 at 21:54