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In an other recent question is said that because of diffusion and thermal causes oxygen and nitrogen are mixed. Nevertheless oxygen is a little bit heavier than oxygen so it should be lower in the atmosphere.

In an other question I read:

"This is why there is a color differential with altitude; at high altitude oxygen red dominates, then oxygen green and nitrogen blue/red, then finally nitrogen blue/red when collisions prevent oxygen from emitting anything."

What causes the beautiful Auroras on the north and south magnetic poles?

So my question is why is at high altitude more aurora from oxygen while concerning diffusing it shouldn't make a difference and because of oxygen is heavier it should be lower.

But in case of an aurora it is higher, so why is that? What makes all the differences in auroras?

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    $\begingroup$ Was the comment about atomic oxygen ($O$) or about molecular oxygen ($O_2$)? The is essentially no atomic oxygen at sea level (or anywhere within the bottom 15km), but there is plenty at very high altitudes where solar radiation can break molecules apart and/or ionize them. $\endgroup$ – Wolfgang Bangerth Feb 2 '16 at 2:55
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The visible emissions from atomic oxygen take place between the fine structure levels of the ground state, and transitions between these states are not quantum-mechanically allowed by electric-dipole radiation. These "forbidden" transitions take much more time to occur, proceeding by magnetic dipole or electric-quadripole radiation. As a result the atom spends a long time in the excited state (~1sec for the 557.7 nm transition, and ~200 s for the 630 nm transition), during which time the atom can make collisions and deactivate without radiating. However, the emissions from molecular nitrogen take place between dipole-allowed transitions, and spend only ns to micro-seconds in the excited state before radiating. Thus, they survive to radiate even in high collision conditions (i.e. low altitudes).

The frequency of collisions an atom or molecule makes increases with decreasing altitude. In addition, the higher the energy of the auroral electrons (2 keV to 20 keV), the lower in the atmosphere they deposit the energy (150 km to 90 km). If there are low energy electrons in the aurora, the emission occurs at very high altitude and both the excited atomic oxygen and the molecular nitrogen make few collisions. Thus they both radiate, but at these altitudes there is more atomic oxygen than molecular nitrogen and the reds and greens of atomic oxygen dominate.

As the auroral energies increase and the electrons deposit their energy at lower altitudes, collisions are much more frequent and the atomic oxygen excited states do not live long enough to radiate. This kills off the green and red emissions at low altitudes. However, the molecular nitrogen, with its short excited state lifetimes, continues to radiate and the lower border of the aurora turns pinkish-purple with the nitrogen emissions.

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Short answer:

Oxygen atoms (not oxygen molecules) cause the dominant red and green auroral emissions at high altitudes. Although there is more atomic $\ce{O}$ at higher altitudes than nitrogen, the key to understand the different colours is the excitation energy. Auroral particles with higher energies penetrate deeper down into the atmosphere causing higher energetic emissions at lower altitudes. The excitation leading to the red $\ce{O}$ emission higher up needs less energy than the green $\ce{O}$ emission further down. Even more so, the purple $\ce{N2+}$ emission at the very bottom can only be excited by very energetic particles.

Some more details:

You are right to note that molecular oxygen ($\ce{O2}$) is heavier than molecular nitrogen ($\ce{N2}$). Hence, at altitudes above the turbopause at around 105 km, where turbulent mixing ceases to exist because the atmosphere gets too thin, there is relatively more $\ce{N2}$ than $\ce{O2}$ and the ratio between the two increases with altitude. However, there is also strong photodissociation of molecular $\ce{O2}$ to atomic $\ce{O}$. As the recombination of two $\ce{O}$ atoms is slow at high altitudes and the atoms are light, their concentration increases with altitude. Above about 200 km atomic $\ce{O}$ becomes more abundant than $\ce{N2}$.

As stated before, auroral particles with higher energies deposit more of their energy at lower altitudes where they encounter more collisions with the air. Lower energetic particles don't get that far. The dominant red and green emissions of the aurora are basic excitions of the $\ce{O}$ atom. The red emission at around 630 nm peaks at above 200 km. altitude. It's caused by the excited state $\ce{O}^1D$ with an energy of $\sim5.6$ eV. The green emission at around 558 nm peaks at around 110 km, considerably lower than the red emission. The corresponding state $\ce{O}^1S$ has a higher excitation energy of around $10$ eV. Peaking even lower at around 90 km altitude, the violet $\ce{N2+} $ emission has a wavelength around 428 nm and an excitation energy of around $100$ eV.

The combination of the concentrations of the chemical species and, most importantly, the altitude dependent energy deposition result in the altitude dependence of the colours of the aurora. The further to the violet the light, the higher its energy per photon.

Note that these discussions about what colour is caused by what atom or molecule at what altitude are somewhat simplified. This all only refers to the dominant emission at a certain peak altitude which may overpower fainter colours. To a certain degree, most colours will be emitted from most altitudes, but not be visible to the ground observer. And there are many more colours emitted than the ones discussed.

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