Is there a theoretical minimum on how low the auroras can occur in the atmosphere? Specifically, can they occur at around 40km up? (the height of a decent helium balloon)
 A: Auroras are produced by forbidden line radiation from excited atoms and ions - radiative transitions that are forbidden by electric dipole selection rules and therefore have very low spontaneous emission probabilities. If such an excited atom/ion exists in a high density gas then it is much more likely to be de-excited by a collisional interaction than by emitting a photon.
Each transition will have a density at which this "quenching" of the radiative transition occurs. Note that this is not an abrupt cut-off but simply the density at which collisional dexcitation becomes more likely.
Since the density of the atmosphere changes with height, then there is some correspondence between the quenching density and the height.
For these reasons it turns out that auroral emission occurs at above 80 km in the atmosphere - below which the various forbidden lines are quenched - but below about 1000 km, presumably because above that there are too few ions to produce significant emission.
Whether you could get significant auroral emission at 40 km would depend on the local state of the atmosphere, the amount of auroral excitation and what you meant by significant; but it seems unlikely.
