Mathematics of Auroral Viewing
When you view the aurora, whether by camera or by being outside with your eyes, what you see is a line integral of the line-of-sight brightness of the optically thin aurora. Mathematically, this is
I = ∫_0 ∞ p(ℓ) dℓ
- I is the intensity seen by your eye or camera pixel
- p(ℓ) is the volume intensity rate of the aurora at each differential point along ℓ
Volume emission rate of aurora is created when particles (electrons or ions) strike the cold gas of the ionosphere, typically N_2, N_2+ or O. As altitude increases above a couple hundred kilometers, oxygen starts to become the dominant gas instead of nitrogen. This affects the color of the aurora, and is part of why aurora appears as green below red.
Unfortunately, many of the images taken of aurora with digital cameras have incorrect white balance, and completely non-physical colors are seen. Yes, there is purple aurora, but it is quite faint and below the green emissions in altitude. So a sky full of purple, yellow, and orange is not believable, it’s an artifact of incorrect white balance.
That’s a big part of why it’s good to save auroral photos in RAW format from your camera so you can fix the images in post-processing.