# A mathematical description of the physics behind Aurora?

• dykuma
In summary, the conversation discusses the physics behind auroras and the factors that contribute to their colors and wavelengths. The main question is how to calculate the chances of molecules emitting light at specific altitudes and wavelengths. Despite familiarity with related equations and concepts, the conversation concludes with a request for a more statistical approach to determining the colors present at different altitudes for different molecules.
dykuma
TL;DR Summary
How do you calculate the chance that a molecule (let's say O2 or N2) will emit light at a specific wavelength?
Maybe a bit of an odd question (not really sure where it would belong on this site to be honest), but I was wondering if anyone can explain, or at least knows of a source that explains in a quantitative way, the physics behind aurora?

Now I've seen websites like this that discuss conceptually how an aurora occures. The basic premise behind the phenominon seems to be a tight balancing act between the number of gas particles (air pressure), the chance that the molecule will get enough energy to emit light at a specific wavelength, the time it takes for the excited molecule to emit that energy as light (between seconds for green light, and minutes for red light), and the chances of something quenching the reaction (collisions with other molecules stealing the energy before it could be emitted as light).

I'm familiar with the Stern-Volmer equation (which might not be helpful here) and the concept of quenching, where the quenchers here seems to be atmospheric pressure and the quantity of the excitable molecule. What I want, more or less, is a way to calculate the chance of a molecule emitting light at a given wavelength at a given altitude. Specifically, I'm interested in a mathematical way to explain the colors of lighting (blue at lower altitudes and red at higher altitudes due to N2) and the colors of aurora (green at lower altitudes, red at higher altitudes due to O2). However, I can't find much on calculating something like this. Does anyone know anything that can help me?

Last edited:
dykuma said:
Summary:: How do you calculate the chance that a molecule (let's say O2 or N2) will emit light at a specific wavelength?

, I'm interested in a mathematical way to explain the colors of lighting (blue at lower altitudes and red at higher altitudes due to N2) and the colors of aurora (green at lower altitudes, red at higher altitudes due to O2).
Blue is only rarely be produced. In the 100's of aurora I have seen and/or photo'ed I don't think I have ever seen blue.
Green is the most common colour with red above it. Yellow would be the 3rd most common colour, mainly produced by mixing.

I have no way of describing it mathematically, maybe look for some articles neon shop signs, the process is pretty much the same.

davenn said:
Blue is only rarely be produced. In the 100's of aurora I have seen and/or photo'ed I don't think I have ever seen blue.

I should have clarified, I was asking about the colors/wavelengths of light of excited gasses (N2 and O2) as a function of altitude. Lightning at lower altitudes is blue, where light from excited nitrogen is dominate, and I was considering the excitation due to lower and upper atmospheric lightning to be roughly the same as aurora, though obviously both are initiated by very different processes (usually).

Anyway, I have a rough understanding of how atoms with electrons level emit light, or how vibrational modes of molecules do the same. My question was more directed at a more statistical approach to figure out the idea altitudes for various emissions. Using your neon sign analogy, if I were to excite a column of air, what I'm looking for it a way to determine what colors are present at a certain altitude for a given molecule.

davenn

## What is an Aurora?

An Aurora, also known as the Northern or Southern Lights, is a natural light display in the Earth's sky. It is caused by the interaction of charged particles from the Sun with the Earth's magnetic field.

## What is the mathematical description of the physics behind Aurora?

The mathematical description of the physics behind Aurora involves the study of plasma physics, electromagnetism, and atmospheric physics. It includes equations that describe the behavior of charged particles in the Earth's magnetic field and the interaction of these particles with the Earth's atmosphere.

## How does the Earth's magnetic field affect the formation of Aurora?

The Earth's magnetic field plays a crucial role in the formation of Aurora. It guides the charged particles from the Sun towards the Earth's poles, where they collide with atoms and molecules in the atmosphere, causing them to emit light.

## What causes the different colors in Aurora?

The colors in Aurora are caused by the different types of atoms and molecules in the Earth's atmosphere. For example, oxygen molecules produce green and red light, while nitrogen molecules produce blue and purple light. The altitude at which the collisions occur also affects the color of the Aurora.

## What are the factors that affect the intensity of Aurora?

The intensity of Aurora is affected by several factors, including the strength of the solar wind, the strength of the Earth's magnetic field, and the altitude and density of the Earth's atmosphere. The time of day and the season can also play a role in the intensity of Aurora.

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