How Would These Phenomena's Occur?

The Aurora Borealis or otherwise known as the "Northern Lights" most often happens because of Solar Winds which from the Sun is pushing the Earth's Magnetic fields or it happens when energectic particles (which is protons and electrons) enter the Earth's Magnetosphere. When disturbances happen in the Solar Winds, the particles are accelerated along field lines, this makes it more dense near magnetic poles which eventually ends up as precipitation into the Earth's ionsphere.

The "Green Ray" is a very rare phenomena that is usually found in the very famous Bermuda Triangle. It only occurs after a total sunset and after sunrise. It looks like a green disc right above the sun that only last for a few minutes. It is caused by a refraction of light in the atmosphere.