How are they formed?
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In short, aurora is created by the collision of electrons originating from the sun with different gases in the atmosphere of the earth. This collision causes light to be released which we then see as aurora.
In a bit more detail, auroras are caused by solar activity and the way it interacts with the magnetic field that surrounds our planet. In addition to this, the gases oxygen and nitrogen that can be found in the atmosphere of the earth play a role. Solar particles (electrons and protons) originating from the sun travel continuously to the earth and hit the magnetic field of the earth. Due to magnetic forces, these solar particles are guided along the protective shell of the earth. As a result of this process, the particles reach two ring-shaped regions which are referred to as the Auroral Ovals. One of them is located close to the North Pole and the other one close to the South Pole (see picture below). For different solar activity, the size of those regions vary. The greater the activity the greater is the area. The current Aurora Ovals can be found here.
During cycles of increased solar wind activity, which are referred to as Solar Flares and which are caused by a higher amount of sunspots, enlarged numbers of particles travel between the sun and the earth. When they hit our magnetic shield they somewhat change the form of it. The Magnetopause, which normally prevents the solar particles from entering the earth’s atmosphere, “breaks”. As a result of this, a number of charged particles enter the atmosphere of the earth at the Auroral Ovals and interact with gases – namely oxygen and nitrogen. During the process of calming down after being excited by the sun particles, light is produced by the molecules of the gases. If a large enough number of collisions occurs, this light is visible as aurora for us. The whole process is showed in the graphic below.
Aurora is, in fact, a proof that particles do affect the magnetic field of our planet.
Note: this is a simplified explanation of the whole process. For a more scientific explanation, we recommended this video.
The post on Wikipedia about Northern Lights is highly recommended if one searches for an easy to follow more extensive explanation of the formation of Northern Lights.