Photographing the aurora, also known as the northern or southern lights, is a challenging but rewarding endeavor for photographers. The aurora is a natural light show that occurs in the upper atmosphere and is caused by the interaction of solar particles with the Earth's magnetic field. Here are some tips to help you capture stunning aurora images:

1. Plan your trip: The best place to see the aurora is in an area with minimal light pollution, such as the Arctic or Antarctic regions. Check the aurora forecast and plan your trip accordingly. In my area, I am usually looking for an area facing south by the coast with little light pollution (I am based in Victoria, Australia), however the closer you can get to the poles the better.
2. Use a tripod: Auroras are typically captured using long exposures, which can cause camera shake if you are not using a tripod. A sturdy tripod will ensure that your camera remains still during the exposure and will help you capture sharp images.
3. Use a remote shutter release: A remote shutter release is a great tool for aurora photography, as it allows you to take the picture without touching the camera, which can cause camera shake. You can also use a self-timer function on your camera.
4. Set your camera to manual mode: Auroras require a lot of control over your camera settings, and manual mode will allow you to adjust your aperture, shutter speed, and ISO to achieve the desired effect.
5. Use a low ISO: A low ISO (typically between 100-400) will help reduce noise in your images and will result in a cleaner and sharper image however, note its better to have a noisy image than no image at all so don't be afraid to push the ISO higher if you need to.
6. Use a wide aperture: A wide aperture (typically between f/2.8-f/5.6) will help to capture as much light as possible and will result in a brighter image.
7. Experiment with shutter speed: Experimenting with different shutter speeds can produce different effects in your aurora images. For example, using a faster shutter speed will freeze the action and capture the aurora in sharp detail, while using a slower shutter speed will create a blur effect that gives the sense of movement.
8. Use a cable release or remote trigger: This allows you to trigger the camera without touching it, which reduces the chance of camera shake and blur.
9. Take multiple shots: Auroras are constantly changing, so take multiple shots of the same scene to increase your chances of capturing the perfect image.
10. Use a wide-angle lens: A wide-angle lens will allow you to capture the full extent of the aurora and the surrounding landscape.

To give an idea of settings, I often start off with something like 10 seconds, f/2.8 and an ISO of 1600 and adjust from there, if I want to capture beams I will try and lower the shutter speed, its really a case of experimentation.

One important thing to note, is that you don't typically see the colour of the aurora to the naked eye, so don't be suprised if it looks dull and not as colourful to the eye (the camera is better at picking up colour than the eye). Futurism has a good article on what it may look like to the naked eye.

In conclusion, photographing the aurora is a challenging but rewarding endeavor that requires planning, technical skill, and patience. By following these tips, you can improve your chances of capturing stunning aurora images that you'll be proud to share. Remember to be safe and never put yourself in danger while trying to capture an aurora image. Also, be mindful of the surrounding and be respectful of nature and other people.