How Do You Measure Something You Can't See?
Dark matter can only be found through its gravitational effect on surrounding astronomical objects and matter such as galaxies. Gravity pulls and moves things toward it and bends light.
When scientists observe galaxies and clusters of galaxies, they observe deflection and bending of light around the foreground galaxies that requires a much greater amount of matter, or gravity, to do the light-bending than exists in the mass of the stars in the galaxies, thus requiring additional dark matter. Scientists measure the difference between the expected velocities or the expected bending of light based simply on the observed galaxies assuming no dark matter, versus the actual observed velocities or bending of light, which are much higher, and use the difference to determine the needed amount of dark matter that can cause these observed gravitational effects.
"Cheshire Cat" shows a beautiful example of the bending of light as it passes close to the mass/gravity of the galaxies which bends and distorts the light- rays, showing the need for dark matter.
Detection
However, dark matter cannot be detected. We can simply determine that it is there based on the evidence around it. Scientists all over the world are trying to figure out how to detect matter that does not interact with baryonic matter. Current experiments include particle colliders like the famous Large Hadron Collider (LHC) in Switzerland as well as underground direct detection experiments of the dark matter. This underground research creates environments that are essentially stable and clean because there is little background radiation, such as from the sun. As of yet, these have not yet detected the dark matter, but the threshold for detection is getting better. Hopefully in the next few years, we will see the first detection of dark matter.
If dark matter is not detected within the next few years, scientists will have to seriously consider what they have to do next to detect it and what may be missing from their understanding currently.
In the Bullet Cluster, the pink masses are hot gas and you can see them colliding. The blue masses on either side have passed right through without interacting with the hot gas. They are dark matter.
Alternate Solution?
Some scientists believe that there is a better solution to the gravity discrepencies we see. They propose that we just don't fully understand the laws of gravity and general relativity yet. They suggest that we may need to alter our current laws of gravity on a large scale by small amounts.
However, general relativity has been tested on many scales and has been confirmed. Therefore this theory does not hold much weight right now in the general scientific community.
3D map of the large-scale distribution of dark matter in the universe, using the Hubble Space Telescope.
"The exploration and ultimate detection of dark matter are led by experiments for direct and indirect detection of this yet mysterious particle."
- Neta Bahcall, PNAS Dark Matter Universe, 2015
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