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“Dark matter”, in astronomy, usually means “cold, non-baryonic dark matter”. This is a form of mass which reacts with other matter via only gravity – and, possibly, the weak force – and which comprises approximately 80% of all matter in the universe. There is also “baryonic dark matter”, which is just ordinary matter, like dust, gas, rocks, and even stars that does not emit radiation yet detected by our telescopes (or absorb it, from more distant sources). And there is also “hot, non-baryonic dark matter”, which is just neutrinos.
The first hints of the existence of dark matter came from an analysis of the line-of-sight velocities of galaxies in the Coma cluster, by Fritz Zwicky, in the early 1930s. Zwicky found that the galaxies are moving much too fast for them to be held together in a cluster, by gravity, if the only mass in the cluster is that in the galaxies themselves (it’s pretty obvious that the galaxies form a bound system). Since Zwicky could find no evidence of mass in the Coma cluster, from the light detected by the telescopes he used, other than in the galaxies, he postulated that there is a lot of matter that is ‘dark’ – does not emit light.
Fast forward to the early 1970s, and the discovery of diffuse x-ray emission from the Perseus and Coma clusters.
Zwicky was right, the Coma cluster contains a great deal of mass outside the galaxies, and that matter does not emit light (it emits x-rays), because it is very hot. But this thin plasma is still not enough, mass-wise, to explain why the galaxies are gravitationally bound to the cluster (and the Coma cluster is nothing special; today we know of thousands of clusters just like it). Further, the plasma is also gravitationally bound to the cluster, but does not have enough mass itself to keep it there. Some more mass is needed, and that mass is dark matter.
Around the same time, Kent Ford and Vera Rubin made a similar discovery, concerning spiral galaxies; namely that they must contain a lot more matter than could be inferred from the stars, gas, and dust observed by various telescopes, in order for the galaxies to be rotating as fast as they are. Dark matter had been discovered in galaxies.
Universe Today, as you’d expect, has many stories and articles on dark matter; here is a random selection for your reading pleasure: Dark Matter Detector Heading to the ISS This Summer, Dark Matter Maps, and First Dark Matter Galaxy Discovered.