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Only 4% of the stuff in our universe is directly visible. Of the remaining 96%, 70% is a mysterious anti-gravitating substance called Dark Energy (see post 1 and post 2 for more). That leaves 26% of less crazy but still exotic stuff called Dark Matter.

Dark Matter cannot be seen, but its presence can be deduced from its gravitational pull on other visible stuff in the universe. It is now believed that each galaxy has a spherical halo of dark matter, typically larger than its size. Recently, using the Chandra X-Ray Observatory, a most dramatic evidence of galactic dark matter was observed - perhaps bringing us the closest we've been to actually seeing this exotic stuff. Two galaxies underwent a graceful collision, each dragging with it its dark matter halo (see post on galaxy collisions). See attached first video for a simulation. The red stuff in the video is visible matter/gas; the blue, dark matter. As the stars and gas in the galaxies skimmed past each other and slowed down, the dark matter whizzed by, past the colliding visible stuff: dark matter interacts weakly hence can travel further during a collision. This effect could be seen in the motion of the visible gas in the galaxies as the dark matter pulled on it and slowed the collision - like the effect of molasses or air drag! 

Currently, there are several candidates for what dark matter may be, from the least exotic to the most lunatic. On the least crazy side, dark matter may be made of MACHO's… yes, MACHO stands for MAssive Compact Halo Object: dead stars - rather small brown dwarves, black holes, neutron stars - littering the universe. We can't see them, but they pull on things gravitationally. Another more exotic category are WIMP's… WIMP stands for Weakly Interacting Massive Particles: subatomic particles that we have not yet discovered in our labs that (1) interact weakly with the rest of known particles - and are hence difficult to detect; and (2) that have potentially large mass, perhaps large enough that it is too energetically costly to create them in the lab. WIMPs can come in different flavors: lame neutrinos (see post on neutrinos), and/or particles needed to have supersymmetry in Nature (see post on supersymmetry), and/or particles that arise from having a universe that has more than three spatial dimensions (see post on higher dimensions). Beside MACHOs and WIMPs, there are other possibilities as well, the most interesting of which are axions - light particles that have an intimate relation to the nuclear force. In short, we have no clue what dark matter is at this point in time. But the thrill of the chase is the way physicists earn their paychecks after all…

The second video accompanying this post is a general discussion of what is known about dark matter so far.

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