Mass in the universe is clumped on a variety of scales. Starting with proximate scales, we see the mass of the solar system mostly concentrated in the sun with a few rocky objects around it, the planets. In the solar neighborhood, there are stars and the density of stars increases towards the center of our galaxy. Galaxies are almost isolated in space. The vacuum of interstellar space contains on average a tenth of an atom per cubic meter, a fantastically good vacuum, almost nothing. The galaxies group by gravity into larger structures, groups and clusters. The largest bound structures in the universe involve thousands of galaxies in regions of space roughly a 100 million light years across, superclusters. The story of the evolution of structure is the story of the operation of a single force, gravity, operating over a vast amount of cosmic time. The formation of structure in the universe takes place in competition against the expansion of space which diffuses the material in the universe. We can imagine that if the universe had expanded faster than it did, gravity might not have been able to form structures against the fleeing matter in the Big Bang. But in fact, gravity is able to form larger and larger structures even as the universe gets larger and larger over time. The largest bound objects in astronomy are galaxy clusters, situations of hundreds or thousands of galaxies contained within a region, a few million light years across. The largest coherent structures that we can see in surveys are actually superclusters that are much larger. But the dynamical evidence indicates that they're still collapsing or forming. Galaxy clusters are what we say virialised, which is their motions are governed by the virial theorem, and so they are in equilibrium. Galaxy clusters provide our best laboratory for the fact that galaxies can change their properties over cosmic time. In the centers of galaxies, we see the effect of galaxy interactions and mergers. Usually, a dense galaxy cluster has a giant cD galaxy at its center. An object with a trillion times the stellar mass of the sun, which is maybe 10 or 20 times more stellar mass in the milky way itself at the center. These galaxies also tend to have intense X-ray emission from the hot gas they contain or attract to them. These are the largest galaxies in the universe and they've got that way by accreting other galaxies of similar size and much larger number of dwarfs over 10 billion years. Galaxy clusters are important laboratories for studying and understanding dark matter. It turns out that there are three completely independent ways to measure the mass of a galaxy cluster. The first is the first method used historically to infer dark matter. In the 1930's, Fritz Zwicky, a Caltech astronomer, measured radial velocities in the Coma Cluster. A large cluster of galaxies in the Northern Hemisphere at a distance of about a 100 million light years. He saw phenomenally fast motions, and back in the mid 1930's, speculated that that cluster would be flying apart unless it was held together by large amounts of unseen matter. It was a case of a speculation that was too far ahead of its time. Other astronomers were not prepared to accept Zwicky's supposition, and so the observation sat in the literature unnoticed. By the 1970's and 1980's, Zwicky's observation [inaudible] replicated for other clusters. It turned out that every cluster of galaxies had velocities of its individual galaxies, too large to be explained by the visible matter. The radial velocities and cluster become evidence for dark matter. The second method involves the hot million degree gas that tends to concentrate at the center of a galaxy cluster. Application of the virial theorem to this gas allows you to measure the mass of the center of the cluster. Once again, dark matter is part of this calculation. The third method involves the deviation of the light of background galaxies by the cluster itself. Background galaxies have light that's amplified, distorted and bent by the intervening cluster. The striking thing is that each of these three methods apply to the same set of clusters, give essentially the same number for the mass of the cluster. In all cases, these three methods indicate that most of the mass of the clusters is dark matter. We can see an example of the lensing geometry that leads to this kind of mass determination. The lensing technique is very mature in terms of giving us the mass of hundreds of clusters in the universe out to distances in nearly a billion light years. One survey has done enormous service to astronomy by mapping out the distribution not only of normal galaxies, but of active galaxies are quasars out to very high redshifts. The Sloan Digital Sky Survey. A pioneer of project using a two and a half meter telescope on Apache Point. This survey was based on phenomenally high-quality and large imagers and spectrographs. Remember, this telescope is considered small by modern standards. It would not break the top 50 of the world's largest telescopes. But it's customized hardware and phenomenal detection systems and it's dedicated purpose on one survey has meant that it's transformed the extra-galactic landscape. The Sloan Digital Sky Survey allows us to place galaxies in three-dimensional space out to distances of a billion or two billion light years, and see the large-scale structure of the universe in exquisite detail. What's the best description of the large-scale structure of the universe? That is the way matter is distributed on the largest scales beyond galaxies. Sometimes phenomenon and nature are strikingly similar even though they're fundamentally different in their regime. One example of this is the scale free structure we'd see in the brain in terms of the network of neuronal connections versus the distribution of mass in the universe. In this case, a dark matter map. Both distributions have what's called a fractal quality, where they're almost equal amounts of power on different scales. It even turns out that the nature of the structure you see in the light reflections on a pool, which are caustic patterns are very similar to the structure seen in the large scale distribution of matter in the universe and the mathematics that describes them is similar. We see structure in the universe on all scales beyond galaxies ranging up to a few hundred million light years across huge, superclusters of galaxies with tens of thousands of galaxies in them. The largest bound structures in the universe are galaxy clusters. Three different ways of measuring their mass affirm that most of the universe on large scales is dark matter. The large-scale structure of the universe has a delicate filigree pattern and it has a fractal dimension of 1.7. If we imagine one as strings, two as sheets and three is a filled volume, 1.7 corresponds to halfway between strings and sheets. That's the pattern we see in the three-dimensional distribution of galaxies on the largest scales.
