Galaxies are like stars in that they tend not to be alone, but occur in small groups or larger clusters of galaxies. Clusters may be comprised of a few galaxies (for example, Stephan's Quartet) or massive systems, such as the Virgo Cluster with some 3,000 members and a total mass of 10 15 solar masses. The smallest clusters have galaxies distributed irregularly through relatively small volumes of space, whereas the largest clusters have their many galaxies quite symmetrically distributed about the centers. Such regularity of form argues that motions within these clusters are in a balance against the self‐gravity of the cluster members.
While clusters of galaxies were once considered the next larger hierarchical structure to be found in the universe, modern studies show that the actual distribution of galaxies in the universe is far more complicated. There are actually sheets (or walls) of galaxies surrounding vast voids that are nearly deficient of galaxies. Clusters and chains of galaxies and clusters of galaxies are found across space where such walls intersect. The actual distribution of visible galaxies in the universe can more properly be compared to the interior structure of a sponge.
The Local Group
The Local Group consists of about 30 galaxies distributed across about 1 Mpc of space. Immediately exterior to the Local Group, galaxies become sparse until the next small groups are encountered at distances of a few Mpc. Most of the mass of this small group is concentrated in the Milky Way Galaxy and its somewhat larger companion, the Andromeda Galaxy, best described as a binary galaxy system. Each of these large spirals is surrounded by a family of smaller dwarf galaxies (their coronas). About half a dozen small galaxies have a wider distribution and appear not to be specifically linked to either of the large spirals, although there is a group of a few galaxies (called the IC 342 group after the catalog number of the largest member) that models suggest may have been gravitationally slingshot away from the Local Group by the Andromeda Galaxy millions of years ago.
Giant clusters of galaxies
At one extreme, giant clusters of galaxies include systems like the Virgo Cluster, which contain some 3,000 members distributed loosely over several Mpc of space; most of these galaxies are spiral galaxies, although the largest galaxies in the cluster are two centrally located elliptical galaxies. At the other extreme are more compact systems like the Coma Cluster, which consists of thousands of galaxies, including about 300 large elliptical galaxies. The types of galaxies that are present are related to the environment in which they are found. Ellipticals are common where galaxies are closely packed together, but spirals predominate in loose, widely spread clusters. Such distribution of galaxy types supports the idea that ellipticals have formed over time from mergers of smaller disk galaxies.
Determination of mass in galaxies
For individual galaxies, measurement of optical rotation curves over the visible images of galaxies (this is a traditional method of study) can be done out to radii of maybe 20 kpc with typical masses on the order of 10 11 solar masses deduced from the relationship M(R) = V 2(R) R / G. With the application of highly sensitive radio astronomy techniques in the 1970s, rotational velocities from neutral hydrogen gas could be detected to radii of 40–50 kpc. Galaxy rotation curves stay constant at large radii; doubling the distance outward for velocity measurement results in doubling the amount of mass associated with galaxies, but the radio observations also show this mass is not hydrogen gas.
Even larger volumes of space associated with individual galaxies may be measured for mass by use of binary galaxy studies. These studies must be done statistically because orbital periods are far too long for actual measurement of individual orbital sizes and periods that are necessary for direct application of Kepler's Third Law. Observation of a large number of galaxy pairs and judicious averaging of the measured separations between galaxies and velocities differences yield effective mass measurements out to an average of 80 kpc, suggesting even larger amounts of mass in each galaxy, ∼4 × 10 11 solar masses.
In the great clusters of galaxies, the Virial Theorem may be used. This principle relates gravitational effects (dependent upon mass and position of galaxies) to the kinetic energy of motions when those motions are random, not circular. Positions of galaxies can be measured in the plane of the sky and the Doppler effect gives the motion along the line of sight. The virial theorem then yields the one factor that cannot be measured directly, but must be inferred, that is the average mass for a typical galaxy. Virial Theorem studies suggest even larger masses of 8 × 10 11 solar masses typically over radii of 150 kpc associated with each galaxy. In other words, these dynamical studies indicate that seven‐eighths of the total mass of a typical galaxy may be outside the visible image of the galaxy, existing in some form that does not emit some form of detectable electromagnetic radiation. As additional studies confirmed these results, this was termed the missing mass problem, now known more appropriately as the dark matter problem.
And this indeed is a major problem facing modern astrophysics, for every condition of normal matter (density, temperature, and so on) can be observed by its emission of some wavelength of electromagnetic radiation. If something does not emit electromagnetic radiation, it almost certainly cannot be the familiar matter that makes up the stars and interstellar matter that otherwise are so well understood.
Neutrinos are among the factors that have been suggested to account for the dark matter associated with galaxies. Many neutrinos have been produced by thermonuclear reactions in stars and especially in the early era of the universe when the primordial helium was formed. If neutrinos have a tiny bit of mass, they are so numerous they could end up being the dominant mass of the universe. And they interact so weakly with everything else that they are essentially invisible. On the other hand, neutrinos probably are too energetic to allow gravitational clumping into galaxy‐sized objects; they simply escape the cluster, and cannot provide the local source of gravity that is needed for clumping. Hence neutrinos are likely not a good explanation for dark matter.
Black holes may also account for the dark matter associated with galaxies. However, the black holes would not be those produced by the evolution of massive stars (there are too few of them), but rather unexpanded pieces of the early, high‐density universe that were somehow left behind when the rest of the universe expanded. How these pieces were left over has yet to be explained.
There are also currently active observational searches for MACHOs ( Massive Compact Halo Objects). These could be normal matter objects, so small (for example, compact) that their surface areas would produce so little electromagnetic radiation that they would be effectively invisible. So far, the preliminary results are significantly improving astronomers' understanding of the halo of the Milky Way Galaxy, but have not revealed the existence of a hitherto unknown type of object.
Theoretical studies, primarily aimed at understanding the formation of galaxies and replicating their distribution and motions throughout the universe, can be done without knowing the precise nature of the dark matter. Astronomers can define two generic types of dark matter: cold dark matter, which moves relatively slowly and is affected by gravitational clumping (like normal matter, it easily forms galaxies), and hot dark matter, which moves too quickly to respond to gravity (and therefore tends to slow the formation of galaxies and clusters of galaxies). Computation results at the present time suggest that the best comparison of theory with the real universe requires the presence of both cold dark matter and hot dark matter, but the ultimate understanding of this problem is yet to be settled.