As a first step in understanding the layout of the Milky Way galaxy, consider the environment of stars. Most stars are not solitary wanderers in space. Four of the first six stars beyond the solar system have known companion stars. Surveys of this kind suggest that more than two-thirds of all stars are in a system of two or more stars orbiting each other. This is quite a surprise! Our Sun is a single star and so our immediate environment does not prepare us for the fact that most stars are not alone. Each pair of co-orbiting stars is called a binary star. Each set of more than two stars is a multiple star system.
The question of pinpointing the number of binary and multiple star systems is a challenge to observers. The nearest stars are easiest to observe but give too small a statistical sample to be reliable. At greater distances there are more stars, but faint companions might not be detected. Spectroscopic binary statistics are biased toward pairs with small separation distances, because according to Kepler's laws these have the fastest velocities and greatest Doppler shifts, thus being the most likely to be discovered. Visual binary statistics are biased toward wide separation distances, which make the two stars easier to resolve. All these biases, which tend to make the data unrepresentative of the whole population, are called selection effects.
Trapezium in Orion, as seen by the Hubble Space Telescope. Click here for original source URL.
A careful study of the 25 stars nearest the Sun shows that about half are single stars. To be specific, 48% are single, 36% are binaries, 12% are triple systems, and 4% are quads. Studies of larger samples reveal that only about 1% of stars inhabit systems with five members. By the time we reach six-member systems, definitions of multiple systems become hazy. It is unclear whether close groupings like the Trapezium in the Orion Nebula should be counted as multiple systems. The 1982 Yale Catalog of 9,096 prominent stars lists multiple systems ranging as high as one system with 17 members. Such systems would present an interesting spectacle. In fact, the percentages quoted are really lower limits — it is likely that many of the seemingly single stars have companions too small and dim to detect. Astronomers estimate that most stars have at least one companion. If true, this would imply that our own Sun is slightly unusual!
The conclusion that our Sun is unusual changes our view of stars entirely. The idea of the night sky full of single, separate stars is wrong. Astronomers must understand the origin and evolution of systems of two, three, four, and more stars in order to claim any understanding of stars in general. It turns out that binaries go through some interesting detours along the road of stellar evolution. The orbital properties of multiple star systems fall into two main categories. In systems that are "heirarchical" the orbits are nested and don't interact with each other. For example, there are quad systems containing two binaries that are widely separated. In this case, each of the two binaries can be treated as a single star and the their orbit of a common center of gravity can be treated simply with Kepler's laws. In systems called "trapezia," the obits of the stars interplay and they are often chaotic and not stable.
Why are these systems important for our understanding of the universe? First, binary stars allow us to measure stellar mass using Kepler's and Newton's laws. This is the only way to measure a star's mass directly, and can be one of the strongest indications that a dark companion star is a black hole. Second, we can learn about stellar evolution by studying stars of different mass that we believe to have formed at the same time — the evolution of a white dwarf around a red giant can be very different from the evolution of a solitary white dwarf. We must be sure that our theories of star formation and evolution account for binaries and multiple systems. Third, there are rare cases in which two stars orbit close enough to transfer material between them. These systems act as fascinating laboratories for high-energy phenomena, as gas moves at high speeds and attains very high temperatures.