Any theory that aspires to explain how stars are born must also explain why the majority of stars in the Galactic disk are members of multiple-star systems, with the majority of those binary-star systems. This is clearly a property that goes back to stellar birth, because newly-formed stars are also predominately in multiple-star systems. Stars do not pick up companions as they age. Either stars capture their companions shortly after birth, or they are born into multiple-star systems.
Binary-star systems have two properties that strongly impact theories of star formation. First, binary-star systems are small in size, with the separations between stars ranging from much less than 1 AU to several thousand AU. Second, for systems with short periods, the mass of the smaller of the two stars in a binary system is generally close to the primary star's mass, averaging half of the primary-star's mass, but, for systems with long periods, the mass is generally small, with a distribution of values similar to the distribution of stellar masses of isolated stars.
In recent years theorists have explored four theories for binary-star birth: the capture of one star by another; the splitting of a star into two stars; the collapse of a star's accretion disk to a companion star, and the fragmentation of a collapsed molecular cloud into multiple stars. The last-three theories treat the birth of a binary system as part of the birth of a star.
The first theory—the capture of a star by a second star—can explain the creation of binary stars in the dense globular clusters, where the gravitational potential energy liberated in the formation of a binary star “heats” the cluster, but it cannot explain the binary systems in the Galactic disk. The problem is that a star cannot capture another star unless kinetic energy is expelled from the system. A third star can be the sink for this kinetic energy, but in the Galactic disk the probability is low that three stars would come together at the same time in a way that leaves two of these stars bound together. Even with the higher stellar densities in star-forming regions, the rate of capture is too low to produce a high number of binary systems with young stars. Tidal heating of the stars can expel kinetic energy from the system, but for tidal forces to dissipate enough energy to cause stellar capture requires the stars to pass very close to one-another, which is a low-probability event. One way around this close-encounter problem is to tidally-heat the accretions disks orbiting each star instead of the stars themselves. Accretions disks are observed orbiting newly-formed stars. These disks are seen by the infrared radiation they emit. They take up angular momentum from the new star, allowing the star to become a slowly-rotating pressure-supported sphere. One can imagine that as a pair of young stars with accretion disks pass each-other, they raise tides in each-other's accretion disks, dissipating kinetic energy. Simulations of this process, however, find that in such an event the accretion disks are disrupted without extracting enough kinetic energy to gravitationally bind the stars. For these reasons, one does not expect stars to capture one-another at a great rate, and certainly not rapidly enough to account for the binary-star systems containing stars that are only several million years old.
The second theory—a rapidly-rotating star can split into two stars—is a theory that is over a century old. It appears to be out of favor in the broad community, although some researchers are still pursuing it. The idea is that a rapidly-spinning spherical star is unstable, distorting first into a bar shape, and then into a barbell shape. The mass that accumulates at each end of the barbell becomes a star, so that the system evolves into a contact binary star. As each star contracts to its main-sequence size, the binary system becomes detached. The problem is in getting the original star to evolve from a bar shape to a barbell shape; numerical simulations tend to find that angular momentum within the star is redistributed, and the star changes from a bar shape to a sphere orbited by an accretion disk.
The third theory—a second star forms from the accretion disk orbiting a newly-formed star—resembles the theory for planetary birth. As stated earlier, stars are born surrounded by accretion disks. The planets around the Sun and around other stars formed from these accretion disks. Compared to a star, the planets in a planetary system are very small. Can an accretion disk give birth to something as large as a star? Theorists have shown that such a birth is possible if the accretion disk is more massive than the central star it is orbiting. The ideas is that after the central star forms from a molecular cloud, the accretion disk surrounding it continues to accumulate gas from the cloud. When the accretion disk becomes more massive than the central star, the disk becomes unstable, with the gas in the disk clumping to one side of the disk. This instability is driven by the self-gravity of the accretion disk. Eventually all of the gas in the disk flows to one part of the disk to form the second star. The advantage of such a theory is that it naturally produces binary stars rather than systems with three or four stars, and it explains why the size of a binary-star system is comparable to the size of a planetary system.
The final theory—a molecular cloud collapses and fragments to form multiple stars—takes advantage of the fact that as a cloud contracts, the length over which it is stable contracts more rapidly. Under the current theories of star formation, a star forms when the densest regions of a molecular cloud collapse through their own self-gravity. Whether a cloud is stable against collapse depends on whether it is larger or smaller than the Jeans length, which is set by the temperature and density of the gas. If a static cloud is larger than the Jeans length, it will collapse. If the cloud is much larger than the Jeans length, it will collapse into several pieces, with the initial size of each piece of order the Jeans length. The interesting feature of this fragmentation is that if a cloud cools as it contracts, the Jeans length for the cloud becomes much smaller than the size of the cloud. This has lead theorists to believe that a collapsing molecular cloud of several solar masses could fragment and give birth to a multiple-star system. The problem in this simple picture, however, is that as long as the cloud is collapsing, it cannot fragment. Computer simulations have shown that the density gradients that form as a cloud collapses prevent the cloud from fragmenting. Not unless the original cloud ceases its collapse and stabilizes itself at a smaller scale can fragmentation and collapse occur. Angular momentum provides the mechanism that halts collapse, causing the cloud to settle down as a large rotating disk. This disk fragments and collapses to form several stars that are gravitationally bound to each-other. The size of the system is set by the size of the stabilized cloud. Whether one can preferentially form binary stars with such a theory is not yet known.
As often happens in astrophysics with frequently-occurring phenomena, the birth of a binary star is difficult to replicate in the laboratory, which in this case is within a computers guts. Astrophysicists are unable to follow the computer realizations of the last-three theories for a sufficient length of time to see stars form. The problem is in the wide range of scales encountered in the problem. Spatially, one is following the three-dimensional evolution of a cloud that is parsecs in size down to a handful of stars separated by several AU and with radii of less than 0.01 AU, so the scale changes by a factor of 10 million. One is also following processes that occur on a variety of timescales. In particular, the gravitational free fall timescale in the densest regions of a molecular cloud are several orders of magnitude shorter than the orbital timescale for the system. These widely-varying scales, which must be resolved within a computer simulation, are why a theory that is over one hundred years old cannot be definitively eliminated from consideration.
How many theories do we need? The different characteristics of binary systems with periods of more than 100 years from those of systems with periods of less than 100 years suggests that two different mechanisms give us binary stars (100 years corresponds to a semimajor axis of around 22 AU for a 1 solar mass system). The researchers who found this difference between long- and short-period systems in the 1970s suggested that a short-period binary system is formed when a rapidly-rotating star split in two, and a long-period system is formed when a molecular cloud fragments. More recently, researchers studying systems of young stars have claimed that molecular cloud fragmentation as the source of all binary-star systems is most consistent with their data. The issue remains unsettled, so we find ourselves with three plausible theories for the origin of binary stars in the Galaxy disk, two of which may be at work creating binary stars. If only one mechanism is at work, it is likely the fragmentation of molecular clouds, but if two are at work, then the collapse of an unstable accretion disk now seems the most likely process creating the short-period binary systems.