Artist's impression of the orbits of HD 188753, a triple star system
A star system or stellar system is a small number of stars which orbit each other, bound by gravitational attraction. A large number of stars bound by gravitation is generally called a star cluster or galaxy, although, broadly speaking, they are also star systems. Star systems are not to be confused with planetary systems, which include planets and similar bodies.
A multiple star consists of three or more stars which appear from the Earth to be close to one another in the sky. This may result from the stars being physically close and gravitationally bound to each other, in which case it is a physical-multiple star, or this closeness may be merely apparent, in which case it is an optical-multiple-star. Physical multiple stars are also commonly called multiple stars or multiple star systems. Most multiple star systems are triple stars. Systems with four or more components are less likely to occur. Multiple-star systems are called triple, trinary or ternary if they contain three stars; quadruple or quaternary if they contain four stars; quintuple or quintenary with five stars; sextuple or sextenary with six stars; septuple or septenary with seven stars, and so on. These systems are smaller than open star clusters, which have more complex dynamics and typically have from 100 to 1,000 stars. Most multiple star systems known are triple; for higher multiplicities, the number of known systems with a given multiplicity decreases exponentially with multiplicity. For example, in the 1999 revision of Tokovinin's catalog of physical multiple stars, 551 out of the 728 systems described are triple. However, because of selection effects, knowledge of these statistics is very incomplete., §2.
Multiple-star systems can be divided into two main dynamical classes: hierarchical systems which are stable and consist of nested orbits that don't interact much and so each level of the hierarchy can be treated as a Two-body problem, or the trapezia which have unstable strongly interacting orbits and are modelled as an n-body problem, exhibiting chaotic behavior. 
The Algol system as it appeared on 12 August 2009. This is not an artistic representation, but rather is a true two-dimensional image with 1/2 milli-arcsecond resolution in the near-infrared H-band, reconstructed from data of the CHARA interferometer. The elongated appearance of Algol B and the round appearance of Algol A are real. The form of Algol C, however, is an artifact.
Algol (β Persei) is a triple-star system (Algol A, B, and C) in the constellation Perseus, in which the large and bright primary Algol A is regularly eclipsed by the dimmer Algol B every 2.87 days. This animation was assembled from 55 images of the CHARA interferometer in the near-infrared H-band, sorted according to orbital phase. Because some phases are poorly covered, B jumps at some points along its path.
Most multiple-star systems are organized in what is called a hierarchical system: the stars in the system can be divided into two smaller groups, each of which traverses a larger orbit around the system's center of mass. Each of these smaller groups must also be hierarchical, which means that they must be divided into smaller subgroups which themselves are hierarchical, and so on. Each level of the hierarchy can be treated as a two-body problem by considering close pairs as if they were a single star. In these systems there is little interaction between the orbits and the stars' motion will continue to approximate stableKeplerian orbits around the system's center of mass, unlike the unstable trapezia systems or the even more complex dynamics of the large number of stars in star clusters and galaxies.
Triple star systems
In a physical triple star system, each star orbits the center of mass of the system. Usually, two of the stars form a close binary system, and the third orbits this pair at a distance much larger than that of the binary orbit. This arrangement is called hierarchical. The reason for this is that if the inner and outer orbits are comparable in size, the system may become dynamically unstable, leading to a star being ejected from the system. Triple stars that are not all gravitationally bound might comprise a physical binary and an optical companion, such as Beta Cephei, or rarely, a purely optical triple star, such as Gamma Serpentis.
Hierarchical multiple star systems with more than three stars can produce a number of more complicated arrangements, which can be illustrated by what Evans (1968) has called a mobile diagram. These are similar to ornamental mobiles hung from the ceiling. Some examples can be seen in the figure to the left. Each level of the diagram illustrates the decomposition of the system into two or more systems with smaller size. Evans calls a diagram multiplex if there is a node with more than two children, i.e. if the decomposition of some subsystem involves two or more orbits with comparable size. Because, as we have already seen for triple stars, this may be unstable, multiple stars are expected to be simplex, meaning that at each level there are exactly two children. Evans calls the number of levels in the diagram its hierarchy.
A simplex diagram of hierarchy 1, as in (b), describes a binary system.
A simplex diagram of hierarchy 2 may describe a triple system, as in (c), or a quadruple system, as in (d).
A simplex diagram of hierarchy 3 may describe a system with anywhere from four to eight components. The mobile diagram in (e) shows an example of a quadruple system with hierarchy 3, consisting of a single distant component orbiting a close binary system, with one of the components of the close binary being an even closer binary.
A real example of a system with hierarchy 3 is Castor, also known as Alpha Geminorum or α Gem. It consists of what appears to be a visual binarystar which, upon closer inspection, can be seen to consist of two spectroscopic binary stars. By itself, this would be a quadruple hierarchy 2 system as in (d), but it is orbited by a fainter more distant component, which is also a close red dwarf binary. This forms a sextuple system of hierarchy 3.
The maximum hierarchy occurring in A. A. Tokovinin's Multiple Star Catalogue, as of 1999, is 4. For example, the stars Gliese 644A and Gliese 644B form what appears to be a close visual binary star; because Gliese 644B is a spectroscopic binary, this is actually a triple system. The triple system has the more distant visual companion Gliese 643 and the still more distant visual companion Gliese 644C, which, because of their common motion with Gliese 644AB, are thought to be gravitationally bound to the triple system. This forms a quintuple system whose mobile diagram would be the diagram of level 4 appearing in (f).
Higher hierarchies are also possible. Most of these higher hierarchies either are stable or suffer from internal perturbations. Others consider complex multiple stars will in time theoretically disintegrate into less complex multiple stars, like more common observed triples or quadruples are possible.
Trapezia are usually very young, unstable systems. These are thought to form in stellar nurseries, and quickly fragment into stable multiple stars, which in the process may eject components as galactic high-velocity stars. They are named after the multiple star known as the Trapezium in the heart of the Orion Nebula. Such systems are not rare, and commonly appear close to or within bright nebulae. These stars have no standard hierarchical arrangements, but compete for stable orbits, where the center of gravity is not fixed at some point but moves as the stars change their mutual positions. This relationship is called interplay. Such stars eventually settle down to a close binary with a distant companion, with the other star(s) previously in the system ejected into interstellar space at high velocities. Example of such events may explain the runaway stars that might have been ejected during a collision of two binary star groups or a multiple system. This event is credited with ejecting AE Aurigae, Mu Columbae and 53 Arietis at above 200 km·s−1 and has been traced to the Trapezium cluster in the Orion Nebula some two million years ago.
Designations and nomenclature
Multiple star designations
The components of multiple stars can be specified by appending the suffixes A, B, C, etc., to the system's designation. Suffixes such as AB may be used to denote the pair consisting of A and B. The sequence of letters B, C, etc. may be assigned in order of separation from the component A. Components discovered close to an existing component may be assigned suffixes such as Aa, Ba, and so forth.
Nomenclature in the Multiple Star Catalogue
Subsystem notation in Tokovinin's Multiple Star Catalogue.
A. A. Tokovinin's Multiple Star Catalogue uses a system in which each subsystem in a mobile diagram is encoded by a sequence of digits. In the mobile diagram (d) above, for example, the widest system would be given the number 1, while the subsystem containing its primary component would be numbered 11 and the subsystem containing its secondary component would be numbered 12. Subsystems which would appear below this in the mobile diagram will be given numbers with three, four, or more digits. When describing a non-hierarchical system by this method, the same subsystem number will be used more than once; for example, a system with three visual components, A, B, and C, no two of which can be grouped into a subsystem, would have two subsystems numbered 1 denoting the two binaries AB and AC. In this case, if B and C were subsequently resolved into binaries, they would be given the subsystem numbers 12 and 13.
Future multiple star system nomenclature
The current nomenclature for double and multiple stars can cause confusion as binary stars discovered in different ways are given different designations (for example, discoverer designations for visual binary stars and variable star designations for eclipsing binary stars), and, worse, component letters may be assigned differently by different authors, so that, for example, one person's A can be another's C. Discussion starting in 1999 resulted in four proposed schemes to address this problem:
KoMa, a hierarchical scheme using upper- and lower-case letters and Arabic and Roman numerals;
The Urban/Corbin Designation Method, a hierarchical numeric scheme similar to the Dewey Decimal system;
The Sequential Designation Method, a non-hierarchical scheme in which components and subsystems are assigned numbers in order of discovery; and
WMC, the Washington Multiplicity Catalog, a hierarchical scheme in which the suffixes used in the Washington Double Star Catalog are extended with additional suffixed letters and numbers.
For a designation system, identifying the hierarchy within the system has the advantage that it makes identifying subsystems and computing their properties easier. However, it causes problems when new components are discovered at a level above or intermediate to the existing hierarchy. In this case, part of the hierarchy will shift inwards. Components which are found to be nonexistent, or are later reassigned to a different subsystem, also cause problems.
During the 24th General Assembly of the International Astronomical Union in 2000, the WMC scheme was endorsed and it was resolved by Commissions 5, 8, 26, 42, and 45 that it should be expanded into a usable uniform designation scheme. A sample of a catalog using the WMC scheme, covering half an hour of right ascension, was later prepared. The issue was discussed again at the 25th General Assembly in 2003, and it was again resolved by commissions 5, 8, 26, 42, and 45, as well as the Working Group on Interferometry, that the WMC scheme should be expanded and further developed.
The sample WMC is hierarchically organized; the hierarchy used is based on observed orbital periods or separations. Since it contains many visual double stars, which may be optical rather than physical, this hierarchy may be only apparent. It uses upper-case letters (A, B, ...) for the first level of the hierarchy, lower-case letters (a, b, ...) for the second level, and numbers (1, 2, ...) for the third. Subsequent levels would use alternating lower-case letters and numbers, but no examples of this were found in the sample.
HR 3617 is a multiple star with three component stars, HR 3617A, HR 3617B, and HR 3617C. A and B form a physical binary star, while C appears to be optical.
Alpha Centauri is a trinary star composed of a main binary yellow dwarf pair (Alpha Centauri A and Alpha Centauri B), and an outlying red dwarf, Proxima Centauri. Both A and B form a physical binary star, designated as Alpha Centauri AB, α Cen AB, or RHD 1 AB, where the AB denotes this is a binary system. The moderately eccentric orbit of the binary can make the components be as close as 11 AU or as far away as 36 AU. Proxima is much further away (~15,000 AU) from α Cen AB than they are to each other. Although this distance is still comparatively small to interstellar distances, it is still debatable whether Proxima, whose orbital period would be more than 500,000 years, is gravitationally bound to α Cen AB.
Polaris or Alpha Ursae Minoris (α UMi), the north star, is a trinary star system in which the closer companion star is extremely close to the main star—so close that it was only known from its gravitational tug on Polaris A (α UMi A) until it was imaged by the Hubble Space Telescope in 2006.
The Kepler 64 system has the planet PH1 (discovered in 2012 by the Planet Hunters group, a part of the Zooniverse) orbiting two of the four stars, making it to be the first known planet to be in a quaternary star system.
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