Editing Star system (section)

== Orbital characteristics ==

In systems that satisfy the assumptions of the [[two-body problem]] – including having negligible [[Tidal force|tidal]] effects, perturbations (from the gravity of other bodies), and [[Mass transfer#Astrophysics|transfer of mass]] between stars – the two stars will trace out a stable [[elliptical orbit]] around the [[barycenter]] of the system. Examples of binary systems are [[Sirius]], [[Procyon]] and [[Cygnus X-1]], the last of which probably consists of a star and a [[black hole]].

Multiple-star systems can be divided into two main dynamical classes:
* Hierarchical systems are stable and consist of nested orbits that do not interact much. Each level of the hierarchy can be treated as a [[two-body problem]].
* Trapezia have unstable, strongly interacting orbits and are modelled as an [[n-body problem]], exhibiting [[chaos theory|chaotic]] behavior.<ref>{{cite book |first=Peter J.T. |last=Leonard |year=2001 |article=Multiple stellar systems: Types and stability |editor-first=P. |editor-last=Murdin |title=Encyclopedia of Astronomy and Astrophysics |edition=online |url=http://eaa.iop.org/ |archive-url=https://archive.today/20120709020850/http://eaa.iop.org/ |archive-date=2012-07-09 |publisher=Institute of Physics}} Nature Publishing Group published the original print edition.</ref> They can have 2, 3, or 4&nbsp;stars.

=== Hierarchical systems ===
[[File:Smoke ring for a halo.jpg|thumb|Star system named [[DI Cha]]. While only two stars are apparent, it is actually a quadruple system containing two sets of binary stars.<ref>{{cite web|title=Smoke ring for a halo|url=http://www.spacetelescope.org/images/potw1543a/|access-date=26 October 2015}}</ref>]]

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.<ref name=evans1968/> 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 stable<ref name=toko /><ref name=heintz1>{{cite book | last=Heintz | first=W. D. | date=1978 | title=Double Stars | publisher=[[D. Reidel]] Publishing Company, Dordrecht | isbn=90-277-0885-1 | pages=[https://archive.org/details/DoubleStars/page/1 1] | url=https://archive.org/details/DoubleStars/page/1 }}</ref> [[Kepler's laws of planetary motion|Keplerian]] orbits around the system's center of mass.<ref>[http://www.ctio.noao.edu/~atokovin/papers/dynamics.pdf Dynamics of multiple stars: observations] {{webarchive|url=https://web.archive.org/web/20060919155603/http://www.ctio.noao.edu/~atokovin/papers/dynamics.pdf |date=19 September 2006 }}, A. Tokovinin, in "Massive Stars in Interacting Binaries", 16–20 August 2004, Quebec (ASP Conf. Ser., in print).</ref>

For example, stable trinary systems consist of two stars in a close [[binary star|binary system]], with a third orbiting this pair at a distance much larger than that of the binary orbit.<ref>{{cite book | last=Heintz | first=W. D. | date=1978 | title=Double Stars | publisher=D. Reidel Publishing Company, Dordrecht | isbn=90-277-0885-1 | pages=[https://archive.org/details/DoubleStars/page/66 66–67] | url=https://archive.org/details/DoubleStars/page/66 }}</ref><ref name=evans1968>{{cite journal | last=Evans | first=David S. | date=1968 | title=Stars of Higher Multiplicity | journal=Quarterly Journal of the Royal Astronomical Society | volume=9 | bibcode=1968QJRAS...9..388E | pages=388–400}}</ref> 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.<ref>{{cite journal |bibcode=1994MNRAS.267..161K |title=A note on the stability of hierarchical triple stars with initially circular orbits |last1=Kiseleva |first1=G. |last2=Eggleton |first2=P. P. |last3=Anosova |first3=J. P. |journal=Monthly Notices of the Royal Astronomical Society |year=1994 |volume=267 |page=161 |doi=10.1093/mnras/267.1.161 |doi-access=free }}</ref> [[EZ Aquarii]] is an example of a physical hierarchical triple system, which has an outer star orbiting an inner binary composed of two more [[red dwarf]] stars.

====Mobile diagrams====
[[File:Mobile-diagrams.png|thumb|''Mobile diagrams'': {{Ordered list |list_style_type=lower-alpha |item_style=margin-left:-12px; |multiplex |simplex, binary system |simplex, triple system, hierarchy 2 |simplex, quadruple system, hierarchy 2 |simplex, quadruple system, hierarchy 3 |simplex, quintuple system, hierarchy 4.}}]]

Hierarchical arrangements can be organized by what Evans (1968) called ''mobile diagrams'', which look similar to ornamental mobiles hung from the ceiling. Each level of the mobile 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 multiplexes 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''.<ref name=evans1968/>

* 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 (star)|Castor]], also known as Alpha Geminorum or α Gem. It consists of what appears to be a [[visual binary]] [[star]] 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.<ref>{{cite book | last=Heintz | first=W. D. | date=1978 | page=[https://archive.org/details/DoubleStars/page/72 72] | title=Double Stars | publisher=D. Reidel Publishing Company, Dordrecht | isbn=90-277-0885-1 | url=https://archive.org/details/DoubleStars/page/72 }}</ref>
* The maximum hierarchy occurring in A. A. Tokovinin's Multiple Star Catalogue, as of 1999, is 4.<ref name=toko/> For example, the stars [[V1054 Ophiuchi|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).<ref>{{cite journal | last1 = Mazeh | first1 = Tzevi | display-authors = etal   | date = 2001 | title = Studies of multiple stellar systems – IV. The triple-lined spectroscopic system Gliese 644 | journal = Monthly Notices of the Royal Astronomical Society | volume = 325 | issue = 1 | pages = 343–357 | doi = 10.1046/j.1365-8711.2001.04419.x | doi-access = free |arxiv = astro-ph/0102451 |bibcode = 2001MNRAS.325..343M | s2cid = 16472347 }}; see §7–8 for a discussion of the quintuple system.</ref>

Higher hierarchies are also possible.<ref name=evans1968/><ref>{{cite book | last=Heintz | first=W. D. | date=1978 | pages=[https://archive.org/details/DoubleStars/page/65 65–66] | title=Double Stars | publisher=D. Reidel Publishing Company, Dordrecht | isbn=90-277-0885-1 | url=https://archive.org/details/DoubleStars/page/65 }}</ref> Most of these higher hierarchies either are stable or suffer from internal [[Perturbation (astronomy)|perturbations]].<ref>{{cite journal | title = Encounter Phenomena in Triple Stars | last1 = Harrington | first1 = R.S. | date = 1970 | bibcode=1970AJ.....75.1140H | journal = Astronomical Journal | volume = 75 | pages = 114–118 |doi = 10.1086/111067 }}</ref><ref>{{cite journal | title = Multiple stars: Anathemas or friends? | last1 = Fekel | first1 = Francis C | date = 1987 | bibcode = 1987VA.....30...69F | journal = Vistas in Astronomy | volume = 30 | issue = 1 | pages = 69–76 | doi=10.1016/0083-6656(87)90021-3}}</ref><ref>{{cite journal | title = Multiple stars with low hierarchy: stable or unstable? | last1 = Zhuchkov | first1 = R. Ya. | last2 = Orlov | first2 = V. V. | last3 = Rubinov | first3 = A. V. | date = 2006 | bibcode=2006POBeo..80..155Z | journal = Publications of the Astronomical Observatory of Belgrade | volume = 80 | pages = 155–160 }}</ref> Others consider complex multiple stars will in time theoretically disintegrate into less complex multiple stars, like more common observed triples or quadruples.<ref>{{cite journal | title = Dynamical Evolution of Multiple Stars: Influence of the Initial Parameters of the System | last1 = Rubinov | first1 = A. V. | date = 2004 | bibcode=2004ARep...48...45R | journal = Astronomy Reports | volume = 48 | issue = 1 | pages = 155–160 |doi = 10.1134/1.1641122 | s2cid = 119705425 }}</ref><ref>{{cite journal | title = Multiple Star Formation from N-Body System Decay | last1 = Harrington | first1 = R. S. | date = 1977 | bibcode=1977RMxAA...3..209H | journal = Rev. Mex. Astron. Astrofís. | volume = 3 | page = 209 }}</ref>

===Trapezia===

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 [[runaway stars|high-velocity stars]].<ref name=heintztrapezia>{{cite book | last=Heintz | first=W. D. | date=1978 | title=Double Stars | publisher=D. Reidel Publishing Company, Dordrecht | isbn=90-277-0885-1 | pages=[https://archive.org/details/DoubleStars/page/67 67–68] | url=https://archive.org/details/DoubleStars/page/67 }}</ref><ref>{{cite journal |bibcode=2006RMxAC..25...13A |title=Runaway Stars, Trapezia, and Subtrapezia |last1=Allen |first1=C.|author1-link=Christine Allen (astronomer) |last2=Poveda |first2=A. |last3=Hernández-Alcántara |first3=A. |journal=Revista Mexicana de Astronomía y Astrofísica, Serie de Conferencias |year=2006 |volume=25 |page=13 }}</ref> They are named after the multiple star system known as the [[Trapezium Cluster]] in the heart of the [[Orion Nebula]].<ref name=heintztrapezia /> Such systems are not rare, and commonly appear close to or within bright [[nebula]]e. These stars have no standard hierarchical arrangements, but compete for stable orbits. This relationship is called ''interplay''.<ref name="Heintz 1978 68">{{cite book | last=Heintz | first=W. D. | date=1978 | page=[https://archive.org/details/DoubleStars/page/68 68] | title=Double Stars | publisher=D. Reidel Publishing Company, Dordrecht | isbn=90-277-0885-1 | url=https://archive.org/details/DoubleStars/page/68 }}</ref> 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.<ref name="Heintz 1978 68" /> This dynamic may explain the [[runaway star]]s 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&nbsp;km·s<sup>−1</sup> and has been traced to the [[Trapezium cluster]] in the [[Orion Nebula]] some two million years ago.<ref name="Blaauw">
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