Editing Binary star (section)

==Astrophysics==
Binaries provide the best method for astronomers to determine the mass of a distant star. The gravitational pull between them causes them to orbit around their common center of mass. From the orbital pattern of a visual binary, or the time variation of the spectrum of a spectroscopic binary, the mass of its stars can be determined, for example with the [[binary mass function]]. In this way, the relation between a star's appearance (temperature and radius) and its mass can be found, which allows for the determination of the mass of non-binaries.

Because a large proportion of stars exist in binary systems, binaries are particularly important to our understanding of the processes by which stars form. In particular, the period and masses of the binary tell us about the amount of [[angular momentum]] in the system. Because this is a [[Conservation law (physics)|conserved quantity]] in physics, binaries give us important clues about the conditions under which the stars were formed.

===Calculating the center of mass in binary stars===
In a simple binary case, the distance ''r''<sub>1</sub> from the center of the first star to the center of mass or [[barycenter]] is given by

<math display="block">r_1 = a \cdot \frac{m_2}{m_1 + m_2} = \frac{a}{1 + \frac{m_1}{m_2}},</math>

where
* ''a'' is the distance between the two stellar centers, and
* ''m''<sub>1</sub> and ''m''<sub>2</sub> are the [[mass]]es of the two stars.

If ''a'' is taken to be the [[semimajor axis]] of the orbit of one body around the other, then ''r''<sub>1</sub> is the semimajor axis of the first body's orbit around the center of mass or ''barycenter'', and {{nowrap|1=''r''<sub>2</sub> = ''a'' − ''r''<sub>1</sub>}} is the semimajor axis of the second body's orbit. When the center of mass is located within the more massive body, that body appears to wobble rather than following a discernible orbit.

=== Center-of-mass animations ===
{{Main|Barycenter}}
The red cross marks the center of mass of the system. These images do not represent any specific real system.

{| class="wikitable" width=480
|valign=top|[[File:orbit1.gif|160px]]<br/>(a) Two bodies of similar mass orbiting around a common center of mass, or ''barycenter''
|valign=top|[[File:orbit2.gif|160px]]<br/>(b) Two bodies with a difference in mass orbiting around a common barycenter, like the Charon–Pluto system
|-
|valign=top|[[File:orbit3.gif|160px]]<br/>(c) Two bodies with a major difference in mass orbiting around a common barycenter (similar to the [[Earth–Moon system]])
|valign=top|[[File:orbit4.gif|160px]]<br/>(d) Two bodies with an extreme difference in mass orbiting around a common barycenter (similar to the [[Sun–Earth system]])
|-
|valign=top colspan=2|[[File:orbit5.gif|320px]]<br/>(e) Two bodies with similar mass orbiting in an [[ellipse]] around a common barycenter
|}

===Research findings===
{| class="wikitable" style="text-align: center; float: right; margin-left: 0.5em;"
|+ Multiplicity likelihood for [[population I]] [[main-sequence]] stars<ref name=Duchene2013>{{citation
 | title=Stellar Multiplicity
 | last1=Duchêne | first1=Gaspard | last2=Kraus | first2=Adam
 | journal=Annual Review of Astronomy and Astrophysics
 | volume=51 | issue=1 | pages=269–310 | date=August 2013
 | doi=10.1146/annurev-astro-081710-102602
 | bibcode=2013ARA&A..51..269D | arxiv=1303.3028 | s2cid=119275313
 }}. See Table 1.</ref>
! Mass range
! Multiplicity<br/> frequency
! Average<br/> companions
|-
| ≤ {{Solar mass|0.1|link=yes}}
| {{Val|22|+6|−4|u=%}}
| {{Val|0.22|+0.06|−0.04}}
|-
| {{Val|0.1|-|0.5|u={{Solar mass}}}}
| {{Val|26|3|u=%}}
| {{Val|0.33|0.05}}
|-
| {{Val|0.7|-|1.3|u={{Solar mass}}}}
| {{Val|44|2|u=%}}
| {{Val|0.62|0.03}}
|-
| {{Val|1.5|-|5|u={{Solar mass}}}}
| ≥ 50%
| {{Val|1.00|0.10}}
|-
| {{Val|8|-|16|u={{Solar mass}}}}
| ≥ 60%
| {{Val|1.00|0.20}}
|-
| ≥ {{Solar mass|16}}
| ≥ 80%
| {{Val|1.30|0.20}}
|}
It is estimated that approximately one third of the [[star system]]s in the [[Milky Way]] are binary or multiple, with the remaining two thirds being single stars.<ref>[https://pweb.cfa.harvard.edu/news/most-milky-way-stars-are-single Most Milky Way Stars Are Single], Harvard-Smithsonian Center for Astrophysics.</ref> The overall multiplicity frequency of [[main sequence star|ordinary stars]] is a [[monotonically increasing]] function of [[stellar mass]]. That is, the likelihood of being in a binary or a multi-star system steadily increases as the masses of the components increase.<ref name=Duchene2013/>

There is a direct correlation between the [[orbital period#Two bodies orbiting each other|period of revolution]] of a binary star and the [[orbital eccentricity|eccentricity]] of its orbit, with systems of short period having smaller eccentricity. Binary stars may be found with any conceivable separation, from pairs orbiting so closely that they are [[contact binary|practically in contact]] with each other, to pairs so distantly separated that their connection is indicated only by their common [[proper motion]] through space. Among gravitationally bound binary star systems, there exists a so-called [[log-normal distribution|log normal distribution]] of periods, with the majority of these systems orbiting with a period of about 100 years. This is supporting evidence for the theory that binary systems are formed during [[star formation]].<ref>{{cite journal |first=D. A. | last=Hubber |author2=A. P. Whitworth |date=2005 |title=Binary Star Formation from Ring Fragmentation |journal=Astronomy & Astrophysics |volume=437 |issue=1 |pages=113–125 |doi=10.1051/0004-6361:20042428 |arxiv=astro-ph/0503412 |bibcode=2005A&A...437..113H |s2cid=118982836 |url=https://cds.cern.ch/record/828359 |type=Submitted manuscript }}</ref>

In pairs where the two stars are of equal [[absolute magnitude|brightness]], they are also of the same [[Stellar classification|spectral type]].
In systems where the brightnesses are different, the fainter star is bluer if the brighter star is a [[giant star]], and redder if the brighter star belongs to the [[main sequence]].<ref>{{cite web | url = http://abyss.uoregon.edu/~js/ast122/lectures/lec11.html | title = Birth and Death of Stars | first = J. | last = Schombert | publisher = University of Oregon}}</ref>

[[File:Artist's concept of exoplanet LTT 1445Ac.jpg|thumb|Artist's impression of the planets orbiting the primary star of [[LTT 1445]], a [[triple star system]].]]

The mass of a star can be directly determined only from its gravitational attraction. Apart from the Sun and stars which act as [[gravitational lens]]es, this can be done only in binary and multiple star systems, making the binary stars an important class of stars. In the case of a visual binary star, after the orbit and the [[Parallax|stellar parallax]] of the system has been determined, the combined mass of the two stars may be obtained by a direct application of the [[Kepler's laws of planetary motion|Keplerian harmonic law]].<ref>{{cite web | url =http://www.astro.cornell.edu/academics/courses/astro201/kepler_binary.htm| title = Binary Star Motions | publisher = Cornell Astronomy}}</ref>

Unfortunately, it is impossible to obtain the complete orbit of a spectroscopic binary unless it is also a visual or an eclipsing binary, so from these objects only a determination of the joint product of mass and the [[trigonometric function|sine]] of the angle of inclination relative to the line of sight is possible. In the case of eclipsing binaries which are also spectroscopic binaries, it is possible to find a complete solution for the specifications (mass, [[density]], size, [[luminosity]], and approximate shape) of both members of the system.

====Planets====
{{main|Habitability of binary star systems}}
[[File:Planets in binary star systems - P- and S-type.svg|thumb|Schematic of a binary star system with one planet on an S-type orbit and one on a P-type orbit]]

While a number of binary star systems have been found to harbor [[extrasolar planets]], such systems are comparatively rare compared to single star systems. Observations by the [[Kepler space telescope]] have shown that most single stars of the same type as the [[Sun]] have plenty of planets, but only one-third of binary stars do. According to theoretical simulations,<ref>{{cite journal | bibcode = 2017AAS...22921905K | title=The Ruinous Influence of Close Binary Companions on Planetary Systems | journal=American Astronomical Society Meeting Abstracts #229 | volume=229 | pages=219.05 | year=2017 | author1=Kraus, Adam L. |author2=Ireland, Michael |author3=Mann, Andrew |author4=Huber, Daniel |author5=Dupuy, Trent J.}}</ref> even widely separated binary stars often disrupt the discs of rocky grains from which [[protoplanets]] form. On the other hand, other simulations suggest that the presence of a binary companion can actually improve the rate of planet formation within stable orbital zones by "stirring up" the protoplanetary disk, increasing the accretion rate of the protoplanets within.<ref name="formation"/>

Detecting planets in multiple star systems introduces additional technical difficulties, which may be why they are only rarely found.<ref>{{cite news | url = http://www.space.com/scienceastronomy/050517_binary_stars.html | title = Planets with Two Suns Likely Common | first = M | last = Schirber | publisher = Space.com | date = 17 May 2005}}</ref> Examples include the [[white dwarf]]-[[pulsar]] binary [[PSR B1620-26]], the [[subgiant]]-[[red dwarf]] binary [[Gamma Cephei]], and the [[white dwarf]]-[[red dwarf]] binary [[NN Serpentis]], among others.<ref>More circumbinary planets are listed in: {{Cite journal |arxiv=1010.4048 |author1=Muterspaugh |author2=Lane |author3=Kulkarni |author4=Maciej Konacki |author5=Burke |author6=Colavita |author7=Shao |author8=Hartkopf |author9=Boss |title=The PHASES Differential Astrometry Data Archive. V. Candidate Substellar Companions to Binary Systems |journal=The Astronomical Journal |volume=140 |issue=6 |pages=1657 |date=2010 |doi=10.1088/0004-6256/140/6/1657 |bibcode=2010AJ....140.1657M |s2cid=59585356}}</ref>

A study of fourteen previously known planetary systems found three of these systems to be binary systems. All planets were found to be in S-type orbits around the primary star. In these three cases the secondary star was much dimmer than the primary and so was not previously detected. This discovery resulted in a recalculation of parameters for both the planet and the primary star.<ref name="exobinary">{{cite journal
| url=http://www.mpia.de/homes/henning/Publications/daemgen.pdf
| title=Binarity of transit host stars – Implications for planetary parameters
| date=2009
| volume=498
| issue=2
| pages=567–574
| last1=Daemgen | first1=S.
| journal=[[Astronomy and Astrophysics]]
| doi=10.1051/0004-6361/200810988
| last2=Hormuth
| first2=F.
| last3=Brandner
| first3=W.
| last4=Bergfors
| first4=C.
| last5=Janson
| first5=M.
| last6=Hippler
| first6=S.
| last7=Henning
| first7=T.
| bibcode=2009A&A...498..567D
| arxiv=0902.2179
| s2cid=9893376
}}</ref>

[[Science fiction]] has often featured [[planet]]s of binary or ternary stars as a setting, for example, George Lucas' [[Tatooine]] from ''[[Star Wars]]'', and one notable story, "[[Nightfall (Asimov short story)|Nightfall]]", even takes this to a six-star system. In reality, some orbital ranges are impossible for dynamical reasons (the planet would be expelled from its orbit relatively quickly, being either ejected from the system altogether or transferred to a more inner or outer orbital range), whilst other orbits present serious challenges for eventual [[biosphere]]s because of likely extreme variations in surface temperature during different parts of the orbit. Planets that orbit just one star in a binary system are said to have "S-type" orbits, whereas those that orbit around both stars have "P-type" or "[[Circumbinary planet|circumbinary]]" orbits. It is estimated that 50–60% of binary systems are capable of supporting habitable terrestrial planets within stable orbital ranges.<ref name="formation">{{cite journal |title=Terrestrial Planet Formation in Binary Star Systems |journal=Extreme Solar Systems |volume=398 |pages=201 |author=Elisa V. Quintana |author2=Jack J. Lissauer |date=2007 |arxiv=0705.3444 |bibcode=2008ASPC..398..201Q}}</ref>