Editing Binary star (section)

===Methods of observation===
Binary stars are classified into four types according to the way in which they are observed: visually, by observation; [[spectroscopy|spectroscopically]], by periodic changes in [[spectral line]]s; [[photometry (astronomy)|photometrically]], by changes in brightness caused by an eclipse; or [[Astrometry|astrometrically]], by measuring a deviation in a star's position caused by an unseen companion.<ref name=Heintz12 /><ref>{{cite web |url=http://astrosun2.astro.cornell.edu/academics/courses/astro201/binstar.htm |title=Binary Stars |publisher=Cornell University |department=Astronomy}}</ref> Any binary star can belong to several of these classes; for example, several spectroscopic binaries are also eclipsing binaries.

====Visual binaries====
{{main|Visual binary}}
A ''[[visual binary]]'' star is a binary star for which the angular separation between the two components is great enough to permit them to be observed as a double star in a [[telescope]], or even high-powered [[binoculars]]. The [[angular resolution]] of the telescope is an important factor in the detection of visual binaries, and as better angular resolutions are applied to binary star observations, an increasing number of visual binaries will be detected. The relative brightness of the two stars is also an important factor, as glare from a bright star may make it difficult to detect the presence of a fainter component.

The brighter star of a visual binary is the ''primary'' star, and the dimmer is considered the ''secondary.'' In some publications (especially older ones), a faint secondary is called the ''[[comes]]'' (plural ''comites''; companion). If the stars are the same brightness, the discoverer designation for the primary is customarily accepted.<ref name=aitken41>{{cite book |title=The Binary Stars |author-link=Robert Grant Aitken |author=Aitken, R.G. |location=New York |publisher=Dover |year=1964 |page=41}}</ref>

The [[position angle]] of the secondary with respect to the primary is measured, together with the angular distance between the two stars. The time of observation is also recorded. After a sufficient number of observations are recorded over a period of time, they are plotted in [[Polar coordinate system|polar coordinate]]s with the primary star at the origin, and the most probable [[ellipse]] is drawn through these points such that the [[Kepler's laws of planetary motion|Keplerian law of areas]] is satisfied. This ellipse is known as the ''apparent ellipse'', and is the projection of the actual elliptical orbit of the secondary with respect to the primary on the plane of the sky. From this projected ellipse the complete elements of the orbit may be computed, where the [[semi-major axis]] can only be expressed in angular units unless the [[Parallax|stellar parallax]], and hence the distance, of the system is known.<ref name = "csep10"/>

====Spectroscopic binaries====<!-- This section is linked from [[Redshift]] -->
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[[File:Algol AB movie imaged with the CHARA interferometer - labeled.gif|thumb|right|[[Algol|Algol B]] orbits [[Algol|Algol A]]. This animation was assembled from 55 images of the [[CHARA array|CHARA interferometer]] in the [[H band (infrared)|near-infrared H-band]], sorted according to orbital phase.]]
Sometimes, the only evidence of a binary star comes from the [[Doppler effect]] on its emitted light. In these cases, the binary consists of a pair of stars where the [[spectral line]]s in the light emitted from each star shifts first towards the blue, then towards the red, as each moves first towards us, and then away from us, during its motion about their common [[center of mass]], with the period of their common orbit.

In these systems, the separation between the stars is usually very small, and the orbital velocity very high. Unless the plane of the orbit happens to be [[perpendicular]] to the line of sight, the orbital velocities have components in the line of sight, and the observed [[radial velocity]] of the system varies periodically. Since radial velocity can be measured with a [[spectrometer]] by observing the [[Doppler effect|Doppler shift]] of the stars' [[spectral line]]s, the binaries detected in this manner are known as ''spectroscopic binaries''. Most of these cannot be resolved as a visual binary, even with [[telescope]]s of the highest existing [[Angular resolution|resolving power]].

In some spectroscopic binaries, spectral lines from both stars are visible, and the lines are alternately double and single. Such a system is known as a double-lined spectroscopic binary (often denoted "SB2"). In other systems, the spectrum of only one of the stars is seen, and the lines in the spectrum shift periodically towards the blue, then towards red and back again. Such stars are known as single-lined spectroscopic binaries ("SB1").

The orbit of a spectroscopic binary is determined by making a long series of observations of the radial velocity of one or both components of the system. The observations are plotted against time, and from the resulting curve a period is determined. If the orbit is [[circle|circular]], then the curve is a [[Trigonometric function|sine]] curve. If the orbit is [[ellipse|elliptical]], the shape of the curve depends on the [[orbital eccentricity|eccentricity]] of the ellipse and the orientation of the major axis with reference to the line of sight.

It is impossible to determine individually the [[semi-major axis]] ''a'' and the inclination of the orbit plane ''i''. However, the product of the semi-major axis and the sine of the inclination (i.e. {{nobr|''a''&thinsp;sin&thinsp;''i''}}) may be determined directly in linear units (e.g. kilometres). If either ''a'' or ''i'' can be determined by other means, as in the case of eclipsing binaries, a complete solution for the orbit can be found.<ref>{{cite web |url=http://www.astro.cornell.edu/academics/courses/astro101/lectures/lec16.htm |title=Stellar Masses |first=T. |last=Herter |publisher=Cornell University |url-status=dead |archive-url=https://web.archive.org/web/20120617150857/http://www.astro.cornell.edu/academics/courses/astro101/lectures/lec16.htm |archive-date=June 17, 2012 |df=dmy-all}}</ref>

Binary stars that are both visual and spectroscopic binaries are rare and are a valuable source of information when found. About 40 are known. Visual binary stars often have large true separations, with periods measured in decades to centuries; consequently, they usually have orbital speeds too small to be measured spectroscopically. Conversely, spectroscopic binary stars move fast in their orbits because they are close together, usually too close to be detected as visual binaries. Binaries that are found to be both visual and spectroscopic thus must be relatively close to Earth.

===={{Anchor|Eclipsing binary}}Eclipsing binaries====<!-- This section is linked from [[Eclipsing binary]] -->
{{redirect|Eclipsing binaries|the novel|E. E. Smith bibliography#Family D'Alembert}}<!-- Redirect necessary as link arrives here -->
An ''eclipsing binary star'' is a binary star system in which the orbital plane of the two stars lies so nearly in the line of sight of the observer that the components undergo mutual [[eclipse]]s.<ref name=B-EBS>{{cite web |url=http://www.physics.sfasu.edu/astro/ebstar/ebstar.html |first=D. |last=Bruton |title=Eclipsing Binary Stars |publisher=Stephen F. Austin State University |url-status=dead |archive-url=https://web.archive.org/web/20070414144827/http://www.physics.sfasu.edu/astro/ebstar/ebstar.html |archive-date=2007-04-14 |df=dmy-all}}</ref> In the case where the binary is also a spectroscopic binary and the [[parallax]] of the system is known, the binary is quite valuable for stellar analysis. [[Algol]], a triple star system in the [[Perseus (constellation)|constellation Perseus]], contains the best-known example of an eclipsing binary.

[[File:Artist’s impression of eclipsing binary.ogv|upright=1.2|thumb|This video shows an artist's impression of an eclipsing binary star system. As the two stars orbit each other they pass in front of one another and their combined brightness, seen from a distance, decreases.]]
Eclipsing binaries are variable stars, not because the light of the individual components vary but because of the eclipses. The [[light curve]] of an eclipsing binary is characterized by periods of practically constant light, with periodic drops in intensity when one star passes in front of the other. The brightness may drop twice during the orbit, once when the secondary passes in front of the primary and once when the primary passes in front of the secondary. The deeper of the two eclipses is called the primary regardless of which star is being occulted, and if a shallow second eclipse also occurs it is called the secondary eclipse. The size of the brightness drops depends on the relative brightness of the two stars, the proportion of the occulted star that is hidden, and the [[surface brightness]] (i.e. [[effective temperature]]) of the stars. Typically the occultation of the hotter star causes the primary eclipse.<ref name=B-EBS/>

An eclipsing binary's period of orbit may be determined from a study of its [[light curve]], and the relative sizes of the individual stars can be determined in terms of the radius of the orbit, by observing how quickly the brightness changes as the disc of the nearest star slides over the disc of the other star.<ref name=B-EBS/> If it is also a spectroscopic binary, the [[orbital elements]] can also be determined, and the mass of the stars can be determined relatively easily, which means that the relative densities of the stars can be determined in this case.<ref>{{cite web |url=http://www.physics.sfasu.edu/markworth/ast105/Binary-Stars.ppt |archive-url= https://web.archive.org/web/20030903072148/http://www.physics.sfasu.edu/markworth/ast105/Binary-Stars.ppt |url-status=dead |archive-date=2003-09-03 |format=[[Microsoft PowerPoint|PowerPoint]] |title=Binary Stars |first=M |last=Worth |publisher=Stephen F. Austin State University |df=dmy-all}}</ref>

Since about 1995, measurement of extragalactic eclipsing binaries' fundamental parameters has become possible with 8-meter class telescopes. This makes it feasible to use them to directly measure the distances to external galaxies, a process that is more accurate than using [[standard candle]]s.<ref name="wilson2008">{{cite journal |journal=The Astrophysical Journal |volume=672 |issue=1 |title=Eclipsing binary solutions in physical units and direct distance estimation |bibcode=2008ApJ...672..575W |doi=10.1086/523634 |author=Wilson, R.E. |date=1 January 2008 |pages=575–589 <!-- |access-date=4 July 2013 --> |df=dmy-all|doi-access=free }}</ref> By 2006, they had been used to give direct distance estimates to the [[Large Magellanic Cloud|LMC]], [[Small Magellanic Cloud|SMC]], [[Andromeda Galaxy]], and [[Triangulum Galaxy]]. Eclipsing binaries offer a direct method to gauge the distance to galaxies to an improved 5% level of accuracy.<ref name="Bonanos2006">{{cite journal |author=Bonanos, Alceste Z. |title=Eclipsing binaries: Tools for calibrating the extragalactic distance scale |year=2006 |journal=Proceedings of the International Astronomical Union |volume=2 |pages=79–87 |arxiv=astro-ph/0610923 |citeseerx=10.1.1.254.2692 |doi=10.1017/S1743921307003845 |bibcode=2007IAUS..240...79B|s2cid=18827791 }}</ref>

====Non-eclipsing binaries that can be detected through photometry====
Nearby non-eclipsing binaries can also be [[Photometry (astronomy)|photometrically]] detected by observing how the stars affect each other in three ways. The first is by observing extra light which the stars reflect from their companion. Second is by observing ellipsoidal light variations which are caused by deformation of the star's shape by their companions. The third method is by looking at how [[relativistic beaming]] affects the apparent magnitude of the stars. Detecting binaries with these methods requires accurate [[Photometry (astronomy)|photometry]].<ref>{{cite journal |arxiv=1410.3074 |title=Seventy-two new non-eclipsing BEER binaries discovered in CoRoT lightcurves and confirmed by RVs from AAOmega |author1=Tal-Or, Lev |author2=Faigler, Simchon |author3=Mazeh, Tsevi |year=2014 |doi=10.1051/epjconf/201510106063 |volume=101 |journal=EPJ Web of Conferences |page=06063|s2cid=118394510 }}</ref>

====Astrometric binaries====
Astronomers have discovered some stars that seemingly orbit around an empty space. ''Astrometric binaries'' are relatively nearby stars which can be seen to wobble around a point in space, with no visible companion. The same mathematics used for ordinary binaries can be applied to infer the [[mass]] of the missing companion. The companion could be very dim, so that it is currently undetectable or masked by the glare of its primary, or it could be an object that emits little or no [[electromagnetic radiation]], for example a [[neutron star]].<ref>{{cite web |url=http://lantern.ncsa.uiuc.edu/~dbock/Vis/NeutronStar/Summary.html |title=Binary neutron star collision |first=D. |last=Bock |publisher=University of Illinois Urbana-Champaign |department=National Center for Supercomputing Applications |url-status=dead |archive-url=https://web.archive.org/web/20120426043619/http://lantern.ncsa.uiuc.edu/~dbock/Vis/NeutronStar/Summary.html |archive-date=2012-04-26 |df=dmy-all}}</ref>

The visible star's position is carefully measured and detected to vary, due to the gravitational influence from its counterpart. The position of the star is repeatedly measured relative to more distant stars, and then checked for periodic shifts in position. Typically this type of measurement can only be performed on nearby stars, such as those within 10&nbsp;[[parsec]]s. Nearby stars often have a relatively high [[proper motion]], so astrometric binaries will appear to follow a ''wobbly'' path across the sky.

If the companion is sufficiently massive to cause an observable shift in position of the star, then its presence can be deduced. From precise [[Astrometry|astrometric]] measurements of the movement of the visible star over a sufficiently long period of time, information about the mass of the companion and its orbital period can be determined.<ref>{{cite journal |first1=H. |last1=Asada |first2=T. |last2=Akasaka |first3=M. |last3=Kasai |title=Inversion formula for determining parameters of an astrometric binary |date=27 September 2004 |bibcode=2004PASJ...56L..35A |pages=L35–L38 |volume=56 |issue=6 |journal=Publ. Astron. Soc. Jpn. |arxiv=astro-ph/0409613 |doi=10.1093/pasj/56.6.L35|s2cid=15301393 }}</ref> Even though the companion is not visible, the characteristics of the system can be determined from the observations using [[Johannes Kepler|Kepler]]'s [[Kepler's laws of planetary motion|law]]s.<ref>{{cite web |url=http://csep10.phys.utk.edu/astr162/lect/binaries/astrometric.html |title=Astrometric Binaries |publisher=University of Tennessee}}</ref>

This method of detecting binaries is also [[Methods of detecting extrasolar planets#Astrometry|used to locate]] [[extrasolar planet]]s orbiting a star. However, the requirements to perform this measurement are very exacting, due to the great difference in the mass ratio, and the typically long period of the planet's orbit. Detection of position shifts of a star is a very exacting science, and it is difficult to achieve the necessary precision. Space telescopes can avoid the blurring effect of [[atmosphere of Earth|Earth's atmosphere]], resulting in more precise resolution.