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Binary star
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===Mass transfer and accretion=== As a [[Main sequence|main-sequence star]] increases in size during its [[stellar evolution|evolution]], it may at some point exceed its [[Roche lobe]], meaning that some of its matter ventures into a region where the [[Gravitation|gravitational pull]] of its companion star is larger than its own.<ref>{{cite book | first = Z. | last = Kopal | title = The Roche Problem | publisher = Kluwer Academic | date = 1989 | isbn = 978-0-7923-0129-5}}</ref> The result is that matter will transfer from one star to another through a process known as Roche lobe overflow (RLOF), either being absorbed by direct impact or through an [[accretion disc]]. The mathematical point through which this transfer happens is called the first [[Lagrangian point]].<ref>"[http://demonstrations.wolfram.com/ContactBinaryStarEnvelopes/ Contact Binary Star Envelopes]" by Jeff Bryant, [[Wolfram Demonstrations Project]].</ref> It is not uncommon that the accretion disc is the brightest (and thus sometimes the only visible) element of a binary star. If a star grows outside of its Roche lobe too fast for all abundant matter to be transferred to the other component, it is also possible that matter will leave the system through other Lagrange points or as [[stellar wind]], thus being effectively lost to both components.<ref>"[http://demonstrations.wolfram.com/MassTransferInBinaryStarSystems/ Mass Transfer in Binary Star Systems]" by Jeff Bryant with Waylena McCully, [[Wolfram Demonstrations Project]].</ref> Since the evolution of a star is determined by its mass, the process influences the evolution of both companions, and creates stages that cannot be attained by single stars.<ref>{{cite journal | first = C.B. | last = Boyle | title = Mass transfer and accretion in close binaries β A review | journal = Vistas in Astronomy | date = 1984 | volume = 27 | issue = 2 | pages = 149β169 | doi = 10.1016/0083-6656(84)90007-2|bibcode = 1984VA.....27..149B }}</ref><ref>{{cite book | first = D. | last = Vanbeveren |author2=W. van Rensbergen|author3=C. de Loore | title = The Brightest Binaries | publisher = Springer | date = 2001 | isbn = 978-0-7923-5155-9}}</ref><ref>{{cite journal | first = Z | last = Chen |author2=A. Frank|author3=E. G. Blackman|author4=J. Nordhaus|author5=J. Carroll-Nellenback| title = Mass Transfer and Disc Formation in AGB Binary Systems| journal = Monthly Notices of the Royal Astronomical Society | date = 2017 | doi = 10.1093/mnras/stx680 | volume=468 | issue = 4 | pages=4465β4477| doi-access = free |arxiv = 1702.06160 |bibcode = 2017MNRAS.468.4465C | s2cid = 119073723 }}</ref> Studies of the eclipsing ternary [[Algol]] led to the ''[[Algol paradox]]'' in the theory of [[stellar evolution]]: although components of a binary star form at the same time, and massive stars evolve much faster than the less massive ones, it was observed that the more massive component Algol A is still in the [[main sequence]], while the less massive Algol B is a [[subgiant]] at a later evolutionary stage. The paradox can be solved by [[mass transfer]]: when the more massive star became a subgiant, it filled its [[Roche lobe]], and most of the mass was transferred to the other star, which is still in the main sequence. In some binaries similar to Algol, a gas flow can actually be seen.<ref>{{cite web | url = http://www.haydenplanetarium.org/hp/vo/ava/avapages/S1200algolbpi.html | title = Mass Transfer in the Binary Star Algol | first = J. M. | last = Blondin | author2 = M. T. Richards | author3 = M. L. Malinowski | publisher = American Museum of Natural History | url-status = dead | archive-url = https://web.archive.org/web/20060408135501/http://haydenplanetarium.org/hp/vo/ava/avapages/S1200algolbpi.html | archive-date = 2006-04-08 }}</ref>
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