Editing ThreeDimensionalConfigurations/BinaryFission

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=Fission Hypothesis of Binary Star Formation=
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"This paper is concerned with one of the oldest hypotheses in stellar-evolution theory, namely, that a binary system originates from the splitting of a single star into two components due to rotational instability during contraction of the star.  In spite of many attempts, no satisfactory theory of this process has been developed &hellip;"</font>
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&#8212; Drawn from &sect;I of [https://ui.adsabs.harvard.edu/abs/1966ApJ...143..111R/abstract Ian W. Roxburgh (1966)] 
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"Broadly speaking, the fission problem may be stated as follows.  Will a single contracting body &#8212; initially endowed with some angular momentum and free from any appreciable external disturbance &#8212; eventually separate into a pair of detached fragments; and if so, how will the separation take place?"<br /><p>"&hellip; So far, no one has yet been able to prove or disprove that</font> [for example] <font color="darkgreen">an elongated pear-shaped figure with one end larger than the other will eventually split into two detached masses in mutual orbital motion.  This would require a ''fully'' nonlinear, time-dependent study of the evolution of a pear-shaped figure, the actual boundary of the configuration being itself an unknown at every instant."</font>
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&#8212; Drawn from &sect;11.3 (pp. 280-281) of [<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>] 
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==Potentially Useful References==

* [https://ui.adsabs.harvard.edu/abs/1965RSPSA.286....1C/abstract S. Chandrasekhar (1965)], Proc. Roy. Soc. London. Series A, Mathematical and Physical Sciences, 286, pp. 1 - 26:  ''The Stability of a Rotating Liquid Drop''
* [https://ui.adsabs.harvard.edu/abs/1966ApJ...143..111R/abstract I. W. Roxburgh (1966)], ApJ, 143, 111:  ''On the Fission Theory of the Origin of Binary Stars''
* [https://trove.nla.gov.au/work/21340423?selectedversion=NBD179107 J. P. Ostriker (1970)], Stellar Rotation: Proceedings of the IAU Colloquium held at the Ohio State University, Columbus, OH, U.S.A., September 8-11, 1969, edited by Arne Slettebak, p. 147:  <font color="maroon">''Fission and the Origin of Binary Stars''</font>
* [https://ui.adsabs.harvard.edu/abs/1972ApJ...175..171L/abstract N. R. Lebovitz (1972)], ApJ, 175, 171:  <font color="maroon">''On the Fission Theory of Binary Stars''</font>
* &sect;IVa of [https://ui.adsabs.harvard.edu/abs/1973ApJ...180..159B/abstract P. Bodenheimer &amp; J. P. Ostriker (1973)], ApJ, 180, 159 [Part VIII]
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<font color="green">The ancient problem of whether a rotating, contracting star will, if it has sufficient angular momentum, subdivide and become a binary system must now be reexamined.  The existence of generalized zero-viscosity polytropic sequences which do not terminate and which do reach the points of dynamical over stability &hellip; answers several of the objections that have been raised against the fission hypothesis.  The new situation was reviewed by [https://trove.nla.gov.au/work/21340423?selectedversion=NBD179107 J. P. Ostriker (1970)] in a discussion which anticipates the results presented in this paper.  A point of view is presented by [https://ui.adsabs.harvard.edu/abs/1972ApJ...175..171L/abstract N. R. Lebovitz (1972)] which envisions a different evolution but predicts fission at the same critical value of</font> <math>~T/|W|</math>.
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* [https://ui.adsabs.harvard.edu/abs/1984Ap%26SS..99...71H/abstract I. Hachisu &amp; Y. Eriguchi (1984)], Astrophysics &amp; Space Sciences, 99, 71:  ''Fission Sequence and Equilibrium Models of Rigidity [sic] Rotating Polytropes''
* [http://www.phys.lsu.edu/astro/movie_captions/fission.html Webpage summary of Cazes' simulations]
* [https://inis.iaea.org/search/search.aspx?orig_q=RN:17071096 R. H. Durisen &amp; J. E. Tohline (1985)], ''Protostars and Planets II'', pp. 534 - 575, Univ. of Arizona Press: <font color="maroon"> ''Fission of Rapidly Rotating Fluid Systems''</font>
* [http://articles.adsabs.harvard.edu//full/1986ormo.conf..487D/0000487.000.html Durisen &amp; Gingold (198x)], <font color="maroon">''Numerical Simulations of Fission''</font>
* [https://ui.adsabs.harvard.edu/abs/1987GApFD..38...15L/abstract N. R. Lebovitz (1987)], Geophysical and Astrophysical Fluid Dynamics, 38, 15: <font color="maroon">''Binary Fission via Inviscid Trajectories''</font>
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<li>Phase-Transition Theory of Instabilities:</li>
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<li>[https://ui.adsabs.harvard.edu/abs/1995ApJ...446..472C/abstract  D. M. Christodoulou, D. Kazanas, I. Shlosman &amp; J. E. Tohline (1995a)], ApJ, 446, 472:  ''Second-Harmonic Instability and Bifurcation Points''</li>
<li>[https://ui.adsabs.harvard.edu/abs/1995ApJ...446..485C/abstract  D. M. Christodoulou, D. Kazanas, I. Shlosman &amp; J. E. Tohline (1995b)], ApJ, 446, 485:  ''Fourth-Harmonic Bifurcations and &lambda;-Transitions''</li>
<li>[https://ui.adsabs.harvard.edu/abs/1995ApJ...446..500C/abstract  D. M. Christodoulou, D. Kazanas, I. Shlosman &amp; J. E. Tohline (1995c)], ApJ, 446, 500:  ''The Third-Harmonic Bifurcation on the Jacobi Sequence and the Fission Problem''</li>
<li>[https://ui.adsabs.harvard.edu/abs/1995ApJ...446..510C/abstract D. M. Christodoulou, D. Kazanas, I. Shlosman &amp; J. E. Tohline (1995d)], ApJ, 446, 510:  ''Critical Points on the Maclaurin Sequence and Nonlinear Fission Processes''</li>
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* [https://ui.adsabs.harvard.edu/abs/2001IAUS..200...23B/abstract I. A. Bonnell (2001)], Proceedings of IAU Symposium 200, held 10 - 15 April, 2000 in Potsdam, Germany, edited by Hans Zinnecker and Robert D. Mathieu, p. 23:  ''The Formation of Close Binary Stars''
* [https://ui.adsabs.harvard.edu/abs/2002ARA%26A..40..349T/abstract J. T. Tohline (2002)], ARAA, 40, 349:  ''The Origin of Binary Stars''

==Illustration==

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'''Figure 1'''
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[[File:SkylabFission.jpg|300px|Droplet Fission]]
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YouTube video:
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[http://www.youtube.com/watch?v=61dH_CS_oqA Skylab Drop Dynamics Experiment (1975)]
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'''Figure 2'''
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[[File:BrownScriven1980_Fig5.jpg|300px|Theoretical Model]]<br>
[http://adsabs.harvard.edu/abs/1980RSPSA.371..331B Brown &amp; Scriven (1980)] 
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(Journal of Fluid Mechanics, 276, 389)
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'''Figure 4'''
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[[File:Wang1994_Fig10.jpg|350px|USML-1 Experiment]]<br>
[http://dx.doi.org/10.1017/S0022112094002612 Wang, Anilkumar, Lee &amp; Lin (1994)] 
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(Proc. Roy. Soc. London, 371, 331)
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'''<font color="black">Figure 3</font>'''
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[[File:HachisuEriguchi1984.jpg|300px|Hachisu &amp; Eriguchi scenario]]<br>
[http://adsabs.harvard.edu/abs/1984Ap%26SS..99...71H Hachisu &amp; Eriguchi (1984)] 
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(Astrophysics and Space Science, 99, 71)
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'''<font color="white">Figure 5</font>'''
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[[File:LSU_Stable.animated.gif|100px|Kimberly New simulation]]<br>
[http://adsabs.harvard.edu/abs/1997ApJ...490..311N Figure 10 from New &amp; Tohline (1997)]<br>
<font color="white">(The Astrophysical Journal, 490, 311)</font>
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=Related Discussions=
==Fission in Nuclear Physics==
The nuclear physics community also draws an analogy between the fission of a rotating fluid drop and the spontaneous fission of atomic nuclei; see, for example, the figure associated with the [http://en.wikipedia.org/wiki/Nuclear_fission#Energetics Wikipedia discussion of the energetics of nuclear fission].

See also [https://ui.adsabs.harvard.edu/abs/1967ApJ...148..825R/abstract C. E. Rosenkilde (1967b)], ApJ, 148, 825:  ''The tensor virial-theorem including viscous stress and the oscillations of a Maclaurin spheroid''.  The first few lines of the Appendix of this paper state &hellip;
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"The virial method has recently been extended to phenomena of interest in the theory of nuclear fission ([https://ui.adsabs.harvard.edu/abs/1967JMP.....8...98R/abstract Rosenkilde 1967a)]</font>, Journal of Mathematical Physics, 8, 98 <font color="green">&hellip;  For a rotating, charged, inviscid liquid drop held together by surface tension, there exist axisymmetric figures of equilibrium which are nearly spheroids.  Moreover, prolate as well as oblate figures are possible.  If these figures are assumed to be spheroids, then the investigation (based on the virial method) of their stability closely resembles the corresponding investigation for the self-gravitating Maclaurin spheroids &hellip;"
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==Drop Dynamics Experiments==
[On '''<font color="red">1 January 2014</font>''', J. E. Tohline wrote ...] As I was putting this chapter together, I had difficulty documenting the various drop dynamics experiments that have been conducted by astronauts in various Earth-orbiting (zero <math>g</math>) environments.  Here is the relevant information that I have found, to date.
===Skylab===
Experiments showing the ''fission'' of liquid drops were evidently conducted during the Skylab 2, Skylab 3, and Skylab 4 missions (circa 1973-1974).  
* As has been documented in a short film review written by Howard Voss and published in the [http://dx.doi.org/10.1119/1.10227 American Journal of Physics (44/10, 1021, Oct 1976)], film footage from a variety of Skylab experiments was produced by NASA, edited by Thomas Campbell &amp; Robert Fuller, and, beginning in 1976, distributed as 12 [http://en.wikipedia.org/wiki/Super_8_film Super 8] film loops by the [http://www.aapt.org/ American Association of Physics Teachers] (AAPT).
* As is documented in [http://web.physics.ucsb.edu/~lecturedemonstrations/Linked%20files/Media%20library/Skylab%20guide%20(videodisc).pdf A Teacher's Guide for the Skylab Physics Videodisc] the content of all 12 Super 8 film loops was made available for distribution in [http://en.wikipedia.org/wiki/Videodisc Videodisc] format in 1987 through the [http://www.aapt.org/ AAPT].
* The YouTube video referenced in and linked to the caption of Figure 1, above, is the digitized version of the Skylab film loop that illustrates fission of a water droplet.

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<font size="-1">According to the [http://web.physics.ucsb.edu/~lecturedemonstrations/Linked%20files/Media%20library/Skylab%20guide%20(videodisc).pdf Teacher's Guide] mentioned above, the activities shown in the above-referenced films were carried out by three teams of Skylab Astronauts:</font>
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[[File:SkylabAstronauts.jpg|500px|center|Skylab Astronauts]]
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[[File:Skylab_2_Kerwin3.jpg|thumb|Kerwin blows water droplet from a straw]]
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[http://en.wikipedia.org/wiki/Skylab_2 Skylab 2] (First Team) 
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===Space Shuttle Flights===
Experiments illustrating the dynamical behavior of liquid drops were conducted during several space shuttle missions.  Some experiments were performed inside the European Space Agency's "spacelab module" and others were performed with the aid of a "Drop Physics Module (DPM)" inside the United States Microgravity Laboratory (USML), each being a "portable" laboratory that was housed in the shuttle's payload bay.
* [[File:Sts51b_patch.jpg|100px|right|Spacelab 3]]Wang, Trinh, Croonquist, and Elleman (1986; [http://adsabs.harvard.edu/abs/1986PhRvL..56..452W Physical Review Letters, 56, 452]) report results from a controlled drop dynamics experiment that was conducted during the "Spacelab III mission" (see the final acknowledgement paragraph of their paper), which took place during shuttle flight [http://en.wikipedia.org/wiki/STS-51-B STS-51-B (29 April - 6 May 1985)].  Taylor Wang &#8212; one of the authors of this ''PRL'' publication &#8212; flew as one of the seven members of the space shuttle crew, specifically as Payload Specialist 2.  His narrated account of some of the experimental activities is available, beginning at 7 minutes 32 seconds into the [http://www.nss.org/resources/library/shuttlevideos/shuttle17.htm STS-51B "Post Flight Presentation" video].
* [[File:fluid_drop.jpg|100px|right|frame|USML-1 Droplet Fission]]Another mission &#8212; [http://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-50.html USML-1 during shuttle flight STS-50] &#8212; took place in early 1992. According to [http://www.jpl.nasa.gov/releases/95/release_1995_9571.html information provided by NASA/JPL's public information office], "&#8230; the transition of rotating liquid drops into a 'dog-bone,' or two-lobed shape, was studied in detail &#8230;"  As can be seen, beginning at 2 minutes 28 seconds into the [http://www.nss.org/resources/library/shuttlevideos/shuttle48.htm STS-50 "Post Flight Presentation" video], Eugene Trinh flew was one of the members of this shuttle mission who conducted these DMP experiments.  Detailed results from DPM experiments during the USML-1 mission have been published in the Journal of Fluid Mechanics:  T. G. Wang, A. V. Anilkumar, C. P. Lee and K. C. Lin (1994).  ''Bifurcation of rotating liquid drops: results from USML-1 experiments in Space.'' [http://dx.doi.org/10.1017/S0022112094002612 Journal of Fluid Mechanics, 276, pp 389-403]
* I think that the three-frame black &amp; white image shown here on the right presents a result from mission USML-1.  That is how this image is referenced in an [http://www.phys.lsu.edu/astro/movie_captions/fission.html online discussion of fission] that I put together about a decade ago.
* Yet another mission &#8212; [http://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-73.html USML-2 during shuttle flight STS-73] &#8212; took place in the fall of 1995.  Some additional drop dynamics experiments were conducted during this mission &#8212; see, for example, about 7 minutes and 40 seconds into the [http://www.nss.org/resources/library/shuttlevideos/shuttle72.htm STS-73 "Post Flight Presentation" video].  Lee, Anilkumar, Hmelo, &amp; Wang (1998; [http://adsabs.harvard.edu/abs/1998JFM...354...43L Journal of Fluid Mechanics, 354, 43]) report results from these controlled drop dynamics experiments. 

===International Space Station===
* See the two "Gallery of Fluid Motions" mpg movies that accompany the preprint by [http://arxiv.org/abs/1210.4073v1 Ueno et al. (2012)].

==Online References==
* [http://www.phys.lsu.edu/astro/movie_captions/fission.html The Fission Mechanism for Binary Star Formation]
* [http://www.phys.lsu.edu/~tohline/fission.movies.html Fission Simulations at LSU]
* T. G. Wang, A. V. Anilkumar, C. P. Lee and K. C. Lin (1994). ''Bifurcation of rotating liquid drops: results from USML-1 experiments in Space.'' [http://dx.doi.org/10.1017/S0022112094002612 Journal of Fluid Mechanics, 276, pp 389-403]
* [http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/18294/1/99-1767.pdf Ohsaka &amp; Trinh (19xx)]

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