Editing Appendix/Ramblings/BordeauxPostDefense (section)

====Fission Hypothesis (Joel's Thoughts)====

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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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Throughout my research career, the question that has most intrigued me is, "How do binary stars form?"  A close second is the question, "Does the classic ''fission hypothesis'' properly describe how &#8212; at least ''some'' if not all &#8212; binary stars form?"  In an [[ThreeDimensionalConfigurations/BinaryFission#Illustration|accompanying chapter]] I have provided a small collection of images &#8212; from diverse scientific &amp; engineering disciplines &#8212; that always come to mind when I think about, or discuss with others the concept of, ''fission.''

The figure from [http://adsabs.harvard.edu/abs/1984Ap%26SS..99...71H Hachisu &amp; Eriguchi (1984)] that is reprinted here on the left, provides a rigorous foundation for discussions of fission (and binary star formation) in the context of astrophysics.  Each of the pictured configurations shows the surface (shape) of an incompressible fluid model whose detailed force-balanced equilibrium structure can be specified precisely.  And while we can identify where each of these configurations is located along a precisely defined equilibrium ''sequence'' &#8212; along, for example, the ''Jacobi ellipsoid sequence'' or the ''Dumbbell-Binary'' sequence &#8212; ''time'' is completely absent from the picture.  Well &hellip; the arrows in the figure ''suggest'' how evolution from one configuration to the next might occur.  But we [''i.e.,'' the astrophysics community] have not yet been able to simulate in a quantitatively robust manner how any one of these fluid configurations evolves toward any other one of the configurations.  I have always hoped that the community will develop the technical tools that will allow us to perform such time-evolutionary simulations, and that I would be able to make a meaningful contribution to these efforts.  But we have not yet succeeded in this task.

As the community attempts to simulate the time-dependent evolution of these and related self-gravitating fluid systems, <font color="red">should we focus on ''incompressible'' fluids</font> (such as the ones depicted in the Hichisu &amp; Eriguchi figure), <font color="red">or should our focus be on incompressible fluids?</font>

<font color="red">COMPRESSIBLE FLUIDS:</font> &nbsp; The physical properties of protostellar gas clouds are <b>''not''</b> well described by an incompressible (n = 0 polytropic) equation of state.  Ideally, then, our attempt to simulate fission should focus on modeling the evolution of self-gravitating fluids that obey a ''compressible'' equation of state (EOS) &#8212; for example, polytopes with n &ge; 1.  This is why, over the years, my research group has invested a great deal of time developing numerical techniques that can be used to accurately (a) construct initial equilibrium models, and (b) follow the subsequent dynamical evolution, of rapidly rotating, compressible fluid systems. Generally speaking, step "a" has involved implementation of the HSCF technique, while step "b" has involved the development of ''finite-volume'' techniques to solve the coupled set of [[PGE#Principal_Governing_Equations|''Principle Governing Equations'']] supplemented by a [[SR#Time-Dependent_Problems|compressible, polytropic EOS]].

incorporate simulation of we should therefore So, ideally, best described by ''compressible'' equations of state.

GOOD NEWS &amp; BAD NEWS:
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   <li>The equilibrium structures displayed by [http://adsabs.harvard.edu/abs/1984Ap%26SS..99...71H Hachisu &amp; Eriguchi (1984)] are uniform-density, ''incompressible'' fluids.  Oscillation frequencies are known for many of these systems, which means that points of instability can be identified along with growth rates in the linear regime.</li>
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