Editing Appendix/Ramblings/BordeauxPostDefense (section)

====Joel's Initial Response Regarding Shapes====
<font color="darkgreen">Regarding the EH binary sequences:  Yes, I agree with your description of the situation ... "the high-omega limit in Baptiste's graph is analogous to EH's (limiting) line for binaries."  (Immediately below, I have displayed the relevant EH plot; in red ink, I have hand-drawn the relevant limiting line.)  My question is, "What gives rise to this locus of termination points in both types of physical systems?"  EH argue convincingly that, in the binary case, each termination point is related to the classic Roche limit.  In the EH paper, it is easy to see this because they explicitly plot individual (constant mass ratio) model sequences.  My guess is that Baptiste's high-omega limit is also a locus of termination points, but for an **axisymmetric** Roche problem.  Did he ever plot individual model sequences (for his axisymmetric configurations) that would be analogous to the EH model sequences (for binaries)?</font>

I am interested in this issue, in part, because some time ago &#8212; in collaboration with two LSU students &#8212; I attempted to analyze some aspects of the "axisymmetric Roche problem."  [See [https://ui.adsabs.harvard.edu/abs/1992ApJ...394..248W/abstract J. W. Woodward, S. Sankaran, &amp; J. E. Tohline (1992)].]  I would now be very interested in figuring out the overlap that this simple analysis has with Baptiste's much more rigorous investigation.

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Fig. 3 extracted (&amp; slightly modified) from p. 270 of [https://ui.adsabs.harvard.edu/abs/1984PASJ...36..259H/abstract Hachisu &amp; Eriguchi (1984)]<p></p>
"''Binary Fluid Star''"<p></p>
Publications of the Astronomical Society of Japan, <p></p>
vol. 36, pp. 259-276 &copy; Astronomical Society of Japan
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[[File:HachisuEriguchi1984Fig3modified.png|center|500px|Figure 3 from Hachisu &amp; Eriguchi (1984)]]
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<tr><td align="left">See also Fig. 1 in [[Apps/EriguchiHachisu/Models#HE84c|HE84c]] where the authors sketch in this approximately horizontal "red" line.</td></tr>
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Fig. 4 extracted without modification from p. 4507 of [https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4504B/abstract Basillais &amp; Hur&eacute; (2019)]<p></p>
"''Rigidly rotating, incompressible spheroid-ring systems: &nbsp; new bifurcations, critical rotations, and degenerate states''"<p></p>
MNRAS, vol. 487, pp. 4504-4509 &copy; Royal Astronomical Society
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[[File:BH2019Fig4.png|center|400px|Figure 4 from Basillais &amp; Hur&eacute; (2019)]]
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