Revision as of 16:28, 24 July 2020

Université de Bordeaux (Part 2)

Exterior Gravitational Potential of Toroids

J. -M. Huré, B. Basillais, V. Karas, A. Trova, & O. Semerák (2020), MNRAS, 494, 5825-5838 have published a paper titled, The Exterior Gravitational Potential of Toroids. Here we examine how their work relates to the published work by C.-Y. Wong (1973, Annals of Physics, 77, 279), which we have separately discussed in detail.

We discuss this topic in a separate, accompanying chapter.

Spheroid-Ring Systems

Through a research collaboration at the Université de Bordeaux, B. Basillais & J. -M. Huré (2019), MNRAS, 487, 4504-4509 have published a paper titled, Rigidly Rotating, Incompressible Spheroid-Ring Systems: New Bifurcations, Critical Rotations, and Degenerate States.

Key References

Here are some relevant publications:

Hachisu (1986a, ApJS, 61, 479): A Versatile Method for Obtaining Structures of Rapidly Rotating Stars
Fujisawa & Eriguchi (2014, MNRAS, 438, L61): Prolate stars due to meridional flows
Huré, Hersant & Nasello (2018, MNRAS, 475, 63): The equilibrium of overpressurized polytropes
& Eriguchi (1984, Ap&SS, 99, 71): Fission Sequence and Equilibrium Models of [Rigidly] Rotating Polytropes
Hachisu, Eriguchi & Nomoto (1986b, ApJ, 311, 214): Fate of merging double white dwarfs. II - Numerical method
Nishida, Eriguchi & Lanza (1992, ApJ, 401, 618): General Relativistic Structure of Star-Toroid Systems
Woodward, Sankaran & Tohline (1992 ApJ, 394, 248): Tidal Disruption of a Star by a Massive Disk (The Axisymmetric Roche Problem)

Especially,

Eriguchi & Hachisu (1983, Prog. Theor. Phys., 69, 1131): Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluids: Two-Ring Sequence and Core-Ring Sequence
Ansorg, Kleinwächter & Meinel (2003, MNRAS, 339, 515): Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids
Hachisu, Eriguchi & Nomoto (1986a, ApJ, 308, 161): Fate of Merging Double White Dwarfs

Key Figures

Eriguchi & Hachisu (1983)

Fig. 3 extracted without modification from p. 1134 of Eriguchi & Hachisu (1983)

"Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluids:
Two-Ring Sequence and Core-Ring Sequence"

Progress of Theoretical Physics,

CAPTION: The angular momentum-angular velocity relations. Solid curves represent uniformly rotating equilibrium sequences.

MS: Maclaurin sequence
JE: Jacobi sequence
OR: one-ring sequence

The number and letter R or C attached to a curve denote mass ratio and two-ring or core-ring sequence, respectively. If differential rotation is allowed, the equilibrium sequences may continue to exist as shown by the dashed curves.

@@ Line 12: / Line 12: @@
 ==Spheroid-Ring Systems==
 Through a research collaboration at the [https://www.u-bordeaux.com Universit&eacute; de Bordeaux], [https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4504B/abstract B. Basillais &amp; J. -M. Hur&eacute; (2019), MNRAS, 487, 4504-4509] have published a paper titled, ''Rigidly Rotating, Incompressible Spheroid-Ring Systems:  New Bifurcations, Critical Rotations, and Degenerate States.''
+===Key References===
 Here are some relevant publications:
@@ Line 25: / Line 27: @@
 Especially,
 <ul>
-<li>[https://ui.adsabs.harvard.edu/abs/1983PThPh..69.1131E/abstract Eriguchi &amp; Hachisu (1983, Prog. Theor. Phys., 69, 1131)]: &nbsp; ''Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluids &#8212; Two-Ring Sequence and Core-Ring Sequence''</li>
+<li>[https://ui.adsabs.harvard.edu/abs/1983PThPh..69.1131E/abstract Eriguchi &amp; Hachisu (1983, Prog. Theor. Phys., 69, 1131)]: &nbsp; ''Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluids:&nbsp; Two-Ring Sequence and Core-Ring Sequence''</li>
 <li>[https://ui.adsabs.harvard.edu/abs/2003MNRAS.339..515A/abstract Ansorg, Kleinw&auml;chter &amp; Meinel (2003, MNRAS, 339, 515)]: &nbsp; ''Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids''</li>
 <li>[https://ui.adsabs.harvard.edu/abs/1986ApJ...308..161H/abstract Hachisu, Eriguchi &amp; Nomoto (1986a, ApJ, 308, 161)]: &nbsp; ''Fate of Merging Double White Dwarfs''</li>
 </ul>
+===Key Figures===
+====Eriguchi &amp; Hachisu (1983)====
+<table border="1" cellpadding="5" align="center" width="75%">
+<tr><td align="center" bgcolor="orange">
+Fig. 3 extracted without modification from p. 1134 of [https://ui.adsabs.harvard.edu/abs/1983PThPh..69.1131E/abstract Eriguchi &amp; Hachisu (1983)]<p></p>
+"''Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluids:<br />Two-Ring Sequence and Core-Ring Sequence''"<p></p>
+Progress of Theoretical Physics, <p></p>
+vol. 69, pp. 1131-1136 &copy; Progress of Theoretical Physics
+</td></tr>
+<tr>
+  <td align="center">
+[[File:EriguchiHachisu83 Fig3.png|center|800px|Figure 3 from Eriguchi &amp; Hachisu (1983)]]
+  </td>
+</tr>
+<tr>
+  <td align="left">
+CAPTION: &nbsp;The angular momentum-angular velocity relations.  Solid curves represent uniformly rotating equilibrium sequences.
+<ul>
+<li>MS: &nbsp; Maclaurin sequence</li>
+<li>JE: &nbsp; Jacobi sequence</li>
+<li>OR: &nbsp; one-ring sequence</li>
+</ul>
+The number and letter ''R'' or ''C'' attached to a curve denote mass ratio and two-ring or core-ring sequence, respectively.  If differential rotation is allowed, the equilibrium sequences may continue to exist as shown by the dashed curves.
+  </td>
+</tr>
+</table>
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