Apps/EriguchiHachisu/Models

Eriguchi, Hachisu, and their various Colleagues

Following the completion of their respective doctoral dissertations, Yoshiharu Eriguchi and Izumi Hachisu embarked upon an extremely fertile research collaboration which, especially over the decade of the 1980s, transformed the international astrophysics community's understanding of the structure and stability of rotating, self-gravitating fluid configurations. Others — including myself (J.E.T.) — were drawn into, and benefitted significantly from participation in, various ones of these collaborative research efforts. In what follows, we list and summarize the key results from a significant number of these "Eriguchi and Hachisu" collaborative publications.

Our list is broken into two broad topical categories:   Principally Uniformly Rotating, Incompressible Configurations (polytropic index, $n=0$) and Principally Differentially Rotating, Compressible Configurations (polytropic index, $n>0$). The efforts by both Eriguchi and Hachisu to extend our understanding of incompressible configurations beyond the Maclaurin spheroid sequence and the Jacobi/Dedekind sequence — more broadly, Riemann S-type ellipsoids — is summarized in HE84c.

Kickoff

Eriguchi78

Y. Eriguchi (1978)
Hydrostatic Equilibria of Rotating Polytropes
Publications of the Astronomical Society of Japan, Vol. 30, pp. 507 - 518
(p. 515):   "This paper is based on the author's dissertation, submitted to the University of Tokyo, in partial fulfillment of the requirements for the doctorate."

Hachisu82

📚 Hachisu (1982)
Gravothermal and Gravogyro Catastrophes of Rotating and Self-Gravitating Gaseous Disks
Publications of the Astronomical Society of Japan, Vol. 34, pp. 313 - 335
(p. 333):   "This paper is based on the author's dissertation, submitted to the University of Tokyo, in partial fulfillment of the requirements for the doctorate."

Principally Uniformly Rotating, Incompressible Configurations

ES81

Concave Hamburger: One-Ring (incompressible case)
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.

Y. Eriguchi & D. Sugimoto (1981)
Another Equilibrium Sequence of Self-Gravitating and Rotating Incompressible Fluid
Progress of Theoretical Physics, Vol. 65, No. 6, pp. 1870 - 1875

NOTE:  Results from an independent effort to construct models along this identical sequence appear in … M. Ansorg A. Kleinächter, & R. Meinel (2003) Uniformly Rotating Axisymmetric Fluid Configurations Bifurcating from Highly Flattened Maclaurin Spheroids Monthly Notices of the Royal Astronomical Society, Vol. 339, Issue 2, pp. 515 - 523
See Table 2 (p. 519) of AKM2003 See the curve labeled "(1)" in Figure 2 (p. 517) of AKM2003 See Figure 6 (p. 520) of AKM2003

HES82

Concave Hamburger: One-Ring (compressible, as well as, incompressible case)
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.

I. Hachisu, Y. Eriguchi, & D. Sugimoto (1982)
Rapidly Rotating Polytropes and Concave Hamburger Equilibrium
Progress of Theoretical Physics, Vol. 68, No. 1, pp. 191 - 205

NOTE:     In this HES82 publication, the authors point out (with attending explanation) that some of the modeling results published earlier by 📚 Fukushima, Eriguchi, Sugimoto, & Bisnovatyi-Kogan (1980) are demonstratively wrong.

EH82

Triangle: Square: Ammonite and Two-Ring (pt. 1)
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c

Y. Eriguchi & I. Hachisu (1982)
New Equilibrium Sequences Bifurcating from Maclaurin Sequence
Progress of Theoretical Physics, Vol. 67, No. 3, pp. 844 - 851

NOTE: Color images copied from our separate discussion of binary mass-transfer simulations.

NOTE:  Results from an independent effort to construct models along this identical "two-ring" sequence appear in …
M. Ansorg A. Kleinächter, & R. Meinel (2003)
Uniformly Rotating Axisymmetric Fluid Configurations Bifurcating from Highly Flattened Maclaurin Spheroids
Monthly Notices of the Royal Astronomical Society, Vol. 339, Issue 2, pp. 515 - 523

n/a

See the curve labeled "(3)" in Figure 2 (p. 517) of AKM2003

See Table 4 (p. 520) of AKM2003

See Figure 8 (p. 521) of AKM2003

EHS82

Dumb-Bell: Pear-Shaped
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.

Y. Eriguchi, I. Hachisu, & D. Sugimoto (1982)
Dumb-Bell-Shape Equilibria and Mass-Shedding Pear-Shape
of Selfgravitating Incompressible Fluid
Progress of Theoretical Physics, Vol. 67, No. 4, pp. 1068 - 1075

EH83a

Two-Ring (pt. 2)
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.

Y. Eriguchi & I. Hachisu (1983a)
Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluid
— Two-Ring Sequence and Core-Ring Sequence —
Progress of Theoretical Physics, Vol. 69, No. 4, pp. 1131 - 1136

EH83b

Multi-Body
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.

Y. Eriguchi & I. Hachisu (1983b)
Gravitational Equilibrium of a Multi-Body Fluid System
Progress of Theoretical Physics, Vol. 70, No. 6, pp. 1534 - 1541

HE84c

Summary

I. Hachisu & Y. Eriguchi (1984c)
Fission Sequence and Equilibrium Models of Rigidity [sic] Rotating Polytropes
in Double Stars, Physical Properties and Generic Relations; Proceedings of IAU Colloquium No. 80 held at Lambing, Java, June 3-7, 1983
Editors: Bambang Hidayat, Zdenek Kopal, Jurgen Rahe; Dordrecht, D. Reidel Publishing Co.
Astrophysics & Space Science, Vol. 99, pp. 71 - 74

Also see our separate discussion of the Fission Hypothesis

HE84

I. Hachisu & Y. Eriguchi (1984)
Bifurcation Points on the Maclaurin Sequence
Publications of the Astronomical Society of Japan, Vol. 36, No. 3, pp. 497 - 503

HE83

I. Hachisu & Y. Eriguchi (1983)
Bifurcations and Phase Transitions of Self-Gravitating and Uniformly Rotating Fluid
Monthly Notices of the Royal Astronomical Society, Vol. 204, pp. 583 - 589

EH85

Differentially Rotating, "Maclaurin Toroid" Sequence
… extending the work of 📚 Marcus, Press, & Teukolsky (1977).

Y. Eriguchi & I. Hachisu (1985)
Maclaurin Hamburger Sequence
Astronomy and Astrophysics, Vol. 148, pp. 289 - 292

Principally Differentially Rotating, Compressible Configurations

Hachisu86a

I. Hachisu (1986a)
A Versatile Method for Obtaining Structures of Rapidly Rotating Stars
The Astrophysical Journal Supplement Series, Vol. 61, pp. 479 - 507

Models having Uniform Rotation — §II.c, Eq. (11), p. 481
Models having Uniform $v_{\phi }$ — §II.c, Eq. (12), p. 481
Models having j-constant rotation — §II.c, Eq. (13), p. 481

See Also

• Properties of Maclaurin Spheroids
• Excerpts from Maclaurin's (1742) A Treatise of Fluxions
• Properties of Homogeneous Ellipsoids