Triaxial bifurcations of rapidly rotating spheroids

Dankova, Ts.; Rosensteel, G.

doi:10.1119/1.19050

Cited by 11 publications

(15 citation statements)

References 7 publications

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“…Newton and Maclaurin showed that forces of rotation and gravitation balance in an oblate spheroid shape [41]; this result is confirmed by the shapes of planets and stars. Regarding galaxies, oblate spheroid geometry is compatible with images ( Fig.…”

Section: Poisson's Orbits or Newton-maclaurin's Spin?supporting

confidence: 60%

The physics of galactic spin

Hofmeister

Criss

2017

Can. J. Phys.

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this article has been changed to the CC BY 4.0 license. The PDF and HTML versions of the article have been modified accordingly.Abstract: Spiral galaxies are discrete spheroidal objects with highly organized, circular internal motions about a special axis. Available models do not describe these key features or explain why the central regions rotate like a solid body. Practically all previous models describe galaxies as a collection of orbiting test particles, utilize numerous fitting parameters, and require either copious amounts of surrounding dark matter that have not been detected, or modifications to Newton's law, to fit the observed dependence of equatorial velocity on radius. Our paper probes the reasonable alternative that galaxies are discrete, spinning objects. Our analytical forward models, constructed by applying the virial theorem and Newton's law to Maclaurin's spinning spheroids with varying internal density, explain why galactic rotation is organized into this three-dimensional shape. Without invoking dark matter, our spin model explains why the outermost rotational velocities are nearly constant, yet depend on galaxy size, and, with no free parameters, provides masses of 14 important galaxies consistent with their luminosities. We show that proposed modifications to Newton's law compensate for the dynamical differences between a flattened, spinning, Newtonian spheroid, and a collection of orbits.Key words: virial theorem, galactic rotation, dark matter, non-Newtonian forces, spin.Résumé : Les galaxies spirales sont des objets discrets avec des mouvements circulaires internes hautement organisés autour d'un axe spécial. Les modèles disponibles ne décrivent pas ces caractéristiques centrales ni n'expliquent pourquoi la région centrale tourne comme un corps rigide. Pratiquement tous les modèles antérieurs décrivent les galaxies comme une collection de particules tests en orbite, utilisent de nombreux paramètres d'ajustement et requièrent des quantités généreuses de matière noire qui n'ont pas été détectées, ou encore des modifications à la loi de Newton, afin de s'ajuster aux résultats observés de la dépendance de la vitesse équatoriale sur le rayon. Nous sondons ici une alternative raisonnable où les galaxies sont des objets discrets en rotation. Notre modèle analytique, construit en appliquant le théorème du viriel et la loi de Newton à des sphéroïdes en rotation de Mclaurin avec une densité interne variable, explique pourquoi la rotation galactique est organisée sous cette forme troisdimensionnelle. Sans besoin de matière noire, notre modèle explique pourquoi les vitesses de rotation externes sont pratiquement constantes, tout en dépendant de la grandeur de la galaxie et, sans paramètre libre, fournit les masses de 14 galaxies importantes cohérentes avec leur luminosité. Nous montrons que les modifications apportées à la loi de Newton compensent pour la différence dynamique entre le spin d'un sphéroïde newtonien aplati et une collection d'orbites. [Traduit par la Rédaction] Mots-clés : théorème d...

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Section: Poisson's Orbits or Newton-maclaurin's Spin?supporting

confidence: 60%

The physics of galactic spin

Hofmeister

Criss

2017

Can. J. Phys.

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“…This shape is furthermore evident in images of the Sun and gas giants. Although the triaxial ellipsoidal shapes of Jacobi are permissible [42], the ostensibly circular motions in spiral galaxies indicate the higher symmetry of the oblate suffices.…”

Section: Background: the Equilibrium Shape Of Rotating Gravitating Omentioning

confidence: 99%

“…Maclaurin evaluated the double integral of (9) for the oblate spheroid. The result [42] is simple for homogeneous density:…”

Section: Internal (Self) Vs External Potentialsmentioning

confidence: 99%

Implications of Geometry and the Theorem of Gauss on Newtonian Gravitational Systems and a Caveat Regarding Poisson’s Equation

Hofmeister

Criss

2017

Galaxies

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Galactic mass consistent with luminous mass is obtained by fitting rotation curves (RC = tangential velocities vs. equatorial radius r) using Newtonian force models, or can be unambiguously calculated from RC data using a model based on spin. In contrast, mass exceeding luminous mass is obtained from multi-parameter fits using potentials associated with test particles orbiting in a disk around a central mass. To understand this disparity, we explore the premises of these mainstream disk potential models utilizing the theorem of Gauss, thermodynamic concepts of Gibbs, the findings of Newton and Maclaurin, and well-established techniques and results from analytical mathematics. Mainstream models assume that galactic density in the axial (z) and r directions varies independently: we show that this is untrue for self-gravitating objects. Mathematics and thermodynamic principles each show that modifying Poisson's equation by summing densities is in error. Neither do mainstream models differentiate between interior and exterior potentials, which is required by potential theory and has been recognized in seminal astronomical literature. The theorem of Gauss shows that: (1) density in Poisson's equation must be averaged over the interior volume; (2) logarithmic gravitational potentials implicitly assume that mass forms a long, line source along the z axis, unlike any astronomical object; and (3) gravitational stability for three-dimensional shapes is limited to oblate spheroids or extremely tall cylinders, whereas other shapes are prone to collapse. Our findings suggest a mechanism for the formation of the flattened Solar System and of spiral galaxies from gas clouds. The theorem of Gauss offers many advantages over Poisson's equation in analyzing astronomical problems because mass, not density, is the key parameter.

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“…With increasing angular momentum the Maclaurin spheroidal mass becomes more oblate until it has an eccentricity of 0.8, which is equivalent to an aspect ratio of 0.6. At this point, the Maclaurin spheroid is unstable and with a decrease in angular momentum will become a Jacobi ellipsoid (Eriguchi & Hachisu 1982;Dankova & Rosensteel 1998). Alternatively, we propose that if a Maclaurin spheroid mass has an aspect ratio ≤0.6 and has a circumferential equatorial disk, the Maclaurin spheroid will morphologically form a "steep profile" while angular momentum remains constant.…”

Section: Formation Of a "Steep Profile" In A Maclaurin Spheroid With mentioning

confidence: 99%

“…The first term is the Maclaurin spheroid's self-energy U sph and is a known quantity (Chandrasekhar 1969;Dankova & Rosensteel 1998),…”

Section: Volume Correctionmentioning

confidence: 99%

Novel explanation for the shape of the lenticular galaxy bulge and its implication for red spiral galaxy evolution

Schachar

Liao

Kirby

et al. 2009

A&A

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Aims. According to Hubble's classification scheme, lenticular galaxies represent an intermediate evolutionary step between elliptical and spiral galaxies. This evolutionary path predicts that the aspect ratios of both lenticular and spiral galaxies should be smaller than the aspect ratios of their E6 or E7 elliptical predecessors. In contradiction to this prediction, observation has demonstrated that the aspect ratio of lenticular galaxies is larger than its immediate elliptical predecessor. In this paper, we suggest a novel explanation for this inconsistency. Methods. The approach described in this paper is primarily based on analytical methods; however, some numerical methods are also used. Results. Our idea comes from theoretical and experimental results, which show that a small increase in the equatorial diameter of an oblate spheroid with an aspect ratio ≤0.6 surprisingly causes its minor axis to also increase. We demonstrate that the same phenomenon occurs in the isodensity contours of elliptical galaxies given by Miyamoto & Nagai (Miyamoto M., & Nagai R., 1975, PASJ, 27, 533) and in a Maclaurin spheroidal mass in response to the gravitational force generated by a circumferential equatorial disk. Conclusions. The result of this paper is our explanation for the transformation of a disky elliptical galaxy into a lenticular galaxy which in response to rotation and equatorial diameter expansion evolves into a red spiral galaxy. This evolutionary path is consistent with the common environmental location of disky ellipticals, lenticular and red spiral galaxies and explains why elliptical galaxies are generally ≤E4. The proposed evolutionary path is opposite to the generally accepted formation of lenticular galaxies from the merger of spiral galaxies.

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Triaxial bifurcations of rapidly rotating spheroids

Cited by 11 publications

References 7 publications

The physics of galactic spin

The physics of galactic spin

Implications of Geometry and the Theorem of Gauss on Newtonian Gravitational Systems and a Caveat Regarding Poisson’s Equation

Novel explanation for the shape of the lenticular galaxy bulge and its implication for red spiral galaxy evolution

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