Figures of equilibrium inside a gravitating ring and the limiting oblateness of elliptical galaxies

Kondratyev, B. P.; Trubitsyna, N. G.; Kireeva, E. N.

doi:10.1134/s1063772916040077

Cited by 4 publications

(5 citation statements)

References 16 publications

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“…Also, the M-spheroid sequence in general does not have a e → 0 limit. This is in accord with the result by Kondratyev et al (2016), and in contrast to the Maclaurin spheroid embedded Fig. 2 The angular frequency squared Ω 2 , normalized by 4πGρc, is plotted as a function of the eccentricity e = 1 − (a 3 /a 1 ) 2 .…”

Section: Angular Frequencysupporting

confidence: 89%

“…When they are surrounded by a massive torus of fallback matter or of merger debris, how does this picture change? If the dark matter distribution around some of the elliptical galaxies or around the bulges of spiral galaxies may be mimicked by that of the ring (as is suggested by Kondratyev et al 2016), do we expect to see the stellar systems as spheroids or triaxial ellipsoids? These questions of completely different scales in the Universe may be related to the simple models considered here.…”

Section: Introductionmentioning

confidence: 93%

“…At a larger scale, the classical ellipsoids are applied to model star clusters (Ivanov and Lin, 2020) or elliptical galaxies surrounded by dark matter haloes (Kondratyev et al, 2015). In fact, closely related studies to ours have been done by Kondratyev and his collaborators (Kondratyev and Trubitsyna, 2010;Kondratyev et al, 2015Kondratyev et al, , 2016, where the effects of a circum-galactic dark matter ring on the elliptical galaxies are investigated to explain the origin of the highly flattened Early-type galaxies. An apparent lack of rotational velocity in some of the highly-flattened ellipsoidal galaxies are attributed to the tidal effect of a massive concentric ring around a uniformly rotating ellipsoid.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation and stability of uniformly rotating homogeneous ellipsoids surrounded by a massive thin ring

Yoshida

2023

Preprint

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We examine the effects of a massive concentric ring around a spheroid or an ellipsoid with uniform density and uniform rotation. Equilibrium sequences of axisymmetric Maclaurin-like spheroid and triaxial Jacobi-like ellipsoids are obtained. Due to the gravitational field of the ring, Maclaurin-like spheroid does not have a spherical limit when the object's angular frequency vanishes. At a critical value of the eccentricity of the spheroid's meridional section, a triaxial Jacobi-like ellipsoid bifurcates. When a parameter characterizing the gravitational field of the ring is smaller than a threshold, the bifurcation points of Maclaurin-like and Jacobi-like ellipsoids exist and the critical eccentricity is slightly larger than that of the classical Maclaurin-to-Jacobi bifurcation. When the parameter exceeds the threshold, the Maclaurin-like spheroid does not have the bifurcation point and the Jacobi-like ellipsoid appears at the lower eccentricity than the Maclaurin-like spheroid. By comparisons of the energy of the ellipsoids with the same angular momentum, it is shown that the critical point of bifurcation does not correspond to the onset of the secular instability of Maclaurin-like spheroid. It is concluded that the gravitational field of a massive ring surrounding a uniformly rotating spheroid stabilizes it against a bar-shaped deformation due to viscous dissipations.

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Section: Angular Frequencysupporting

confidence: 89%

Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Bifurcation and stability of uniformly rotating homogeneous ellipsoids surrounded by a massive thin ring

Yoshida

2023

Preprint

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“…The center of mass of the cloud is located in the principal plane of the galaxy at a distance R = R 0 from its center and orbits around the center of the stellar system at an angular velocity of Ω (R, x 3 ). It follows from the balance of the Galactic gravitational and centrifugal forces (Kondratyev 2003) that…”

Section: Formulation Of the Problem The Total Potentialmentioning

confidence: 99%

“…There are sev-eral reasons for this. First, studying heterogeneous equilibrium figures is a rather challenging mathematical task (Kondratyev 1989). Second, such clouds around other stars are difficult to observe.…”

Section: Introductionmentioning

confidence: 99%

On Equilibrium Figures of Particle Clouds around the Sun and Stars

Kondratyev

Trubitsina

2015

Open Astronomy

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Abstract. Equilibrium figures of cold gas-dust (or cometary) clouds are studied in a more general setting than the classical Roche problem. The cloud is considered to be under the influence of gravitational attraction of the central star and the tidal field of the Galaxy. Our analysis also takes into account the centrifugal forces due to the rotation of the cloud, which moves around the center of the stellar system together with the star. The limit equilibrium figure is found to have three planes of symmetry and to be shaped like a "lemon" with lateral swellings and two singular points. The shape of this figure and its cusp angles in the planes of two main sections are calculated. The average density inside the equilibrium figure is shown to be almost exactly equal to the average density of matter in the Galaxy. This coincidence cannot be accidental and means that equilibrium figures with the critical level of the total surface potential fill the entire volume of the Galaxy. A possible consequence is that the cometary clouds of neighboring stars in the Galaxy may touch each other (or even intersect because of the presence of dark matter). Hence stars may exchange comets and part of the comets in the Solar System may belong to other stars.

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Dynamical Models and Anisotropy of the Velocity Dispersions in Elliptical Galaxies

Kireeva

Kondratyev

2019

Astron. Rep.

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Figures of equilibrium inside a gravitating ring and the limiting oblateness of elliptical galaxies

Cited by 4 publications

References 16 publications

Bifurcation and stability of uniformly rotating homogeneous ellipsoids surrounded by a massive thin ring

Bifurcation and stability of uniformly rotating homogeneous ellipsoids surrounded by a massive thin ring

On Equilibrium Figures of Particle Clouds around the Sun and Stars

Dynamical Models and Anisotropy of the Velocity Dispersions in Elliptical Galaxies

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