The Gravitational Collapse of a Uniform Spheroid.

Lin, C. C.; Mestel, L.; Shu, Frank H.

doi:10.1086/148428

Cited by 256 publications

(230 citation statements)

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“…However, as one may easily show (see Ref. [9] for the gravitational case), its uniform ellipsoidal character will be preserved during the expansion. The internal space-charge forces will therefore remain linear, although the ratios of the lengths of the major axes, and therefore the form factors M x , M y , and M z , will change.…”

Section: How To Realize Uniform Three-dimensional Ellipsoidal Electromentioning

confidence: 85%

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How to Realize Uniform Three-Dimensional Ellipsoidal Electron Bunches

et al. 2004

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Section: How To Realize Uniform Three-dimensional Ellipsoidal Electromentioning

confidence: 85%

“…(2) with A B > C] will collapse under its own weight into a flat disk, i.e., an oblate spheroid with the short axis C reduced to zero [9], whose density distribution is given by…”

Section: How To Realize Uniform Three-dimensional Ellipsoidal Electromentioning

confidence: 99%

How to Realize Uniform Three-Dimensional Ellipsoidal Electron Bunches

et al. 2004

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“…the direction orthogonal to the initial major semi-axis collapse to the center in a shorter time than those along this axis: this is the Lin, Mestel & Shu (1965) instability whose effect is to amplify the initial small eccentricity. The particles initially in the outermost shells which arrive latest then travel through the rapidly decreasing potential created by the other mass which is already re-expanding, and gain energy.…”

Section: Symmetry Breaking Of Relaxed Statementioning

confidence: 99%

“…For α 2, most of mass now collapses at very short times and accordingly ι80(t) shows a very fast growth for t < τc followed by a decrease when the external particles pass through the center. The hypothesis that the amplification of the initial triaxiality is due to finite N effects via the instability described by Lin, Mestel & Shu (1965), and the subsequent role of energy gain in amplifying the triaxiality, can be tested for straightforwardly. Firstly, we would expect that the major semi-axis at any time t should be correlated to its value at t = 0.…”

Section: Symmetry Breaking Of Relaxed Statementioning

confidence: 99%

On the generation of triaxiality in the collapse of cold spherical self-gravitating systems

Labini¹,

Benhaiem²,

Joyce

2015

Monthly Notices of the Royal Astronomical Society

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Initially cold and spherically symmetric self-gravitating systems may give rise to a virial equilibrium state which is far from spherically symmetric, and typically triaxial. We focus here on how the degree of symmetry breaking in the final state depends on the initial density profile. We note that the most asymmetric structures result when, during the collapse phase, there is a strong injection of energy preferentially into the particles which are localized initially in the outer shells. These particles are still collapsing when the others, initially located in the inner part, are already reexpanding; the motion of particles in a time varying potential allow them to gain kinetic energy -in some cases enough to be ejected from the system. We show that this mechanism of energy gain amplifies the initial small deviations from perfect spherical symmetry due to finite N fluctuations. This amplification is more efficient when the initial density profile depends on radius, because particles have a greater spread of fall times compared to a uniform density profile, for which very close to symmetric final states are obtained. These effects lead to a distinctive correlation of the orientation of the final structure with the distribution of ejected mass, and also with the initial (very small) angular fluctuations.

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“…Numerical simulations of this collapse reveal that the gas streaming into these potential wells exhibits filamentary and knotty structure (e.g., Bromm et al 1999;Clark et al 2008;Greif et al 2011). Indeed, gravity is well known to enhance such anisotropic structure during collapse (e.g., Lin et al 1965).…”

Section: The Case For Population III Star Clustersmentioning

confidence: 99%

The luminosity of Population III star clusters

DeSouza¹,

Basu²

2015

Monthly Notices of the Royal Astronomical Society

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We analyze the time evolution of the luminosity of a cluster of Population III protostars formed in the early universe. We argue from the Jeans criterion that primordial gas can collapse to form a cluster of first stars that evolve relatively independently of one another (i.e., with negligible gravitational interaction). We model the collapse of individual protostellar clumps using 2+1D nonaxisymmetric numerical hydrodynamics simulations. Each collapse produces a protostar surrounded by a massive disk (i.e., M disk /M * 0.1), whose evolution we follow for a further 30-40 kyr. Gravitational instabilities result in the fragmentation and the formation of gravitationally bound clumps within the disk. The accretion of these fragments by the host protostar produces accretion and luminosity bursts on the order of 10 6 L ⊙ . Within the cluster, we show that a simultaneity of such events across several protostellar cluster members can elevate the cluster luminosity to 5-10× greater than expected, and that the cluster spends ∼ 15% of its star-forming history at these levels. This enhanced luminosity effect is particularly enabled in clusters of modest size with ≃ 10-20 members. In one such instance, we identify a confluence of burst events that raise the luminosity to nearly 1000× greater than the cluster mean luminosity, resulting in L > 10 8 L ⊙ . This phenomenon arises solely through the gravitational-instability-driven episodic fragmentation and accretion that characterizes this early stage of protostellar evolution.

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The Gravitational Collapse of a Uniform Spheroid.

Cited by 256 publications

References 0 publications

How to Realize Uniform Three-Dimensional Ellipsoidal Electron Bunches

How to Realize Uniform Three-Dimensional Ellipsoidal Electron Bunches

On the generation of triaxiality in the collapse of cold spherical self-gravitating systems

The luminosity of Population III star clusters

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