A systematic approach to self-similarity in Newtonian space-time

Carter, B.; Henriksen, R. N.

doi:10.1063/1.529103

Cited by 64 publications

(87 citation statements)

References 7 publications

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“…(See Henriksen & Widrow [1999] for a discussion of the self-similar infall model based on the collisionless Boltzmann equation. This formulation [see also Carter & Henriksen 1991] allows for more general types of self-similarity. )…”

Section: Self-similar Infall Modelsmentioning

confidence: 99%

On Universal Halos and the Radial Orbit Instability

MacMillan

Widrow

Henriksen

2006

ApJ

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The radial orbit instability drives the density profile of a collapsing nearly spherical density perturbation toward the universal form found in cosmological simulations. This conclusion, first noted by Huss and coworkers, is explored in detail through a series of numerical experiments involving isolated halos. Simulations are run with and without the nonradial forces responsible for the instability. In the absence of the instability, the density profile is a pure power law, the differential energy distribution is close to a Boltzmann distribution, and the orbits are radially biased. The instability transforms the density profile to the NFW form, induces an energy cutoff at high binding energy, and isotropizes the orbits near the center of the system. New insights into the underlying physics of the radial orbit instability are presented. Subject headingg s: cosmology: theory -dark matter -large-scale structure of universe

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Section: Self-similar Infall Modelsmentioning

confidence: 99%

On Universal Halos and the Radial Orbit Instability

MacMillan

Widrow

Henriksen

2006

ApJ

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“…They showed that it corresponds to self-similarity of the homothetic class in the context of Newtonian theory and is known as KSS of the first kind. Later, self-similarity of the second, zeroth and infinite kinds were introduced by Carter and Henriksen [11,12]. There is a great literature available [2,3,[13][14][15][16][17][18] which contain several KSS perfect fluid solutions of the EFEs.…”

Section: Introductionmentioning

confidence: 99%

Kinematic self-similar solutions of locally rotationally symmetric spacetimes

Sharif¹,

Amir²

2010

Braz. J. Phys.

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This paper contains locally rotationally symmetric kinematic self-similar perfect fluid and dust solutions. We consider three families of metrics which admit kinematic self-similar vectors of the first, second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the orthogonal case gives contradiction both in perfect fluid and dust cases for all the three metrics while the tilted case reduces to the parallel case in both perfect fluid and dust cases for the second metric. The remaining cases give self-similar solutions of different kinds. We obtain a total of seventeen independent solutions out of which two are vacuum. The third metric yields contradiction in all the cases.

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“…We use, in this paper as in the previous (I, II), the Carter-Henriksen (Carter & Henriksen 1991) procedure. In this way we obtain a quasi-self-similar system of coordinates (Henriksen 2006a,b) that enables expression of the CBE-Poisson set with explicit reference to a previous transient self-similar dynamical relaxation.…”

Section: Introductionmentioning

confidence: 99%

Black holes and galactic density cusps

Delliou

Henriksen

MacMillan

2010

A&A

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Aims. In this paper we continue our study of density cusps that may contain central black holes. Methods. Our previous thus attempts to use distribution functions with a memory of self-similar relaxation apply mainly in restricted regions of the global system. We are forced to consider related distribution functions that are steady but not self-similar. Results. One remarkably simple distribution function that has a filled loss cone describes a bulge that transits from a near black hole domain to an outer "zero flux" regime where ρ ∝ r −7/4 . The transition passes from an initial inverse square profile through a region having a 1/r density profile. The structure is likely to be developed at an early stage in the growth of a galaxy. A central black hole is shown to grow exponentially in this background with an e-folding time of a few million years. Conclusions. We derive our results from first principles, using only the angular momentum integral in spherical symmetry. The initial relaxation probably requires bar instabilities and clump-clump interactions.

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A systematic approach to self-similarity in Newtonian space-time

Cited by 64 publications

References 7 publications

On Universal Halos and the Radial Orbit Instability

On Universal Halos and the Radial Orbit Instability

Kinematic self-similar solutions of locally rotationally symmetric spacetimes

Black holes and galactic density cusps

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