Fractional derivative approach to the self-gravitation equation

Pedraza, Juan F.; Ramos-Caro, Javier; González, Guillermo

doi:10.1111/j.1745-3933.2008.00548.x

Cited by 15 publications

(12 citation statements)

References 24 publications

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“…A number of methods to construct self-consistent stellar models have appeared in the literature over the years [7,8,9,10,11,12,13]. A first approach consists in starting with known profiles for the matter distribution and gravitational fields (which can be inferred directly from photometric and kinematic observations).…”

Section: Introductionmentioning

confidence: 99%

Anisotropic models for globular clusters, Galactic bulges, and dark halos

Nguyen¹,

Pedraza²

2013

Phys. Rev. D

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Spherical systems with polytropic equations of state are of great interest in astrophysics. They are widely used to describe neutron stars, red giants, white dwarfs, brown dwarfs, main sequence stars, galactic halos, and globular clusters of diverse sizes. In this paper we construct analytically a family of self-gravitating spherical models in the post-Newtonian approximation of general relativity. These models present interesting cusps in their density profiles which are appropriate for the modeling of galaxies and dark matter halos. The systems described here are anisotropic in the sense that their equiprobability surfaces in velocity space are nonspherical, leading to an overabundance of radial or circular orbits, depending on the parameters of the model under consideration. Among the family of models, we find the post-Newtonian generalization of the Plummer and Hernquist models. A close inspection of their equation of state reveals that these solutions interpolate smoothly between a polytropic sphere in the asymptotic region and an inner core that resembles an isothermal sphere. Finally, we study the thermodynamics of these models and argue for their stability. 1

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Section: Introductionmentioning

confidence: 99%

Anisotropic models for globular clusters, Galactic bulges, and dark halos

Nguyen¹,

Pedraza²

2013

Phys. Rev. D

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“…From the statistical standpoint, the most straightforward way to construct self-consistent stellar systems is by means of finding the distribution function (DF) for a stellar system with a known gravitational potential and matter distribution. Since the mass density is the integration of the distribution function over the velocity variable in the phase space of the system, the problem of finding a DF is that of solving an integral equation (see [1,2,3,4,5] and the references therein). This construction is also the so-called "from ρ to f " approach for finding a self-consistent distribution function f [6], although the opposite procedure is also used sometimes.…”

Section: Introductionmentioning

confidence: 99%

Kinetic theory of collisionless self-gravitating gases: Post-Newtonian polytropes

2011

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In this paper we study the kinetic theory of many-particle astrophysical systems and we present a consistent version of the collisionless Boltzmann equation in the 1PN approximation. We argue that the equation presented by Rezania and Sobouti in A&A 354 1110 (2000) is not the correct expression to describe the evolution of a collisionless selfgravitating gas. One of the reasons that account for the previous statement is that the energy of a free-falling test particle, obeying the 1PN equations of motion for static gravitational fields, is not a static solution of the mentioned equation. The same statement holds for the angular momentum, in the case of spherical systems. We provide the necessary corrections and obtain an equation that is consistent with the corresponding equations of motion and the 1PN conserved quantities. We suggest some potential relevance for the study of high density astrophysical systems and as an application we construct the corrected version of the post-Newtonian polytropes.

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“…So, by requiring that the surface density behaves as a monotonously decreasing function of the radius, with a maximum at the centre of the disc and vanishing at the edge, the detailed expressions for the gravitational potential and the rotational velocity were obtained as a series of elementary functions. Also, some two-integral DFs for the first four members of this family were recently obtained by Pedraza, Ramos-Caro & González (2008). Now then, as the generalized Kalnajs models correspond to discs of finite extension, one can consider that they describe the mass distribution of a flattened galaxy more accurately than Toomre's family.…”

Section: Introductionmentioning

confidence: 99%

An infinite family of self-consistent models for axisymmetric flat galaxies

Pedraza

Ramos-Caro

González

2008

Monthly Notices of the Royal Astronomical Society

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We present the formulation of a new infinite family of self-consistent stellar models, designed to describe axisymmetric flat galaxies. The corresponding density-potential pair is obtained as a superposition of members belonging to the generalized Kalnajs family, by imposing the condition that the density can be expressed as a regular function of the gravitational potential, in order to derive analytically the corresponding equilibrium distribution functions (DFs). The resulting models are characterized by a well-behaved surface density, as in the case of generalized Kalnajs discs. Then, we present a study of the kinematical behaviour which reveals, in some particular cases, a very satisfactory behaviour of the rotational curves (without the assumption of a dark matter halo). We also analyse the equatorial orbit's stability, and Poincaré surfaces of section are performed for the three-dimensional orbits. Finally, we obtain the corresponding equilibrium DFs, using the approaches introduced by Kalnajs and Dejonghe.

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Fractional derivative approach to the self-gravitation equation

Cited by 15 publications

References 24 publications

Anisotropic models for globular clusters, Galactic bulges, and dark halos

Anisotropic models for globular clusters, Galactic bulges, and dark halos

Kinetic theory of collisionless self-gravitating gases: Post-Newtonian polytropes

An infinite family of self-consistent models for axisymmetric flat galaxies

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