Stability of Dense Stellar Clusters against Relativistic Collapse. II. Maxwellian Distribution Functions with Different Cutoff Parameters

Бисноватый-Коган, Г. С.; Merafina, Marco; Ruffini, Remo; Vesperini, Enrico

doi:10.1086/305689

Cited by 15 publications

(28 citation statements)

References 12 publications

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“…The 2D map of the binding energy was constructed by applying a bicubic spline interpolator to the model points. The models nicely cover the first maximum of f , where dynamical instability is expected to set in (Bisnovatyi-Kogan et al 1998;Bisnovatyi-Kogan & Merafina 2006).…”

Section: Binding Energymentioning

confidence: 83%

“…To the right of the white dot are models with deeper potential wells and correspondingly higher central redshifts. This situation is reminiscent to that of the family of models discussed by Bisnovatyi-Kogan et al (1998) which also exhibits both bifurcations (i.e. more than one solution for a given set of model parameters) and limiting values for a parameter connected to the energy at the outer boundary.…”

Section: Existence Of Solutionsmentioning

confidence: 88%

“…The first hint that large redshifts are possible came from numerical integrations of the relativistic Boltzmann equation (Rasio, Shapiro, Teukolsky 1989) that was later on backed up by detailed analytical calculations (Merafina & Ruffini 1995). It was subsequently shown in Bisnovatyi-Kogan et al (1998);Bisnovatyi-Kogan & Merafina (2006) that arbitrarily large central redshifts are possible in stable models with a distribution function of the form F (E) ∝ exp(−E/T ), with T the uniform kinetic temperature as observed from infinity, only if T /mc 2 0.06. "Hotter" models are stable only for redshifts below ≈ 0.5.…”

Section: A Generalized Polytropic Distribution Functionmentioning

confidence: 99%

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The dynamics of general relativistic isotropic stellar cluster models: Do relativistic extensions of the Plummer model exist?

Rijcke¹,

Verbeke²,

Boelens³

2014

Monthly Notices of the Royal Astronomical Society

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We show that the general relativistic theory of the dynamics of isotropic stellar clusters can be developed essentially along the same lines as the Newtonian theory. We prove that the distribution function can be derived from any isotropic momentum moment and that every higher-order moment of the distribution can be written as an integral over a zeroth-order moment.We propose a mathematically simple expression for the distribution function of a family of isotropic general relativistic cluster models and investigate their dynamical properties. In the Newtonian limit, these models obtain a distribution function of the form F (E) ∝ (E − E 0 ) α , with E binding energy and E 0 a constant that determines the model's outer radius. The slope α sets the steepness of the distribution function and the corresponding radial density and pressure profiles. We show that the field equations only yield solutions with finite mass for α ≤ 3.5. Moreover, in the limit α → 3.5, only Newtonian models exist. In other words: within the context of this family of models, no general relativistic version of the Plummer model exists. The most strongly bound model within the family is characterized by α = 2.75 and a central redshift z c ≈ 0.55.

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Section: Binding Energymentioning

confidence: 83%

Section: Existence Of Solutionsmentioning

confidence: 88%

Section: A Generalized Polytropic Distribution Functionmentioning

confidence: 99%

See 1 more Smart Citation

The dynamics of general relativistic isotropic stellar cluster models: Do relativistic extensions of the Plummer model exist?

Rijcke¹,

Verbeke²,

Boelens³

2014

Monthly Notices of the Royal Astronomical Society

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“…Different values of these parameters give a two-dimensional family of equilibrium solutions. The set of solutions forρ Λ = 0 at different values of W 0 was obtained by Bisnovatyi-Kogan et al (1998). We solved numerically the Poisson equation for gravitational equilibrium at different values of the two parameters (W 0 ,ρ Λ ) mentioned above.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Bisnovatyi- Kogan et al (1998) found the set of solutions at Λ = 0 forM(ρ m0 ) andM(α) curves in the Newtonian case. These curves are shown in Figs.…”

Section: Numerical Resultsmentioning

confidence: 99%

Galaxy clusters in presence of dark energy: a kinetic approach

Merafina

Бисноватый-Коган

Donnari

2014

A&A

Self Cite

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Context. The external regions of galaxy clusters may be under strong influence of the dark energy, which was discovered by observations of supernovae Ia at redshift z < 1. The presence of the dark energy in the gravitational equilibrium equation, with the Einstein Λ term, balances the gravity, and extends the equilibrium configuration more in radius. Aims. We investigate the features of the equilibrium configurations to analyse how the presence of the dark energy affects the density profiles and radial extension by specifying the conditions for which the gravitational equilibrium begins. Methods. We derived the kinetic equation for an equilibrium configuration in presence of dark energy and solved the gravitational equilibrium equation by considering a Maxwell-Boltzmann distribution function with a cut-off in the framework of the Newtonian regime, because the observed velocities of galaxies inside a cluster are much lower than the velocity of light.Results. The prevalence of dark energy effects on the gravity shows a wide region in the W 0 -ρ Λ diagram where equilibrium solutions are not possible. In these particular conditions, the galaxies located in the external regions of a cluster can flow out, following the accelerating expansion of the Universe.

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Gravitational instability of finite isothermal spheres in general relativity. Analogy with neutron stars

Chavanis

2002

A&A

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Abstract.We investigate the effects of relativity on the gravitational instability of finite isothermal gaseous spheres. In the first part of the paper, we treat the gravitational field within the framework of Newtonian mechanics but we allow the speed of the particles to be close to the velocity of light so that special relativity must be taken into account. In the second part of the paper, we study the full general relativistic problem for a gas described by an equation of state p = q such that the pressure is proportional to the energy density ("isothermal" distribution). For q = 1/3, this equation of state describes the core of neutron stars. The mass-density diagram displays some damped oscillations and there exists a critical value of mass-energy above which no equilibrium state is possible. We show analytically that the mass peaks are associated with new modes of instability. These results are strikingly similar to those obtained by Antonov (1962) and Lynden-Bell & Wood (1968) for a classical isothermal gas. Our study completes the analogy between isothermal spheres and neutron stars investigated by Yabushita (1974).

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Stability of Dense Stellar Clusters against Relativistic Collapse. II. Maxwellian Distribution Functions with Different Cutoff Parameters

Cited by 15 publications

References 12 publications

The dynamics of general relativistic isotropic stellar cluster models: Do relativistic extensions of the Plummer model exist?

The dynamics of general relativistic isotropic stellar cluster models: Do relativistic extensions of the Plummer model exist?

Galaxy clusters in presence of dark energy: a kinetic approach

Gravitational instability of finite isothermal spheres in general relativity. Analogy with neutron stars

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