Related papers: Local virial relation for self-gravitating system
We investigate the quasi-equilibrium state of one-dimensional self-gravitating systems. If the null virial condition is satisfied at initial time, it is found that the number density around the center of the system at the quasi-equilibrium…
This paper develops a concise procedure for the study on local behavior of solutions to anisotropically weighted quasi-linear singular parabolic equations of $p$-Laplacian type, which is realized by improving the energy inequalities and…
In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider $f(R)=R+{\epsilon}R^2$ model and assume hydrostatic equilibrium of the axial…
In Newtonian gravity the final states of cold dissipationless collapses are characterized by several structural and dynamical properties remarkably similar to those of observed elliptical galaxies. Are these properties a peculiarity of the…
We show that under particular circumstances a general relativistic spherically symmetric bounded distribution of matter could satisfy a nonlocal equation of state. This equation relates, at a given point, the components of the corresponding…
We propose an approach to find out when a self-gravitating system is in a quasi-equilibrium state. This approach is based on a comparison between two quantities identifying behavior of the system: a measure of interactions intensity and the…
A re-investigation of the gravothermal catastrophe is presented. By means of a linear perturbation analysis, we study the dynamical stability of a spherical self-gravitating isothermal fluid of finite volume and find that the conditions for…
In the present work we apply virial analysis to the model of self-gravitating turbulent cloud ensembles introduced by Donkov \& Stefanov in two previous papers, clarifying some aspects of turbulence and extending the model to account not…
One can solve the Jeans equation analytically for equilibrated dark matter structures, once given two pieces of input from numerical simulations. These inputs are 1) a connection between phase-space density and radius, and 2) a connection…
N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…
We show that it is possible to obtain credible static anisotropic spherically symmetric matter configurations starting from known density profiles and satisfying a nonlocal equation of state. These particular types of equation of state…
In this paper, a quantitative characterization for the evolutionary sequence of stellar self-gravitating system is investigated, focusing on the pre-collapse stage of the long-term dynamical evolution. In particular, we consider the…
Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density $\rho$ which either falls off at infinity or has compact support. The solutions have finite mass, finite…
We present density profiles, that are solutions of the spherical Jeans equation, derived under the following two assumptions: (i) the coarse grained phase-density follows a power-law of radius, rho/(sigma^3) proportional to r^{-alpha}, and…
We propose the self-organized relaxation process which drives a collisionless self-gravitating system (SGS) to the equilibrium state satisfying local virial (LV) relation. During the violent relaxation process, particles can move widely…
We study the stability of a spherically symmetric density profile. We analyze the case of a collisionless system with a power-law profile given by rho propto r^-alpha, in the Newtonian regime using the Jeans equation. The Jeans equation is…
The self-gravitating gas in thermal equilibrium is studied using a Newtonian potential regularized at short distances. This short distance cutoff permits us to obtain a complete description of the gas including its collapsed phase. We give…
The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…
Static solutions of white dwarfs with spherical symmetry and local anisotropy are studied in the post-Newtonian approximation. It is argued that the condition for equilibrium must be that the total energy is a minimum for given baryon…