相关论文: Polytropic gas spheres: An approximate analytic so…

We present a useful analytic approximation to the solution of the Lane-Emden equation for infinite polytropic index - the isothermal sphere. The optimized expression obtained for the density profile can be accurate to within 0.04% within 5…

The aim of this study is to construct a simple stellar model with non-uniform polytropic index. We find that the Emden equation cannot deal with the polytrope gas sphere with non-uniform polytropic index in a real star, and then we…

In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model…

The perturbation method is applied to numerical solution of the Lane-Emden Equation of arbitrary index n, and the global parameters of polytropes are found as function of polytropic index n.

In this paper we will discuss charged stars with polytropic equation of state, where we will try to derive an equation analogous to the Lane-Emden equation. We will assume that these stars are spherically symmetric, and the electric field…

Lane Emden differential equation of the polytropic gas sphere could be used to construct simple models of stellar structures, star clusters and many configurations in astrophysics. This differential equation suffers from the singularity at…

The very accurate analytical solutions are found to Lane-Emden equation of arbitrary index, n, using Picard type iteration scheme and rational Pade approximants. For n=2 the dimensionless polytropic "radius" and "mass" are 4.35287459595 and…

Lane-Emden differential equations describe different physical and astrophysical phenomena that include forms of stellar structure, isothermal gas spheres, gas spherical cloud thermal history, and thermionic currents. This paper presents a…

Lane-Emden equation could be used to model stellar interiors, star clusters and many configurations in astrophysics. Unfortunately, there is an exact solution only for the polytropic index and . In the present paper, a series solution for…

We experimentally determine the equation of state of a laser cooled gas. By employing the Lane-Emden formalism, widely used in astrophysics, we derive the equilibrium atomic profiles in large magneto optical traps where the thermodynamic…

We propose a novel mathematical method to construct an exact polytropic sphere in self-gravitating hydrostatic equilibrium, improving the non-linear Poisson equation. The central boundary condition for the present equation requires a ratio…

A general formalism to find the density profile of a slowly rotating stellar object in modified gravity is presented. We derive a generic Lane-Emden equation and its analytical solution for a wide class of modified theories of gravity.

We compute multiprecision solutions of the Lane-Emden equation. This differential equation arises when introducing the well-known polytropic model into the equation of hydrostatic equilibrium for a nondistorted star. Since such…

We describe an ansatz for symmetry reduction of the Lane-Emden equation for an arbitrary polytropic index n, admitting only one symmetry generator. For the reduced first order differential equation it is found that standard reduction…

The so-called "global polytropic model" is based on the assumption of hydrostatic equilibrium for the solar system, or for a planet's system of statellites (like the jovian system), described by the Lane-Emden differential equation. A…

In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known…

A fundamental assumption in the so-called "global polytropic model" is hydrostatic equilibrium for a system of planets or statellites. By solving the Lane-Emden differential equation for such a system in the complex plane, we find…

The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the…

The modified Lane-Emden equation for stellar hydrostatic equilibrium in f(R)-gravity is numerically solved by using an iterative procedure. Such an integro-differential equation can be obtained in the weak field limit approximation of…

To approximately compute the non-relativistic ground state of an electrically non-neutral star, an exactly solvable model was recently introduced, and partly solved, by Krivoruchenko, Nadyozhin, and Yudin. The model generalizes the…