Related papers: Lane-Emden stars, selfgravitating disks and the So…
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…
As a formation route for objects such as giant planets and low-mass stars in protostellar discs (as well as stars in AGN discs), theories of self-gravitating disc fragmentation need to be able to predict the initial masses of fragments. We…
By solving analytically the various types of Lane-Emden equations with rotation, we have discovered two new coupled fundamental properties of rotating, self-gravitating, gaseous disks in equilibrium: Isothermal disks must, on average,…
We establish a nonlinear instability of the Euler-Poisson system for polytropic gases whose adiabatic exponents take value in $6/5<\gamma<4/3$ around the Lane-Emden equilibrium star configurations.
We investigate accreting disk systems with polytropic gas in Keplerian motion. Numerical data and partial analytic results show that the self-gravitation of the disk speeds up its rotation -- its rotational frequency is larger than that…
Polytropic models play a very important role in galactic dynamics and in the theory of stellar structure and evolution. However, in general, the solution of the Lane-Emden equation can not be given analytically but only numerically. In the…
We characterize stellar, gas, and dark matter mass distributions for 17 nearby massive disk galaxies from the PHANGS sample. This allows us to compute the gravitational potential that vertically confines the interstellar gas and determines…
In the supercritical range of the polytropic indices $\gamma\in(1,\frac43)$ we show the existence of smooth radially symmetric self-similar solutions to the gravitational Euler-Poisson system. These solutions exhibit gravitational collapse…
We consider Lane-Emden ground states with polytropic index $0\leq q-1\leq 1$, that is, minimizers of the Dirichlet integral among $L^q$-normalized functions. Our main result is a sharp lower bound on the $L^2$-norm of the normal derivative…
We investigate the structure of self-gravitating polytropic stellar systems. We present a method which allows to obtain approximate analytical solutions, $\psi_{n+\epsilon}({\bf x})$, of the nonlinear Poisson equation with the polytropic…
There have been several recent detections of candidate Keplerian discs around massive young protostars. Given the relatively large disc-to-star mass ratios in these systems, and their young ages, it is worth investigating their propensity…
Gaseous rotating razor-thin discs are a testing ground for theories of spiral structure that try to explain appearance and diversity of disc galaxy patterns. These patterns are believed to arise spontaneously under the action of…
Gravitational polarization is examined for equilibrium self-gravitating polytropic sheets perturbed by gravitational field due to test mass sheet. We find equilibrium solutions to the corresponding perturbed Lane-Emden equations for…
In the present work we have investigated a new anisotropic solution for polytropic star in the framework of $4D$ Einstein-Gauss-Bonnet (EGB) gravity. The possibility of determining the masses and radii of compact stars which puts some…
We formulate and solve by semi-analytic means the axisymmetric equilibria of relativistic self-similar disks of infinitesimal vertical thickness. These disks are supported in the horizontal directions against their self-gravity by a…
In this work, we study self-gravitating objects that obey a polytropic equation of state in hyperbolic symmetry. Specifically, we describe in detail the steps to derive the Lane-Emden equation from the structure equations of the system. To…
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…
The thickness of the equilibrium isothermal gaseous layers and their volume densities \rho_{gas}(R) in the disc midplane are calculated for 7 spiral galaxies (including our Galaxy) in the frame of self-consistent axisymmetric model. Local…
We consider the compressible Euler-Poisson equations for polytropes $P(\rho)=K\rho^{\gamma}$ with $\gamma\in \left(\frac{6}{5},\frac{4}{3} \right]$ and the white dwarf stars. For $\gamma=\frac{4}{3},$ we establish the existence of a global…
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.