Polytropes: Applications in Astrophysics and Related Fields / Edition 1

by Georg P. Horedt

Overview

While it seems possible to present a fairly complete uni?ed theory of undistorted polytropes, as attempted in the previous chapter, the theory of distorted polytropes is much more extended and - phisticated, so that I present merely a brief overview of the theories that seem to me most interesting and important. Basically, the methods proposed to study the hydrostatic equilibrium of a distorted self-gravitating mass can be divided into two major groups (Blinnikov 1975): (i) Analytic or semia- lytic methods using a small parameter connected with the distortion of the polytrope. (ii) More or less accurate numerical methods. Lyapunov and later Carleman (see Jardetzky 1958, p. 13) have demonstrated that a sphere is a unique solution to the problem of hydrostatic equilibrium for a ?uid mass at rest in tridimensional space. The problem complicates enormously if the sphere is rotating rigidly or di?erentially in space round an axis, and/or if it is distorted magnetically or tidally. Even for the simplest case of a uniformly rotating ?uid body with constant density not all possible solutions have been found (Zharkov and Trubitsyn 1978, p. 222). The sphere becomes an oblate ?gure, and we have no a priori knowledge of its strati?cation, boundary shape, planes of symmetry, transfer of angular momentum in di?erentially rotating bodies, etc.

Product Details

ISBN-13:	9789048166459
Publisher:	Springer Netherlands
Publication date:	12/06/2010
Series:	Astrophysics and Space Science Library , #306
Edition description:	Softcover reprint of the original 1st ed. 2004
Pages:	724
Product dimensions:	6.10(w) x 9.25(h) x 0.06(d)

Table of Contents

Polytropic and Adiabatic Processes.- Undistorted Polytropes.- Distorted Polytropes.- Relativistic Polytropes.- Stability and Oscillations.- Further Applications to Polytropes.