Polytropes: Applications in Astrophysics and Related Fields (Astrophysics and Space Science Library, 306)

This Book Provides The Most Complete Academic Treatment On The Application Of Polytropes Ever Published. It Is Primarily Intended For Students And Scientists Working In Astrophysics And Related Fields. It Provides A Full Overview Of Past And Present Research Results And Is An Indispensible Guide For Everybody Wanting To Apply Polytropes. 1: Polytropic And Adiabatic Processes -- 2: Undistorted Polytropes -- 3: Distorted Polytropes -- 4: Relativistic Polytropes -- 5: Stability And Oscillations -- 6: Further Applications To Polytropes -- Acknowledgments -- Appendix A -- Appendix B -- Appendix C -- References And Author Index -- Subject Index. By G.p. Horedt. Includes Bibliographical References (p. 674-713) And Indexes. 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. "This book provides the most complete academic treatment on the application of polytropes ever published. It is primarily intended for students and scientists working in astrophysics and related fields. It provides a full overview of past and present research results and is an indispensible guide for everybody wanting to apply polytropes."--Jacket Polytropic and Adiabatic Processes....Pages 1-25 Undistorted Polytropes....Pages 27-136 Distorted Polytropes....Pages 137-285 Relativistic Polytropes....Pages 287-340 Stability and Oscillations....Pages 341-548 Further Applications to Polytropes....Pages 549-666