Enumerating polytropes

Stability analysis of Newtonian polytropes

We analyze the stability of Newtonian polytropic static fluid spheres, described by the Lane-Emden equation. In the general case of arbitrary polytropic indices the Lane-Emden equation is a non-linear second order ordinary differential equation. By introducing a set of new variables, the Lane-Emden equation can be reduced to an autonomous system of two ordinary differential equations, which in ...

Resonance Effects in Polytropes

Stability of Polytropes

This paper is an investigation of the stability of some ideal stars. It is intended as a study in General Relativity, with emphasis on the coupling to matter, eventually aimed at a better understanding of very strong gravitational fields and “Black Holes”. This contrasts with the usual attitude in astrophysics, where Einstein’s equations are invoked as a refinement of classical thermodynamics a...

Second-Order Pulsations In Polytropes

A theory due to Eddington is employed to calculate second-order corrections to the usual linear, quasi-adiabatic pulsational amplitudes. Such corrections are necessary in order to evaluate the pulsational stability of stars in thermal imbalance (dSo/dt ;c 0). The second-order quantities are calculated, and their properties discussed, for a wide variety of polytropic models. Subsequently, a numb...

Pulsation modes for increasingly relativistic polytropes

We present the results of a numerical study of the fluid f , p and the gravitational w modes for increasingly relativistic nonrotating polytropes. The results for f and w-modes are in good agreement with previous data for uniform density stars, which supports an understanding of the nature of the gravitational wave modes based on the uniform density data. We show that the p-modes can become ext...