Magnetostatic Equilibrium of 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 ...

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...

Resonance Effects in Polytropes

Shear-Driven Field-Line Opening and the Loss of a Force-Free Magnetostatic Equilibrium

This paper discusses a quasi-static evolution of a force-free magnetic field under slow sheared footpoint motions on the plasma’s boundary, an important problem with applications to the solar and accretion disk coronae. The main qualitative features of the evolution (such as field-line expansion and opening) are considered and a comparison is made between two different geometrical settings: the...

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...