Newtonian Stellar Models

Abstract

We investigate static spherically symmetric perfect fluid models in Newtonian gravity for barotropic equations of state that are asymptotically polytropic at low and high pressures. This is done by casting the equations into a 3-dimensional regular dynamical system with bounded dependent variables. The low and high central pressure limits correspond to two 2-dimensional boundary subsets, described by homology invariant equations for exact polytropes. Thus the formulation naturally places work about polytropes in a more general context. The introduced framework yields a visual aid for obtaining qualitative information about the solution space and is also suitable for numerical investigations. Last, but not least, it makes a host of mathematical tools from dynamical systems theory available. This allows us to prove a number of theorems about the relationship between the equation of state and properties concerning total masses and radii.