Scale invariant stellar structure

TL;DR

This paper derives a unified, scale-invariant framework for stellar structure equations, providing analytical approximations for polytropic stars, including white dwarfs and ZAMS stars, enhancing understanding of their properties.

Contribution

It introduces a scale-invariant approach to hydrostatic stellar models, deriving analytical solutions and approximations for polytropes, especially for relativistic white dwarfs and ZAMS stars.

Findings

Derived analytical approximations for Lane-Emden functions.

Unified scale-invariant formulation for polytropic stellar models.

Applicable to relativistic white dwarfs and ZAMS stars.

Abstract

In scale invariant hydrostatic barotropes, the radial evolutionary equation linearly relates the local gravitational and internal energies. From this first-order equation, directly follow all the properties of polytropes and the important mass-radius relation. Quadrature then leads to the regular Lane-Emden functions and their Picard and Pade approximations, which are useful wherever stars are approximately or exactly polytropic. We illustrate this particularly for the n=3 regular polytrope and obtain analytic approximations to the solution of the Lane-Emden equation, valid over the bulk of relativistic degenerate stars (massive white dwarfs) and chemically homogeneous stars in radiative equilibrium (ZAMS stars).