Perturbative solution to the Lane-Emden equation: an eigenvalue approach
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AbstractUnder suitable scaling, the structure of self-gravitating polytropes is described by the standard Lane-Emden equation (LEE), which is characterized by the polytropic index n. Here, we use the known exact solutions of the LEE at n= 0 and n= 1 to solve the equation perturbatively. We first introduce a scaled LEE (SLEE) where polytropes with different polytropic indices all share a common scaled radius. The SLEE is then solved perturbatively as an eigenvalue problem. Analytical approximants of the polytrope function, the radius and the mass of polytropes as a function of n are derived. The approximant of the polytrope function is well defined and uniformly accurate from the origin down to the surface of a polytrope. The percentage errors of the radius and the mass are bounded by 8.1 x 10(-7) per cent and 8.5 x 10(-5) per cent, respectively, for n is an element of [0, 1]. Even for n is an element of [1, 5), both percentage errors are still less than 2 per cent.
All Author(s) ListYip KLS, Chan TK, Leung PT
Journal nameMonthly Notices of the Royal Astronomical Society
Volume Number465
Issue Number4
Pages4265 - 4280
LanguagesEnglish-United Kingdom
Keywordshydrodynamics, methods, analytical, stars, interiors, stars, neutron, white dwarfs
Web of Science Subject CategoriesAstronomy & Astrophysics;Astronomy & Astrophysics

Last updated on 2020-18-09 at 01:42