{"paper":{"title":"Perturbative solution to the Lane-Emden equation: An eigenvalue approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.SR","authors_text":"Kenny L. S. Yip, P. T. Leung, T. K. Chan","submitted_at":"2016-11-22T08:56:00Z","abstract_excerpt":"Under suitable scaling, the structure of self-gravitating polytropes is described by the standard Lane-Emden equation (LEE), which is characterised by the polytropic index $n$. Here we use the known exact solutions of the LEE at $n=0$ and $1$ 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 app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07202","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}