{"paper":{"title":"The Structure of Self-Gravitating Polytropic Systems with n around 5","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"George Rybicki (Harvard), Mikhail V. Medvedev (Harvard & CITA)","submitted_at":"2000-10-30T22:05:48Z","abstract_excerpt":"We investigate the structure of self-gravitating polytropic stellar systems. We present a method which allows to obtain approximate analytical solutions, $\\psi_{n+\\epsilon}({\\bf x})$, of the nonlinear Poisson equation with the polytropic index $n+\\epsilon$, given the solution $\\psi_n({\\bf x})$ with the polytropic index n, for any positive or negative $\\epsilon$ such that $|\\epsilon|\\ll1$. Application of this method to the spherically symmetric stellar polytropes with $n\\simeq5$ yields the solutions which describe spatially bound systems if n<5 and the formation of a second core if n>5. A heuri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0010621","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/astro-ph/0010621/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}