{"paper":{"title":"Self-consistent potential-density pairs of thick disks and flattened galaxies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"(2) IoA Cambridge), J. An (1), N.W. Evans (2) ((1) KASI Daejeon","submitted_at":"2019-04-10T18:00:11Z","abstract_excerpt":"We analyze the Miyamoto--Nagai substitution, which was introduced over forty years ago to build models of thick disks and flattened elliptical galaxies. Through it, any spherical potential can be converted to an axisymmetric potential via the replacement of spherical polar $r^2$ with $R^2 + ( a + \\!\\sqrt{z^2+b^2} )^2$, where ($R,z$) are cylindrical coordinates and $a$ and $b$ are constants. We show that if the spherical potential has everywhere positive density, and satisfies some straightforward constraints, then the transformed model also corresponds to positive density everywhere. This is i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05366","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"}