{"paper":{"title":"The Free-Fall time of finite Sheets and Filaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.SR","authors_text":"Enrique V\\'azquez-Semadeni, Gilberto C. G\\'omez, Jes\\'us A. Toal\\'a","submitted_at":"2011-10-05T08:09:00Z","abstract_excerpt":"Molecular clouds often exhibit filamentary or sheet-like shapes. We compute the free-fall time ($\\tff$) for finite, uniform, self-gravitating circular sheets and filamentary clouds of small but finite thickness, so that their volume density $\\rho$ can still be defined. We find that, for thin sheets, the free-fall time is larger than that of a uniform sphere with the same volume density by a factor proportional to $\\sqrt{A}$, where the aspect ratio $A$ is given by $A=R/h$, $R$ being the sheet's radius and $h$ is its thickness. For filamentary clouds, the aspect ratio is defined as $A=L/\\calR$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0917","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":""},"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"}