{"paper":{"title":"Local virial relation and velocity anisotropy for collisionless self-gravitating systems","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"A.Nakamichi, M.Morikawa, O.Iguchi, Y.Sota","submitted_at":"2005-08-13T15:03:01Z","abstract_excerpt":"The collisionless quasi-equilibrium state realized after the cold collapse of self-gravitating systems has two remarkable characters. One of them is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. Another is the local virial (LV) relation, the virial relation which holds even locally in collisionless systems through phase mixing such as cold-collapse. A family of polytropes are examined from a view point of these two characters. The LV relation imposes a strong constraint on these models: only polytropes with index $n \\sim 5$ with a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0508308","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/0508308/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"}