{"paper":{"title":"On the Submillimeter Opacity of Protoplanetary Disks","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"B.T. Draine (Princeton University)","submitted_at":"2005-07-12T16:10:05Z","abstract_excerpt":"Solid particles with the composition of interstellar dust and power-law size distribution dn/da propto a^{-p} for a < a_max with a_{max} > 3 lambda and 3 < p < 4 will have submm opacity spectral index beta(lambda) = dln(kappa)/dln(nu) approx (p-3) beta_{ism}, where beta_{ism} approx 1.7 is the opacity spectral index of interstellar dust material in the Rayleigh limit. For the power-law index p approx 3.5 that characterizes interstellar dust, and that appears likely for particles growing by agglomeration in protoplanetary disks, grain growth to sizes a > 3 mm will result in beta(1 mm) < ~1. Gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0507292","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/astro-ph/0507292/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"}