{"paper":{"title":"A Log-Quadratic Relation Between the Nuclear Black-Hole Masses and Velocity Dispersions of Galaxies","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Stuart Wyithe","submitted_at":"2005-03-21T03:00:47Z","abstract_excerpt":"We demonstrate that a log-linear relation does not provide an adequate description of the correlation between the masses of Super-Massive Black-Holes (SMBH, M_bh) and the velocity dispersions of their host spheroid (sigma). An unknown relation between log(M_bh) and log(sigma) may be expanded to second order to obtain a log-quadratic relation of the form log(M_bh)=alpha+beta log(sigma/200) + beta_2[log(sigma/200)]^2. We perform a Bayesian analysis using the Nuker sample, and solve for beta, beta_2 and alpha, in addition to the intrinsic scatter (delta). We find unbiased parameter estimates of b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0503435","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/0503435/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"}