{"paper":{"title":"Plain fundamentals of Fundamental Planes: Analytics and algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Mariangela Bernardi (UPenn), Ravi K. Sheth (ICTP, UPenn)","submitted_at":"2012-02-15T21:00:05Z","abstract_excerpt":"The coefficients a and b of the Fundamental Plane relation R ~ Sigma^a I^b depend on whether one minimizes the scatter in the R direction or orthogonal to the Plane. We provide explicit expressions for a and b (and confidence limits) in terms of the covariances between logR, logSigma and logI. Our analysis is more generally applicable to any other correlations between three variables: e.g., the color-magnitude-Sigma relation, the L-Sigma-Mbh relation, or the relation between the X-ray luminosity, Sunyaev-Zeldovich decrement and optical richness of a cluster, so we provide IDL code which implem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3438","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"}