{"paper":{"title":"Error formulae for the energy-dependent cross-spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM"],"primary_cat":"astro-ph.HE","authors_text":"Adam Ingram","submitted_at":"2019-09-03T18:14:59Z","abstract_excerpt":"I present analytic error formulae for the energy-dependent cross-spectrum and rms spectrum, which are Fourier statistics widely used to probe the rapid X-ray variability observed from accreting compact objects. The new formulae cover the modulus, phase, real and imaginary parts of the cross-spectrum, and are valid for any value of intrinsic coherence between variability in different energy bands. I show that existing error formulae (including that for the phase lag), which are valid for a single cross-spectrum or power spectrum, lead to over-fitting when applied to the energy-dependent cross-s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.01385","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/1909.01385/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"}