{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/velocity-anisotropy-and-shape-bias-in-the","title":"Velocity Anisotropy and Shape Bias in the Caustic Technique","arxiv_id":"1307.0018","date":"2013-06-28","proceeding":null,"authors":["Daniel Gifford","Christopher J. Miller"],"abstract":"We use the Millennium Simulation to quantify the statistical accuracy and precision of the escape velocity technique for measuring cluster-sized halo masses at z~0.1. We show that in 3D, one can measure nearly unbiased (<4%) halo masses (>1.5x10^14 M_solar h^-1) with 10-15% scatter. Line-of-sight projection effects increase the scatter to ~25%, where we include the known velocity anisotropies. The classical \"caustic\" technique incorporates a calibration factor which is determined from N-body simulations. We derive and test a new implementation which eliminates the need for calibration and utilizes only the observables: the galaxy velocities with respect to the cluster mean v, the projected positions r_p, an estimate of the Navarro-Frenk-White (NFW) density concentration and an estimate of the velocity anisotropies, beta. We find that differences between the potential and density NFW concentrations induce a 10% bias in the caustic masses. We also find that large (100%) systematic errors in the observed ensemble average velocity anisotropies and concentrations translate to small (5%-10%) biases in the inferred masses.","url_abs":"https://arxiv.org/abs/1307.0018v1","url_pdf":"https://arxiv.org/pdf/1307.0018v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"velocity-anisotropy-and-shape-bias-in-the","repo_url":"https://github.com/giffordw/CausticMass","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}