{"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/separate-universe-calibration-of-the","title":"Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy","arxiv_id":"2007.03711","date":"2020-07-07","proceeding":null,"authors":["Sujatha Ramakrishnan","Aseem Paranjape"],"abstract":"We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias $b_1$ and $b_2$ on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy $\\alpha$ to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work which exploits the near-Lognormal shape of the distribution of $\\alpha$ and results in very high precision calibrations. We present convenient fitting functions for the dependence of $b_1$ and $b_2$ on $\\alpha$ over a wide range of halo mass for redshifts $0\\leq z\\leq1$. Our calibration of $b_2(\\alpha)$ is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results which showed that $\\alpha$ is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of $b_1$ and $b_2$ on any such secondary property which has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using $\\alpha$ as a segregating variable in multi-tracer analyses.","url_abs":"https://arxiv.org/abs/2007.03711v2","url_pdf":"https://arxiv.org/pdf/2007.03711v2.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":"separate-universe-calibration-of-the","repo_url":"https://github.com/rsujatha/CAB","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}