{"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/tdcosmo-iv-hierarchical-time-delay","title":"TDCOSMO IV: Hierarchical time-delay cosmography -- joint inference of the Hubble constant and galaxy density profiles","arxiv_id":"2007.02941","date":"2020-07-06","proceeding":null,"authors":["S. Birrer","A. J. Shajib","A. Galan","M. Millon","T. Treu","A. Agnello","M. Auger","G. C. -F. Chen","L. Christensen","T. Collett","F. Courbin","C. D. Fassnacht","L. V. E. Koopmans","P. J. Marshall","J. -W. Park","C. E. Rusu","D. Sluse","C. Spiniello","S. H. Suyu","S. Wagner-Carena","K. C. Wong","M. Barnabè","A. S. Bolton","O. Czoske","X. Ding","J. A. Frieman","L. Van de Vyvere"],"abstract":"The H0LiCOW collaboration inferred via gravitational lensing time delays a Hubble constant $H_0=73.3^{+1.7}_{-1.8}$ km s$^{-1}{\\rm Mpc}^{-1}$, describing deflector mass density profiles by either a power-law or stars plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in $H_0$. We quantify any potential effect of the MST with flexible mass models that are maximally degenerate with H0. Our calculation is based on a new hierarchical approach in which the MST is only constrained by stellar kinematics. The approach is validated on hydrodynamically simulated lenses. We apply the method to the TDCOSMO sample of 7 lenses (6 from H0LiCOW) and measure $H_0=74.5^{+5.6}_{-6.1}$ km s$^{-1}{\\rm Mpc}^{-1}$. In order to further constrain the deflector mass profiles, we then add imaging and spectroscopy for 33 strong gravitational lenses from the SLACS sample. For 9 of the SLAC lenses we use resolved kinematics to constrain the stellar anisotropy. From the joint analysis of the TDCOSMO+SLACS sample, we measure $H_0=67.4^{+4.1}_{-3.2}$ km s$^{-1}{\\rm Mpc}^{-1}$, assuming that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. While our new analysis does not statistically invalidate the mass profile assumptions by H0LiCOW, and thus their $H_0$ measurement relying on those, it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on $H_0$ derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data, chiefly spatially resolved kinematics of lens galaxies.","url_abs":"https://arxiv.org/abs/2007.02941v1","url_pdf":"https://arxiv.org/pdf/2007.02941v1.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":"tdcosmo-iv-hierarchical-time-delay","repo_url":"https://github.com/TDCOSMO/hierarchy_analysis_2020_public","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"tdcosmo-iv-hierarchical-time-delay","repo_url":"https://github.com/nataliehogg/tdcosmo_ext","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2007.02941","atlas_url":"https://app.syntology.ai/?focus=2007.02941","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}