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| Navarro–Frenk–White | |
|---|---|
| Name | Navarro–Frenk–White profile |
| Discoverers | Julio Navarro; Carlos Frenk; Simon D. M. White |
| Field | Astrophysics; Cosmology; Computational astrophysics |
| Introduced | 1996 |
Navarro–Frenk–White is an empirical radial density profile for dark matter halos introduced by Julio Navarro, Carlos Frenk, and Simon D. M. White. It summarizes results from numerical simulations led by teams at the Institute of Astronomy, Cambridge, the Max Planck Institute for Astrophysics, and the California Institute of Technology and has become foundational in studies by groups associated with the Virgo Consortium, the Millennium Simulation, and the Bolshoi simulation.
The profile was proposed after a sequence of N-body studies by Navarro, Frenk, and White that synthesized earlier work by researchers at the Royal Greenwich Observatory, the Princeton University, and the University of California, Santa Cruz and built on methods developed by groups including the European Southern Observatory and the National Aeronautics and Space Administration. Early simulations used algorithms from the Barnes–Hut algorithm lineage and codes inspired by efforts at the Los Alamos National Laboratory and the Lawrence Livermore National Laboratory and compared to analytical expectations from the Press–Schechter formalism and models by Yakov Zeldovich and Peebles. The 1996–1997 papers unified results across halo masses from studies related to the Coma Cluster, the Virgo Cluster, and galaxy-sized halos relevant to the Sloan Digital Sky Survey era, influencing later large projects like the Two Micron All Sky Survey and the Dark Energy Survey.
The NFW density profile is written ρ(r) = ρ_s / ((r/r_s)(1 + r/r_s)^2), where ρ_s and r_s are scale density and radius parameters introduced in the original fits by Navarro, Frenk, and White and later used in analyses by teams at the Harvard–Smithsonian Center for Astrophysics, the Kavli Institute for Cosmology, and the University of Oxford. The profile implies a cumulative mass M(r) = 4πρ_s r_s^3 [ln(1 + r/r_s) − r/(r + r_s)] used in studies by researchers at the University of Cambridge, the Max Planck Society, and the University of Chicago to define concentration parameters and virial masses tied to conventions from the Planck Collaboration, the Wilkinson Microwave Anisotropy Probe, and the Hubble Space Telescope community. Common parametrizations employ a concentration c = r_vir / r_s and relations calibrated by groups behind the Millennium-II simulation, the Illustris project, and the EAGLE simulation.
Physically, the profile describes a cuspy inner slope ρ ∝ r^−1 and an outer slope ρ ∝ r^−3, a behavior contrasted in theoretical comparisons with results from analytic collapse models of Gunn–Gott and hierarchical assembly scenarios articulated by White & Rees and others at the University of California, Berkeley. Its universality across halo mass scales was emphasized in comparisons involving the Bullet Cluster, the Coma Cluster, and Milky Way–sized halos studied by teams at the Max Planck Institute for Astrophysics, the University of Michigan, and the Carnegie Institution for Science. The profile’s divergence of phase-space density toward the center has been analyzed in the context of processes studied by researchers at the CERN Theory Division, the Institute for Advanced Study, and the Perimeter Institute, and its implications for annihilation signals have been explored by collaborations including the Fermi Gamma-ray Space Telescope team and groups at the European Space Agency.
The NFW form is used to populate halos in semi-analytic models developed at the Institute of Astronomy, Cambridge, implement halo occupation distributions used by the Sloan Digital Sky Survey consortium, and as input to lensing analyses by teams at the Hubble Space Telescope, the Subaru Telescope, and the Atacama Cosmology Telescope. It underpins mock catalogs produced for the Dark Energy Survey, the Euclid mission, and the Large Synoptic Survey Telescope (now Vera C. Rubin Observatory) and enters halo modeling in work from the Planck Collaboration, the South Pole Telescope, and the BOSS survey. Hydrodynamical simulations such as IllustrisTNG, EAGLE, and Horizon-AGN test how baryonic physics from groups at the Max Planck Institute for Astrophysics, the University of Cambridge, and Princeton University modify the NFW shape.
Observational constraints come from rotation curves of galaxies studied by teams at Palomar Observatory, the Keck Observatory, and the Arecibo Observatory; strong lensing systems surveyed by the Sloan Lens ACS Survey, Hubble Space Telescope programs, and the Keck Observatory; and X-ray and Sunyaev–Zel'dovich measurements of clusters from the Chandra X-ray Observatory, XMM-Newton, and the Planck Collaboration. Tensions with cored profiles inferred in dwarf galaxies from work by groups at the Royal Astronomical Society, the Max Planck Institute for Astrophysics, and the University of California, Irvine have motivated observational programs by the Very Large Array, the Gemini Observatory, and the European Southern Observatory to refine constraints.
Alternatives and extensions include the Einasto profile studied by researchers at the Max Planck Society, the Burkert profile explored by groups at the University of Groningen, and self-interacting dark matter models advanced by teams at the California Institute of Technology, SLAC National Accelerator Laboratory, and the Perimeter Institute. Modifications informed by baryonic feedback from simulations at the Illustris project, the EAGLE simulation, and the FIRE collaboration, and analytic approaches tied to the Extended Press–Schechter framework and models developed at the Institute for Advanced Study provide extensions used by the CosmoSim database, the Millennium Simulation team, and the Bolshoi simulation consortium.
Category:Dark matter halos