1999/06/24 by Taihei Yano, Naoteru Gouda · 1 citation
Physics and Astronomy · #Correlation function (quantum field theory) #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Dark matter #Dark matter halo #Galaxies: Formation, Evolution, Phenomena #Halo #Limit (mathematics) #Power index #Power law #Spectral density #astro-ph
paper · pdf · doi:10.1086/309246
published as Astrophys.J. 539 (2000) 493-496 · 15 pages with no figures, submitted to Astrophysical Journal
arxiv created 1999/06/24 · openalex publication_date 2000/08/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We have found the relation between the two-point spatial correlation function and the density profile of dark matter halos in the strongly nonlinear regime. It is well known that when the density fluctuations grow into dark matter halos whose density profile is ρ ∝ r - (3/2 < < 3) on almost all mass scales, the two-point spatial correlation function obeys a power law with the power index γ = 2 - 3 in the strongly nonlinear regime. We find that the two-point spatial correlation function does not obey the power law when the power index is smaller than , such as the density profile ρ ∝ r -1 around the center of the halo, which was proposed by Navarro, Frenk, & White in 1996 and 1997. By using the BBGKY equation in the strongly nonlinear regime, it is also found that the velocity parameter h ≡ -⟨ v ⟩/ x is not a constant even in the strongly nonlinear regime ( ≡ x / x nl → 0), although it is a constant when > 3/2, and then the two-point spatial correlation function can be regarded as the power law. The velocity parameter h becomes zero at the nonlinear limit of → 0, that is, the stable clustering hypothesis cannot be satisfied when < 3/2.