Origin of Cusp in Dark Matter Halo

Hierarchical clustering model has been extensively used in studies of the cosmological structure formation. In the hierarchical model, such as the standard Cold Dark Matter (CDM) dominated universe, the structures are formed in a bottom-up fashion. In this letter, we show that dark halos formed through the hierarchical clustering have non-isothermal structure and central density cusp shallower than ρ ∝ r, by means of high-resolution N-body simulations. We also give a physical mechanism of formation of such non-isothermal structure. Recently, several claims were made that the central cusp of dark matter halo has the profile of ρ ∼ r [1] [2], which resembles to recent HST results of large ellipticals[3]. However, cusp obtained in our simulations, which employs more than 10 times more particles than what used in previous studies, is noticeably more steep, which resembles to nearly isothermal cusp of less massive ellipticals. Recent high resolution ground-based and Hubble Space Telescope observations[3] have revealed that elliptical galaxies do not have a constant-density core and the densities continue to rise until the resolution limit. In faint ellipticals, the density profile at the central region increases roughly as ρ ∝ r, and in bright ellipticals it increases as ρ ∝ r or shallower. Several simulations demonstrated that the dark matter halos formed through hierarchical clustering were not well approximated by isothermal spheres, and better fitted by a Hernquist model[4] or similar model which