The Halo Density Profiles with Non-Standard N-body Simulations
  We propose a new numerical procedure to simulate a single dark halo of any size and mass in a hierarchical framework coupling the extended Press-Schechter formalism (EPSF) to N-body simulations. The procedure consists of assigning cosmological initial conditions to the particles of a single halo with a EPSF technique and following only the dynamical evolution using a serial N-body code. The computational box is fixed with a side of $0.5 h^{-1}$ Mpc. This allows to simulate galaxy cluster halos using appropriate scaling relations, to ensure savings in computing time and code speed. The code can describe the properties of halos composed of collisionless or collisional dark matter. For collisionless Cold Dark Matter (CDM) particles the NFW profile is reproduced for galactic halos as well as galaxy cluster halos. Using this numerical technique we study some characteristics of halos assumed to be isolated or placed in a cosmological context in presence of weak self-interacting dark matter: the soft core formation and the core collapse. The self-interacting dark matter cross section per unit mass is assumed to be inversely proportional to the particle collision velocity: $\sigma/m_{x} \propto 1/v$. 
Elena D'Onghia (1), Claudio Firmani (2), Guido Chincarini (2,3)((1)   Max-Planck-Institute for Astronomy (Heidelberg),(2) Os...