The redshift evolution of Λ cold dark matter halo parameters: Concentration, spin and shape

We present a detailed study of the redshift evolution of dark matter halo structural parameters in a Λ cold dark matter cosmology. We study the mass and redshift dependence of the concentration, shape and spin parameter in N-body simulations spanning masses from 10¹⁰ to 10¹⁵h^-1M_⊙ and redshifts from 0 to 2. We present a series of fitting formulae that accurately describe the time evolution of the concentration-mass (c_vir-M_vir) relation since z= 2. Using arguments based on the spherical collapse model, we study the behaviour of the scalelength of the density profile during the assembly history of haloes, obtaining physical insights into the origin of the observed time evolution of the c_vir-M_vir relation. We also investigate the evolution with redshift of dark matter halo shape and its dependence on mass. Within the studied redshift range, the relation between the halo shape and mass can be well fitted by a redshift-dependent power law. Finally we show that although for z= 0 the spin parameter is practically mass independent, at increasing redshift it shows an increasing correlation with mass.