Density profiles of dark matter halos with anisotropic velocity tensors

Abstract

We present density profiles, that are solutions of the spherical Jeans equation, derived under the following two assumptions: (i) the coarse grained phase-density follows a power-law of radius, rho/(sigma^3) proportional to r^{-alpha}, and (ii) the velocity anisotropy parameter is given by the relation beta_a(r) = beta_1 + 2 beta_2 {(r/r_*)/(1+(r/r_*)^2)} where beta_1, beta_2 are parameters and r_* equals twice the virial radius, r_{vir}, of the system. These assumptions are well motivated by the results of N-body simulations. Density profiles have increasing logarithmic slopes gamma, defined by gamma = - {(d ln rho)/(d ln r)}. The values of gamma at r = 10^{-2.5}r_{vir}, a distance where the systems could be resolved by large N-body simulations, lie in the range 1. - 1.6. These inner values of gamma increase for increasing beta_1 and for increasing concentration of the system. On the other hand, slopes at r = r_{vir} lie in the range 2.42 - 3.82. A model density profile that fits well the results at radial distances between 10^{-3}r_{vir} and r_{vir} and connects kinematic and structural characteristics of spherical systems is described.