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, ρ/σ 3 ∝ r −α , and (ii) the velocity anisotropy parameter is given by the relation β a ( r)= β 1+2 β 2 ( r/ r *)/[1+( r/ r *) 2] where β 1, β 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 γ, defined by γ=− d ln ρ d ln r . The values of γ at r=10 −2.5 r vir, a distance where the systems could be resolved by large N-body simulations, lie in the range 1.0–1.6. These inner values of γ increase for increasing β 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.