  We make a simple analytical study of radial profiles of dark matter
structures, with special attention to the question of the central radial
density profile. We let our theoretical assumptions be guided by results from
numerical simulations, and show that at any radius where both the radial
density profile, rho, and the phase-space-like density profile,
rho/sigma^epsilon, are exact power laws, the only allowed density slopes in
agreement with the spherical symmetric and isotropic Jeans equation are in the
range 1< beta <3, where beta = - dln(rho)/dln(r). We also allow for a radial
variation of these power laws, as well as anisotropy, and show how this allows
for more shallow central slopes.
