  Inverse mass cascade is a key feature of the intermediate statistically
steady state for self-gravitating collisionless dark matter flow (SG-CFD). This
paper focus on effects of mass cascade on halo energy, momentum, dispersion,
size, and density. Halo with fast mass accretion has an expanding core. Mass
cascade forms a new layer of mass that deforms the original halo and induces
nonzero radial flow (outwards in core and inwards in outer regions). The
inward/outward flow leads to an extra length scale (scale radius) that is not
present in isothermal profile. Halo concentration c=3.5 can be derived for fast
growing halos. For cusp-core controversy, a double-power-law density is
proposed as a result of nonzero radial flow. The inner/outer density are
controlled by halo deformation rate and halo growth, respectively. The slower
deformation at center, the steeper density. For fast growing halos, radial flow
at center is simply Hubble flow that leads to the existence of central core.
Mass cascade leads to nonzero halo surface energy/tension and radial flow that
enhances dispersion in outer region. An effective exponent of gravity
$n_e$=-1.3 (not -1) is obtained due to halo surface energy. Halo size follows a
geometric Brownian motion and lognormal distribution. Brownian motion of
particles in evolving halos leads to Fokker-Planck equations for particle
distribution that is dependent on the radial and osmotic flow. Complete
solutions of particle distribution are presented based on a simple model of
osmotic flow. The proposed model agrees with N-body simulation for various halo
group sizes. With reference pressure/density defined at center, equation of
state can be established for relative pressure/density. Pressure, density, and
dispersion at halo center are presented. The core size $x_c$ is obtained where
Hubble flow is dominant. Simple closures are proposed for self-consistent halo
density.
