  In this paper a prescription for generating an equilibrium spherical system
depicted with cuspy density profiles is extended to a core density profile, the
Burkert profile, which is observationally more suitable to dwarfs. By using a
time-saving Monte Carlo method instead of N-body simulations, we show that the
Burkert halo initialized with the distribution function that depends only on
energy is in a practically stable equilibrium. The one generated using the
local Maxwellian approximation is unstable, where the flat core density
structure tends to steepen. This is fundamentally different from the previous
study on a halo with cuspy density profile. The deviation of the unstable
"Burkert" from the initial Burkert profile is found to be closely related to
taking a Gaussian as the velocity distribution at any given point. The
significance of not using the local Maxwellian approximation is further
demonstrated by exploring the dynamical evolution of compact super star
clusters in the Burkert halo. In particular, the local Maxwellian approximation
will result in underestimating the dynamical friction and overestimating
sinking time scale. Accordingly, it will lead to lower probability of forming
massive bulges and young nuclear star clusters in bulgeless galaxies.
