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In this paper a prescription for generating an equilibrium spherical systemdepicted with cuspy density profiles is extended to a core density profile, theBurkert profile, which is observationally more suitable to dwarfs. By using atime-saving Monte Carlo method instead of N-body simulations, we show that theBurkert halo initialized with the distribution function that depends only onenergy is in a practically stable equilibrium. The one generated using thelocal Maxwellian approximation is unstable, where the flat core densitystructure tends to steepen. This is fundamentally different from the previousstudy on a halo with cuspy density profile. The deviation of the unstable"Burkert" from the initial Burkert profile is found to be closely related totaking a Gaussian as the velocity distribution at any given point. Thesignificance of not using the local Maxwellian approximation is furtherdemonstrated by exploring the dynamical evolution of compact super starclusters in the Burkert halo. In particular, the local Maxwellian approximationwill result in underestimating the dynamical friction and overestimatingsinking time scale. Accordingly, it will lead to lower probability of formingmassive bulges and young nuclear star clusters in bulgeless galaxies.Comment: 12 pages, 3 figures, accepted for publication in PAS

An Equilibrium Dark Matter Halo with the Burkert Profile