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We report a series of high-resolution cosmological N-body simulationsdesigned to explore the formation and properties of dark matter halos withmasses close to the damping scale of the primordial power spectrum of densityfluctuations. We further investigate the effect that the addition of a randomcomponent, v_rms, into the particle velocity field has on the structure ofhalos. We adopted as a fiducial model the Lambda Warm Dark Matter cosmologywith a non-thermal sterile neutrino mass of 0.5 keV. The filtering masscorresponds then to M_f = 2.6x10^12 M_sun/h. Halos of masses close to M_f weresimulated with several million of particles. The results show that, on onehand, the inner density slope of these halos (at radii <~0.02 the virial radiusRvir) is systematically steeper than the one corresponding to the NFW fit or tothe CDM counterpart. On the other hand, the overall density profile (radiilarger than 0.02Rvir) is less curved and less concentrated than the NFW fit,with an outer slope shallower than -3. For simulations with v_rms, the innerhalo density profiles flatten significantly at radii smaller than 2-3 kpc/h(<~0.010-0.015Rvir). A constant density core is not detected in oursimulations, with the exception of one halo for which the flat core radius is~1 kpc/h. Nevertheless, if ``cored'' density profiles are used to fit the haloprofiles, the inferred core radii are ~0.1-0.8 kpc/h, in rough agreement withtheoretical predictions based on phase-space constrains, and on dynamicalmodels of warm gravitational collapse. A reduction of v_rms by a factor of 3produces a modest decrease in core radii, less than a factor of 1.5. We discussthe extension of our results into several contexts, for example, to thestructure of the cold DM micro-halos at the damping scale of this model.

On the Structure of Dark Matter Halos at the Damping Scale of the Power Spectrum with and without Relict Velocities