  The damping on the fluctuation spectrum and the presence of thermal
velocities as properties of warm dark matter particles like sterile neutrinos
imprint a distinct signature found from the structure formation mechanisms to
the internal structures of halos. Using warm dark matter simulations we explore
these effects on the structure formation for different particle energies and we
find that the formation of structure is more complex than originally assumed, a
combination of top-down collapse and hierarchical (bottom-up) clustering on
multiple scales. The degree on which one scenario is more prominent with
respect to the other depends globally on the energy of the particle and locally
on the morphology and architecture of the analyzed region. The presence of
shells and caustics in warm dark matter halos is another important effect seen
in simulations. Furthermore, we discuss the impact of thermal velocities on the
structure formation from theoretical considerations as well as from the
analysis of the simulations. We re-examine the assumptions considered when
estimating the velocity dispersion for warm dark matter particles that have
been adopted in previous works for more than a decade and we give an
independent estimation for the velocities. We identify some inconsistencies in
previous published results. The relation between the warm dark matter particle
mass and its corresponding velocity dispersion is strongly model dependent,
hence the constraints on particle mass from simulation results are weak.
Finally, we review the technical difficulties that arise in warm dark matter
simulations along with possible improvements of the methods.
