  A recent study shows that gravitational scattering of dark matter, in the
form of massive objects with mass $m \sim 10^3-10^4M_{\odot}$, could provide a
possible solution to alleviate the small-scale structure problems of cold dark
matter. The scattering cross section is velocity-dependent so that this
scenario can explain why self-interaction of dark matter is significant in
dwarf galaxies, but not in massive galaxies and galaxy clusters. In this
Letter, we show that this kind of dark massive objects could be made of sterile
neutrinos with a possible rest mass range $m_{\nu} \sim 7.6$ keV $-$ 71 MeV.
This mass range generally satisfies most of the current observational
constraints. The entire structure of the sterile neutrino halos can be simply
predicted from standard physics.
