  Recent observations indicate that core-like dark matter structures exist in
many galaxies, while numerical simulations reveal a singular dark matter
density profile at the center. In this article, I show that if the annihilation
of dark matter particles gives invisible sterile neutrinos, the Sommerfeld
enhancement of the annihilation cross-section can give a sufficiently large
annihilation rate to solve the core-cusp problem. The resultant core density,
core radius, and their scaling relation generally agree with recent empirical
fits from observations. Also, this model predicts that the resultant core-like
structures in dwarf galaxies can be easily observed, but not for large normal
galaxies and galaxy clusters.
