Sommerfeld enhancement of invisible dark matter annihilation in galaxies and galaxy clusters

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.