Effective Self-interaction of Dark Matter from Gravitational Scattering

I show that gravitational scattering of dark matter objects of mass ∼104M⊙ and speeds of ∼10 km s−1, provides the cross section per unit mass required in self-interacting dark matter models that alleviate the small-scale structure challenges to the collisionless cold dark matter model. For primordial objects of mass 104M4 M⊙, moving at the velocity dispersion characteristic of dwarf galaxies, 10v1 km s−1, the cross section per unit mass for gravitational scattering is $\sim 10\,({M}_{4}/{v}_{1}^{4})\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$. The steep decline in interaction with increasing velocity explains why self-interaction is not evident in data on massive galaxies and clusters of galaxies.