Effective Self-interaction of Dark Matter from Gravitational Scattering

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I show that gravitational scattering of dark matter objects of mass ∼104 M ⊙ 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 104 M 4 M ⊙, moving at the velocity dispersion characteristic of dwarf galaxies, 10v 1 km s−1, the cross section per unit mass for gravitational scattering is . The steep decline in interaction with increasing velocity explains why self-interaction is not evident in data on massive galaxies and clusters of galaxies.