Can the WIMP annihilation boost factor be boosted by the Sommerfeld enhancement?

Abstract

We demonstrate that the Sommerfeld correction to CDM annihilations can be appreciable if even a small component of the dark matter is extremely cold. Subhalo substructure provides such a possibility given that the smallest clumps are relatively cold and contain even colder substructure due to incomplete phase space mixing. Leptonic channels can be enhanced for plausible models and the solar neighbourhood boost required to account for PAMELA/ATIC data is plausibly obtained, especially in the case of a few TeV mass neutralino for which the Sommerfeld-corrected boost is found to be $\sim10^4-10^5.$ Saturation of the Sommerfeld effect is shown to occur below $\beta\sim 10^{-4},$ thereby constraining the range of contributing substructures to be above $\sim 10^5\rm M_\odot.$ We find that the associated diffuse gamma ray signal from annihilations would exceed EGRET constraints unless the channels annihilating to heavy quarks or to gauge bosons are suppressed. The lepton channel gamma rays are potentially detectable by the FERMI satellite, not from the inner galaxy where substructures are tidally disrupted, but rather as a quasi-isotropic background from the outer halo, unless the outer substructures are much less concentrated than the inner substructures and/or the CDM density profile out to the virial radius steepens significantly.