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

Understand

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.