The annihilation cross section of thermal relic dark matter determines both its relic density and indirect detection signals .
We determine how large indirect signals may be in scenarios with Sommerfeld-enhanced annihilation , subject to the constraint that the dark matter has the correct relic density .
This work refines our previous analysis through detailed treatments of resonant Sommerfeld enhancement and the effect of Sommerfeld enhancement on freeze out .
Sommerfeld enhancements raise many interesting issues in the freeze out calculation , and we find that the cutoff of resonant enhancement , the equilibration of force carriers , the temperature of kinetic decoupling , and the efficiency of self-interactions for preserving thermal velocity distributions all play a role .
These effects may have striking consequences ; for example , for resonantly-enhanced Sommerfeld annihilation , dark matter freezes out but may then chemically recouple , implying highly suppressed indirect signals , in contrast to naive expectations .
In the minimal scenario with standard astrophysical assumptions , and tuning all parameters to maximize the signal , we find that , for force-carrier mass m _ { \phi } = 250 ~ { } \text { MeV } and dark matter masses m _ { X } = 0.1 , 0.3 , and 1 TeV , the maximal Sommerfeld enhancement factors are S _ { \text { eff } } = 7 , 30 , and 90 , respectively .
Such boosts are too small to explain both the PAMELA and Fermi excesses .
Non-minimal models may require smaller boosts , but the bounds on S _ { \text { eff } } could also be more stringent , and dedicated freeze out analyses are required .
For concreteness , we focus on 4 \mu final states , but we also discuss 4 e and other modes , deviations from standard astrophysical assumptions and non-minimal particle physics models , and we outline the steps required to determine if such considerations may lead to a self-consistent explanation of the PAMELA or Fermi excesses .