$F_N(m_\chi)$ determines additional suppression from a nuclear form-factor. This approximate formula holds for both spin-independent and spin-dependent scattering, but it is important to bear in mind that coherent scattering in the former case means that heavier nuclei, such as He, O, and Fe tend to dominate the capture rate despite their reduced abundance. The lack of nuclear coherence in spin-dependent scattering means that accounting for scattering off hydrogen is generally sufficient. More general formulae may be found in Ref. [@Gould].

For most models the trapping rate in the Sun determines the overall annihilation rate, as the two processes, trapping and annihilation, are usually in dynamical equilibrium. With an $S$-wave annihilation rate of order 1 pb as dictated by the relic abundance, a per-nucleon scattering cross-section of order $10^{-48}$cm$^2$ or larger is generally sufficient for thermalization to occur over the lifetime of the Sun. Then the trapping rate $C_{\odot}$ and the probability of a single annihilation event to produce gamma quanta reaching the Earth, which we denote as $P_{\gamma}$, determines the overall flux of solar WIMP-generated gamma rays at the Earth’s location:

$$\begin{aligned}
\Phi_{\gamma\odot} = {\frac{1}{2}} \times {\frac{C_\odot P_{\gamma} }{4\pi ~ ({\rm A.U.})^2}} 
=  1.8 \times 10^{-7} ~{\rm cm}^{-2}~{\rm s}^{-1} \times 
