gP\_[out]{} \_ \_V. \[pgamma\] Here, $g=g_\gamma g_V$ where $g_\gamma$ and $g_V$ are the multiplicities of the photon and the mediator particle $V$ being produced along the chain of reactions. If the loss of $V$ due to re-scattering inside the sun can be neglected, the mediator escape probability $P_{out}$ is well-approximated by P\_[out]{} {- R\_/(c)}, while the branching ratios ${\rm Br}_{V}$ and ${\rm Br}_{\gamma}$ and the multiplicities are model dependent. For example, ${\rm Br}_{\gamma}$ may be close to 1 in some secluded models, or more commonly may lie in the $10^{-3}-10^{-2}$ range for models where gammas are produced as radiation accompanying the decay to charged particles.

The general relations (\[scaling\]) and (\[flux\]) use elastic cross sections normalized to $10^{-42} $ cm$^2$, in conflict with the current bounds on spin-independent elastic WIMP-nucleon scattering [@SI], but well below the bounds on spin-dependent scattering [@SD]. Therefore, the best sensitivity to secluded WIMPs will occur for models where nucleon scattering is predominantly spin-dependent. Alternatively, scattering may be predominantly inelastic $\chi_1\to \chi_2$, with a small mass gap between the two WIMP states relaxing the most stringent constraints on spin-independent $\sigma_p$. We will consider examples in both these categories in Section 3.

### 2.2 Angular and spectral 