= Dark-matter annihilation radiation
For identical self-conjugate <dark matter> particles, the pair-annihilation rate per volume is $\langle\sigma v\rangle n_\chi^2/2$. If each annihilation releases radiated energy $E_a$, volume emissivity is $j=E_a\langle\sigma v\rangle\rho^2/(2m_\chi^2)$. Optically thin isotropic <surface brightness> is $(4\pi)^{-1}\int j\,dz$. The squared-density dependence assumes a spatially constant rate coefficient and a smooth density; unresolved substructure changes the average of the square.
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