distributions {#angular-and-spectral-distributions .unnumbered}

We now turn to the angular and spectral distributions of gamma quanta. We will comment at the end of this section on how these distributions may be generalized for charged particles, such as $e^\pm$, for which the propagation effects of the magnetic fields of the Sun and Earth must be taken into account. For simplicity we shall assume a decay of the mediator into a pair of gammas, which are monochromatic and isotropic in the rest frame of the mediator. The Lorentz boost of the mediator then determines both the angular and energy resolution. In the absence of the boost, $\gamma \sim 1$, one would expect the Sun to acquire a constant surface brightness in gamma-rays, assuming that the decays happen not far from the solar radius, although its side would appear brighter due to simple geometrical reasons. However, in the most interesting case of large boosts, $\gamma > 10^2$, the gamma quanta in the decay products are emitted within an angle $\theta \sim 1/\gamma$ from the original direction of the mediator. For $\gamma$ as large as $10^3$, the majority of gamma rays would come from an angular spot in the sky smaller than the solar radius, 