telescope. For a detector with angular resolution poorer than the angular size of the Sun, the integration of over ${\textrm{d}}\Omega$ produces a flat spectrum as long as $p_0/\gamma\le p\le p_0\sqrt{\frac{1+\beta}{1-\beta}}$. However, some detectors, such as Fermi, have an angular resolution smaller than the solar angular size. For demonstration purposes, we take $\gamma\sim 1000$, and average assuming a Gaussian-profile and an angular resolution $\Delta \theta$ of one-tenth the solar size. Since $\gamma$ is quite large, almost all the photons that reach the detector come from within an angle of $1/\gamma$ that is comparable to the smallest angular size the detector can resolve. Consequently, the signal that would be seen by the detector represents a (relatively) bright central spot of the Sun with an almost exactly flat spectrum. The photon flux drops rather quickly with angle. If detectable, the photon spectrum at $\theta > \Delta \theta$ is again mostly flat except for a very sharp peak near the low momentum end. We illustrate these results in Fig. \[fig:spec\_smeared\].

![\[fig:spec\_smeared\] [Angular and spectral distributions of the photon flux generated by two-photon decays of the mediators with $\gamma v\tau=0.5 R_\odot$ and $\gamma=1000$. (a) The normalized angular distribution $\frac{{\textrm{d}}\Phi(\theta)}{{\textrm{d}}\Omega}/(C_\odot \textrm{Br}_V \textrm{Br}_\gamma
\cdot 10^{-21}\textrm{cm}^{-2})$; and (b) 