and such a tight correlation is observable with modern gamma ray telescopes. Also, the gamma energy spectrum would be peaked in the direction of the solar center, although this effect is significantly smoothed out by the finite angular resolution of the detectors. In this subsection, we illustrate these angular distributions and energy spectra for the case of $m_\chi = 1$ TeV WIMPs annihilating into two metastable mediators, that further decay into $2\gamma$, so that the multiplicity factors in Eq. (\[pgamma\]) are $g_V=g_\gamma=2$ .

In the rest frame of the intermediate particle $V$, photons are emitted isotropically with a momentum distribution $f'(p')=\frac{2}
{\pi m^2_V}\delta(p'-m_V/2)$, where $p=|\vec p|$. After a Lorentz transformation, the distribution function $f(\vec p)$ measured in the observer’s frame becomes $$f(p,\alpha)=\gamma(1-\beta\cos\alpha)f'[\gamma(1-\beta\cos\alpha)p],$$ where $\beta\equiv v/c$, and $\alpha$ is the angle between the momentum of the outgoing photon and that of the particle $V$ measured in the observer’s frame. Consequently, photons are emitted with an angular distribution given by $1/[4\pi\gamma^2(1-\beta\cos\alpha)^2]$. The density of the photons arriving at the detector with an incoming angle $\theta$ whose momenta are within a small solid angle ${\textrm{d}}\Omega$ is calculated by integrating the particle density of $V$ along the line of sight weighed by an appropriate 