tightness of the optimum angular separation around the GC, $\rm \Psi$, for high WIMP masses (Table \[tab:qresultsfour\]).

The neutrino flux from the self-annihilation of dark matter particles at the GC can be expressed as:

$$\begin{aligned}
\rm{\Phi_{\nu_{\mu}+\bar{\nu}_\mu}} & = & \rm{\Xi_{\nu_{\mu}+\bar{\nu}_\mu}^{PP} \times J(\Delta\Omega)} \, , \label{phinupsieqone} \\
\rm{\Xi_{\nu_{\mu}+\bar{\nu}_\mu}^{PP}} & = & \rm{\frac{1}{4\pi}\frac{<\sigma_{A}v>}{2M_{WIMP}^{2}} N_{\nu_{\mu}+\bar{\nu}_\mu}} \, , \label{phinupsieqtwo} \\
\rm{J(\Delta\Omega)} & = & \rm{\int_{\Delta\Omega} \int \rho_{DM}^{2}dl\,d\Omega} \, , \label{phinupsieqthree}\end{aligned}$$

with $\rm{\Xi_{\nu_{\mu}+\bar{\nu}_\mu}^{PP}}$ as the particle physics term, which depends on the WIMP velocity averaged self-annihilation cross-section, $\rm <\sigma_{A}v>$, and the number of neutrinos, $N_{\nu_{\mu}+\bar{\nu}_\mu}$, that reach the surface of the Earth. $N_{\nu_{\mu}+\bar{\nu}_\mu}$ is computed from the integration over the neutrino energy of the GC’s self-annihilation spectra. The astrophysical J-Factor is the integral over the line of sight, $l$, and the solid angle around the GC, $\Omega$, of the dark matter density, $\rm \rho_{DM}$, squared. The density $\rm \rho_{DM}$ depends on the chosen dark matter galactic halo profile. The Navarro-Frenk-White (NFW) profile [@nfw] is selected as a reference for which the density profile of dark matter is expressed as:

$$\rm{\rho(r) = \frac{\rho_{s}}{(r/r_{s})(1+r/r_{s})^{2}}} \, ,
\label{nfwprofile}$$

with $\rm r_{s} = 21.7$ kpc. The normalization of the profile density, $\rm \rho_{s}$, is computed by fixing the dark 