matter density at the Sun’s position $\rm \rho(r_{Sun} = 8.5\,kpc) = 0.4\,GeV \cdot cm^{-3}$ [@catena; @salucci]. The systematic uncertainty introduced by the choice of a specific halo profile is discussed at the end of this section.

The J-Factor can be computed using the package CLUMPY [@clumpy] with the contribution from clumps turned off. As demonstrated in Equation \[phinupsieqthree\], the J-Factor is a function of the solid angle $\rm \Delta\Omega = 2\pi(1-\cos(\Psi))$. Figure \[jfactorpsi\] shows the result of the computation of the integrated J-Factor for the NFW profile as a function of $\rm \Psi$. Upper limits for the WIMP velocity-averaged self-annihilation cross-section, $\rm <\sigma_{A}v>$, can be set following Equation \[phinupsieqone\] for each benchmark self-annihilation channel, with known J-Factor for a given optimum angular separation $\rm \Psi$ for each $\rm M_{WIMP}$, and upper limits $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$ as given in Figure \[phinulimitfig\]. Figure \[sigmalimitfig\] shows the $90$% C.L. upper limits on $\rm <\sigma_{A}v>$ as a function of the WIMP mass in the range $\rm 25\,GeV < M_{WIMP} < 10\,TeV$ for the whole set of self-annihilation channels from Expression \[benchch\].

The $\rm <\sigma_{A}v>$ upper limits obtained from the 2007-2012 ANTARES data are comparable with those obtained by other experiments. Figure \[sigmalimitothersfig\] shows the resulting 