Conservative upper limits on WIMP annihilation cross section from Fermi-LAT γ-rays

The spectrum of an isotropic extragalactic $\gamma$-ray background (EGB) has been measured by the Fermi-LAT telescope at high latitudes. Two new models for the EGB are derived from the subtraction of unresolved point sources and extragalactic diffuse processes, which could explain from 30% to 70% of the Fermi-LAT EGB. Within the hypothesis that the two residual EGBs are entirely due to the annihilation of dark matter (DM) particles in the Galactic halo, we obtain $conservative$ upper limits on their annihilation cross section \sigmav. Severe bounds on a possible Sommerfeld enhancement of the annihilation cross section are set as well. Finally, would {\sigmav} be inversely proportional to the WIMP velocity, very severe limits are derived for the velocity-independent part of the annihilation cross section.