The Fermi Gamma-ray Space Telescope discovered two \gamma -ray emitting bubble-shaped structures that extend nearly symmetrically on either side of our Galaxy and appear morphologically connected to the Galactic center .
The origin of the emission is still not entirely clear .
It was recently shown that the spectral shape of the emission from the Fermi bubbles is well described by an approximately 50 ~ { } { GeV } dark matter particle annihilating to b \bar { b } , with a normalization corresponding to a velocity average annihilation cross section \langle \sigma _ { b } v \rangle \approx 8 \times 10 ^ { -27 } { cm } ^ { 3 } / { s } .
We study the minimal hidden sector recently introduced by Weinberg and examine to what extent its weakly interacting massive particles ( W -WIMPs ) are capable of accommodating both the desired effective annihilation rate into quarks and the observed dark matter density .