The Fermi Bubbles are enigmatic \gamma -ray features of the Galactic bulge .
Both putative activity ( within few \times Myr ) connected to the Galactic center super-massive black hole and , alternatively , nuclear star formation have been claimed as the energising source of the Bubbles .
Likewise , both inverse-Compton emission by non-thermal electrons ( ‘ leptonic ’ models ) and collisions between non-thermal protons and gas ( ‘ hadronic ’ models ) have been advanced as the process supplying the Bubbles ’ \gamma -ray emission .
An issue for any steady state hadronic model is that the very low density of the Bubbles ’ plasma seems to require that they accumulate protons over a multi-Gyr timescale , much longer than other natural timescales occurring in the problem .
Here we present a mechanism wherein the timescale for generating the Bubbles ’ \gamma -ray emission via hadronic processes is \sim few \times 10 ^ { 8 } years .
Our model invokes collapse of the Bubbles ’ thermally-unstable plasma , leading to an accumulation of cosmic rays and magnetic field into localised , warm ( \sim 10 ^ { 4 } K ) , and likely filamentary condensations of higher density gas .
Under the condition that these filaments are supported by non-thermal pressure , the hadronic emission from the Bubbles is L _ { \gamma } \simeq 2 \times 10 ^ { \mathrm { 37 } } erg/s \dot { M } _ { \mathrm { in } } / ( 0.1 { M _ { \odot } } / year ) T _ { \mathrm { FB } } ^ { 2 } / ( 3.5 \times 10 ^ { 7 } K ) ^ { 2 } M _ { fil } / M _ { pls } , equal to their observed luminosity ( normalizing to the star-formation-driven mass flux into the Bubbles and their measured plasma temperature and adopting the further result that the mass in the filaments , M _ { fil } is approximately equal to the that of the Bubbles ’ plasma , M _ { pls } ) .