  The Fermi Bubbles are enigmatic \gamma-ray features of the Galactic bulge.
Both putative activity (within $\sim$ 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 hadronic model where the timescale for generating the
Bubbles' hadronic \gamma -ray emission 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, we can
predict the hadronic emission from the Bubbles to be $L_\gamma \simeq 2 \times
10^{37}$ erg/s $\ \dot{M}_\mathrm{in}/(0.1 \ M_{Sun}/$ year $) \
T_\mathrm{FB}^2/(3.5 \times 10^7 K) ^2 M_{fil}/M_{pls}$ ; precisely 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 that
of the Bubbles' plasma, $M_{pls}$).
