  The Fermi Bubbles are giant, gamma-ray emitting lobes emanating from the
nucleus of the Milky Way discovered in ~1-100 GeV data collected by the Large
Area Telescope on board the Fermi Gamma-Ray Space Telescope. Previous work has
revealed substructure within the Fermi Bubbles that has been interpreted as a
signature of collimated outflows from the Galaxy's super-massive black hole.
Here we show via a spatial template analysis that much of the gamma-ray
emission associated to the brightest region of substructure -- the so-called
cocoon -- is likely due to the Sagittarius dwarf spheroidal (Sgr dSph) galaxy.
This large Milky Way satellite is viewed through the Fermi Bubbles from the
position of the Solar System. As a tidally and ram-pressure stripped remnant,
the Sgr dSph has no on-going star formation, but we nevertheless demonstrate
that the dwarf's millisecond pulsar (MSP) population can plausibly supply the
gamma-ray signal that our analysis associates to its stellar template. The
measured spectrum is naturally explained by inverse Compton scattering of
cosmic microwave background photons by high-energy electron-positron pairs
injected by MSPs belonging to the Sgr dSph, combined with these objects'
magnetospheric emission. This finding plausibly suggests that MSPs produce
significant gamma-ray emission amongst old stellar populations, potentially
confounding indirect dark matter searches in regions such as the Galactic
Centre, the Andromeda galaxy, and other massive Milky Way dwarf spheroidals.
