  Milagro observations have found bright, diffuse TeV emission concentrated
along the galactic plane of the Milky Way. The intensity and spectrum of this
emission is difficult to explain with current models where gamma-ray production
is dominated by hadronic mechanisms, and has been named the "TeV excess". We
show that TeV emission from pulsars naturally explains this excess. In
particular, recent observations have detected "TeV halos" surrounding pulsars
that are either nearby or particularly luminous. Here, we show that the full
population of Milky Way pulsars will produce diffuse TeV emission concentrated
along the Milky Way plane. The total gamma-ray flux from TeV halos is expected
to exceed the hadronic gamma-ray flux at energies above ~500 GeV. Moreover, the
spectrum and intensity of TeV halo emission naturally matches the TeV excess.
If this scenario is common to all galaxies, it will decrease the contribution
of star-forming galaxies to the IceCube neutrino flux. Finally, we show that
upcoming HAWC observations will resolve a significant fraction of the TeV
excess into individual TeV halos, conclusively confirming, or ruling out, this
model.
