  The flat star formation (SF) history of the Milky Way (MW) requires gas in
the Galactic disc to be replenished, most likely from a reservoir outside the
Galaxy. Such a replenishment may be achieved by a form of `positive' feedback,
whereby SF feedback creates a Galactic fountain cycle that collects and cools
additional gas from the hot halo surrounding the Galaxy. In this paper we
present a model of this process for the MW. A section of the Galactic disc is
allowed to form stars which subsequently explode as supernovae (SNe) and send
gas out into the hot halo. The gas that is sent out is colder than the hot halo
gas and, as it mixes, the halo gas is cooled, providing fuel for further SF as
the mixture falls back onto the Galactic disc. We find that this process can be
sufficient to maintain a roughly-constant cold gas mass in the MW over at least
3 Gyr. Our results further suggest that there is a positive feedback trend
whereby increasing SF leads to an increase in the cold gas budget at average SF
rates below 0.5 solar masses per year but above which becomes negative, where
further increasing the SFR causes the cold gas budget to decrease. We have
constructed an analytical model for this that reproduces the data well and
could have profound implications for galaxy evolution in feedback-dominated
regimes.
