A bathtub model for the star-forming interstellar medium
  The bathtub model of the star forming interstellar medium is based on the
powerful constraint that mass has to be conserved when gas flows through its
various thermal and density phases, ending up eventually in a young star or
being blown away by stellar feedback. It predicts that the star formation rate
of a molecular cloud is not determined by the cloud's mass or its internal
collapse timescale, but rather by the accretion rate of new gas. For the most
simple case of a constant accretion flow an equilibrium state is reached
quickly where the star formation rate equals the accretion rate and where the
dense gas mass is constant and independent of time. The mass of the young star
cluster, on the other hand, increases linearly with time. The stellar mass
fraction therefore represents a sensitive clock to measure the age of the
star-forming region. The bathtub model predicts that the efficiency of star
formation is small, of order 1%, even in the dense filamentary phases of
molecular clouds. It provides a simple explanation for the dense gas fraction
of order 10% in molecular clouds and for the large gas depletion timescales of
star-forming galaxies of order $5 \times 10^8 - 10^9$ yrs.
