We present a two-zone theory for feedback-regulated star formation in galactic discs , consistently connecting the galaxy-averaged star formation law with star formation proceeding in giant molecular clouds ( GMCs ) .
Our focus is on galaxies with gas surface density \Sigma _ { g } \gtrsim 100 M _ { \odot } pc ^ { -2 } , where the interstellar medium ( ISM ) can be assumed to be fully molecular .
This regime includes most star formation in the Universe and our basic framework can be extended to other galaxies .
In our theory , the galactic disc consists of Toomre-mass GMCs embedded in a volume-filling ISM .
Radiation pressure on dust disperses GMCs and most supernovae explode in the volume-filling medium .
A galaxy-averaged star formation law is derived by balancing the momentum input from supernova feedback with the vertical gravitational weight of the disc gas .
This star formation law is in good agreement with observations for a CO conversion factor depending continuously on \Sigma _ { g } .
We argue that the galaxy-averaged star formation efficiency per free fall time , \epsilon _ { ff } ^ { gal } , is only a weak function of the efficiency with which GMCs convert their gas into stars , \epsilon _ { int } ^ { GMC } .
This is possible because the rate limiting step for star formation is the rate at which GMCs form : for large efficiency of star formation in GMCs , the Toomre Q parameter obtains a value slightly above unity so that the GMC formation rate is consistent with the galaxy-averaged star formation law .
We contrast our results with other theories of turbulence-regulated star formation and discuss predictions of our model .
Using a compilation of data from the literature , we show that the galaxy-averaged star formation efficiency per free fall time is non-universal and increases with increasing gas fraction , as predicted by our model .
We also predict that the fraction of the disc gas mass in bound GMCs decreases for increasing values of the GMC star formation efficiency .
This is qualitatively consistent with the smooth molecular gas distribution inferred in local ultra-luminous infrared galaxies and the small mass fraction in giant clumps in high-redshift galaxies .