A Universal, Local Star Formation Law in Galactic Clouds, Nearby
  Galaxies, High-Redshift Disks, and Starbursts
  [abridged] While observations of Local Group galaxies show a very simple,
local star formation law in which the star formation rate per unit area in each
patch of a galaxy scales linearly with the molecular gas surface density,
recent observations of both Milky Way molecular clouds and high redshift
galaxies apparently show a more complicated relationship, in which regions of
equal surface density can form stars at quite different rates. These data have
been interpreted as implying either that different star formation laws apply in
different circumstances, that the star formation law is sensitive to
large-scale galaxy properties rather than local properties, or that there are
high density thresholds for star formation. Here we collate resolved
observations of Milky Way molecular clouds, kpc-scale observations of Local
Group galaxies, and unresolved observations of both disk and starburst galaxies
in the local universe and at high redshift. We show that all of these data are
in fact consistent with a simple, local, volumetric star formation law. The
apparent variations stem from the fact that the observed objects have a wide
variety of 3D size scales and degrees of internal clumping, so even at fixed
gas column density the regions being observed can have wildly varying volume
densities. We provide a simple theoretical framework to remove this projection
effect, and we show that all the data, from small Solar neighborhood clouds
with masses ~10^3 Msun to sub-mm galaxies with masses ~10^11 Msun, fall on a
single star formation law in which the SFR is simply ~1% of the molecular gas
mass per local free-fall time. In contrast, proposed star formation laws in
which the star formation timescale is set by the galactic rotation period or
the SFR is linearly proportional to the gas mass above some density threshold
fail to match at least some of the data.
