  One of the most puzzling properties of observed galaxies is the universality
of the empirical correlation between the star formation rate and average gas
surface density on kiloparsec scales (the Schmidt law). In this study I present
results of self-consistent cosmological simulations of high-redshift galaxy
formation that reproduce the Schmidt law naturally, without assuming it, and
provide some clues to this puzzle. The simulations incorporate the main
physical processes critical to various aspects of galaxy formation and have a
dynamic range high enough to identify individual star forming regions. The
results indicate that the global Schmidt law is a manifestation of the overall
density distribution of the interstellar medium (ISM). In particular, the
density probability distribution function (PDF) in the simulated disks is
similar to that observed in recent state-of-the-art modeling of the turbulent
ISM and has a well-defined generic shape. The shape of the PDF in a given
region of the disk depends on the local average surface density Sigma_g. The
dependence is such that the fraction of gas mass in the high-density tail of
the distribution scales as Sigma_g^{n-1} with n~1.4, which gives rise to the
Schmidt-like correlation. The high-density tail of the PDF is remarkably
insensitive to the inclusion of feedback and details of the cooling and heating
processes. This indicates that the global star formation rate is determined by
the supersonic turbulence driven by gravitational instabilities on large
scales, rather than stellar feedback or thermal instabilities on small scales.
