On the Origin of the Global Schmidt Law of Star Formation

Abstract

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.