Density structure of the interstellar medium and the star formation rate in galactic disks

The probability distribution functions (PDFs) of the density of the interstellar medium ( ISM) in galactic disks and the global star formation rate (SFR) are discussed. Three-dimensional hydrodynamic simulations show that the PDFs in a globally stable, inhomogeneous ISM in galactic disks are well fitted by a single lognormal function over a wide density range. The dispersion of the lognormal PDF (LN-PDF) is larger for more gas-rich systems, whereas the characteristic density of the LN-PDF, for which the volume fraction becomes the maximum, does not significantly depend on the initial conditions. Supposing the galactic ISM is characterized by the LN-PDF, we give a global SFR as a function of average gas density, a critical local density for star formation, and the star formation efficiency (SFE). Although the present model is more appropriate for massive and geometrically thin disks (similar to 10 pc) in inner galactic regions (< a few kpc), we can make a comparison between our model and observations in terms of the SFR, provided that the LN nature of the density field is also the case in the real galactic disk with a large scale height (similar to 100 pc). We find that the observed SFR is well-fitted by the theoretical SFR over a wide range of the global gas density (10-10(4) M-circle dot pc(-2)). The star formation efficiency ( SFE) for high-density gas (n > 10(3) cm(-3)) is SFE = 0.001-0.01 for normal spiral galaxies and 0.01-0.1 for starburst galaxies. The LN-PDF and SFR proposed here could be applicable for modeling star formation on a kiloparsec scale in galaxies or numerical simulations of galaxy formation, in which the numerical resolution is not fine enough to describe the local star formation.