Density Structure of the Interstellar Medium and the Star Formation Rate in Galactic Disks

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