Gas Density and the Volume Schmidt Law for Spiral Galaxies

The thickness of the equilibrium isothermal gaseous layers and their volume densities \rho_{gas}(R) in the disc midplane are calculated for 7 spiral galaxies (including our Galaxy) in the frame of self-consistent axisymmetric model. Local velocity dispersions of stellar discs were assumed to be close to marginal values necessary for the discs to be in a stable equilibrium state. Under this condition the stellar discs of at least 5 of 7 galaxies reveal a flaring. Their volume densities decrease with R faster than \rho_{gas}, and, as a result, the gas dominates by the density at the disc periphery. Comparison of the azimuthally averaged star formation rate SFR with the gas density shows that there is no universal Schmidt law SFR \rho_{gas}^n, common to all galaxies. Nevertheless, SFR in different galaxies reveals better correlation with the volume gas density than with the column one. Parameter n in the Schmidt law SFR \rho_{gas}^n, formally calculated by the least square method, lies within 0.8-2.4 range and it's mean value is close to 1.5. Values of n calculated for molecular gas only are characterized by large dispersion, but their mean value is close to 1. Hence the smaller \rho_{gas} the less is a fraction of gas actively taking part in the process of star formation.Comment: 24 pages, 11 figures, to be published in Astronomy Reports, 200