The gas density and "Volume" Schmidt law for spiral galaxies

The equilibrium thickness of the isothermal layers of interstellar gas and volume gas densities in the plane of the disk as a function of galactocentric distance R are computed for seven spiral galaxies (including the Milky Way) using an axisymmetrical model. In this model, the thickness of the stellar disk varies with R and remains approximately equal to the minimum thickness of a stable equilibrium disk. We found the disk thickness to increase toward the periphery in at least five of the seven galaxies. The density of the stellar disk decreases with R faster than rho(gas), so that gas dominates at the disk peripheries in terms of density. A comparison of the azimuthally averaged star formation rate SFR and the gas density shows the absence of a universal Schmidt law SFR similar to rho(n)(gas) for galaxies. However, the SFRs in various galaxies are better correlated with the volume than the gas surface density. The parameter n in the Schmidt law formally calculated using the least-squares method ties in the interval 0.8-2.4, being, on average, close to 1.5. The values of n calculated separately for the molecular gas display substantial scatter, but are, on average, close to unity. The value of n appears to increase with decreasing rho(gas) so that the fraction of gas that actively participates in star formation decreases with n.