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We measure the gas disc thicknesses of the edge-on galaxy NGC 4013 and theless edge-on galaxies (NGC 4157 and 5907) using CO (CARMA/OVRO) and/or HI(EVLA) observations. We also estimate the scale heights of stars and/or thestar formation rate (SFR) for our sample of five galaxies using Spitzer IR data(3.6 $\mu$m and 24 $\mu$m). We derive the average volume densities of the gasand the SFR using the measured scale heights along with radial surface densityprofiles. Using the volume density that is more physically relevant to the SFRthan the surface density, we investigate the existence of a volumetric starformation law (SFL), how the volumetric SFL is different from thesurface-density SFL, and how the gas pressure regulates the SFR based on ourgalaxy sample. We find that the volumetric and surface SFLs in terms of thetotal gas have significantly different slopes, while the volumetric and surfaceSFLs in terms of the molecular gas do not show any noticeable difference. Thevolumetric SFL for the total gas has a flatter power-law slope of 1.26 with asmaller scatter of 0.19 dex compared to the slope (2.05) and the scatter (0.25dex) of the surface SFL. The molecular gas SFLs have similar slopes of 0.78(volume density) and 0.77 (surface density) with the same rms scatter. We showthat the interstellar gas pressure is strongly correlated with the SFR but findno significant difference between the correlations based on the volume andsurface densities.

Volumetric Star Formation Prescriptions in Vertically Resolved Edge-on Galaxies