Threshold between Spontaneous and Cloud-Collisional Star Formation

Based on simple physical and geometric assumptions, we have calculated the mean surface molecular density of spiral galaxies at the threshold between star formation induced by cloud-cloud collision and spontaneous gravitational collapse. The calculated threshold is approximately $\log \Sigma_\mathrm{crit} \sim 2.5$, where $ \Sigma \quad \mathrm{M_{\solar}}\cdot \mathrm{pc}^{-2}$ is the observed surface mass density of an assumed flat gas disk. Above this limit, the rate of molecular cloud collisions dominates over spontaneous molecular cloud collapse. This model may explain the apparent discontinuity in the Schmidt law found recently at $2 \lesssim \log \Sigma \lesssim 3$.