The Schmidt Law at High Molecular Densities

Abstract We combined $\mathrm{H}\alpha$ and recent high-resolution ${{12\atop} \mathrm{CO}}$ ($J = 1 \hbox{--} 0$) data to consider the quantitative relation between the gas mass and the star-formation rate, or the so-called Schmidt law in nearby spiral galaxies at regions of high molecular density. The relation between the gas quantity and the star-formation rate has not been previously studied for high-density regions, but using high-resolution CO data obtained at the Nobeyama Millimeter Array, we found that the Schmidt law is valid at densities as high as $10^3 \,{{{M}_{\odot}}} \,\mathrm{pc}^{-2}$ for sample spiral galaxies, which is an order of magnitude denser than what has been known to be the maximum density at which the empirical law holds for non-starburst galaxies. Furthermore, we obtained a Schmidt law index of $N = 1.33 \pm 0.09$ and a roughly constant star-formation efficiency over the entire disk, even within several hundred parsecs of the nucleus. These results imply that the physics of star formation does not change in the central regions of spiral galaxies. Comparisons with starburst galaxies are also given. We find a possible discontinuity in the Schmidt law between normal and starburst galaxies.