The Schmidt Law at High Molecular Densities

We have combined Halpha and recent high resolution CO(J=1-0) data to consider the quantitative relation between gas mass and star formation rate, or the so-called Schmidt law in nearby spiral galaxies at regions of high molecular density. The relation between gas quantity and star formation rate has not been previously studied for high density regions, but using high resolution CO data obtained at the NMA(Nobeyama Millimeter Array), we have found that the Schmidt law is valid at densities as high as $10^3 \mathrm{M_\odot} \mathrm{pc}^{-2}$ for the 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 obtain a Schmidt law index of $N=1.33\pm0.09$ and roughly constant star formation efficiency over the entire disk, even within the 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.