We have combined H \alpha and recent high resolution \atom { CO } { } { 12 } ( 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 \pm 0.09 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 .