We have mapped the northern area (30 times 20) of a local group spiral galaxy M33 in 12CO(J=1-0) line with the 45-m telescope at the Nobeyama Radio Observatory. Along with Halpha and Spitzer 24-micron data, we have investigated the relationship betwe
en the surface density of molecular gas mass and that of star formation rate (SFR) in an external galaxy (Kennicutt-Schmidt law) with the highest spatial resolution (~80pc) to date, which is comparable to scales of giant molecular clouds (GMCs). At positions where CO is significantly detected, the SFR surface density exhibits a wide range of over four orders of magnitude, from Sigma(SFR)<10^{-10} to ~10^{-6}M_solar yr^{-1} pc^{-2}, whereas the Sigma(H2) values are mostly within 10 to 40 M_solar pc^{-2}. The surface density of gas and that of SFR correlate well at a 1-kpc resolution, but the correlation becomes looser with higher resolution and breaks down at GMC scales. The scatter of the Sigma(SFR)-Sigma(H2) relationship in the 80-pc resolution results from the variety of star forming activity among GMCs, which is attributed to the various evolutionary stages of GMCs and to the drift of young clusters from their parent GMCs. This result shows that the Kennicutt-Schmidt law is valid only in scales larger than that of GMCs, when we average the spatial offset between GMCs and star forming regions, and their various evolutionary stages.
