We report a super-linear correlation for the star formation law based on new CO ( J =1-0 ) data from the CARMA and NOBEYAMA Nearby-galaxies ( CANON ) CO survey .
The sample includes 10 nearby spiral galaxies , in which structures at sub-kpc scales are spatially resolved .
Combined with the star formation rate surface density traced by H \alpha and 24 \mu m images , CO ( J =1-0 ) data provide a super-linear slope of N = 1.3 .
The slope becomes even steeper ( N = 1.8 ) when the diffuse stellar and dust background emission is subtracted from the H \alpha and 24 \mu m images .
In contrast to the recent results with CO ( J =2-1 ) that found a constant star formation efficiency ( SFE ) in many spiral galaxies , these results suggest that the SFE is not independent of environment , but increases with molecular gas surface density .
We suggest that the excitation of CO ( J =2-1 ) is likely enhanced in the regions with higher star formation and does not linearly trace the molecular gas mass .
In addition , the diffuse emission contaminates the SFE measurement most in regions where star formation rate is law .
These two effects can flatten the power law correlation and produce the apparent linear slope .
The super linear slope from the CO ( J =1-0 ) analysis indicates that star formation is enhanced by non-linear processes in regions of high gas density , e.g. , gravitational collapse and cloud-cloud collisions .