The James Clerk Maxwell Telescope Nearby Galaxies Legacy Survey IX: $^{12}$CO $J=3\to2$ Observations of NGC 2976 and NGC 3351

We present $^{12}$CO \textit{J=3$\rightarrow$2} maps of NGC 2976 and NGC 3351 obtained with the James Clerk Maxwell Telescope (JCMT), both early targets of the JCMT Nearby Galaxy Legacy Survey (NGLS). We combine the present observations with $^{12}$CO \textit{J=1$\rightarrow$0} data and find that the computed $^{12}$CO \textit{J=3$\rightarrow$2} to $^{12}$CO \textit{J=1$\rightarrow$0} line ratio ($R_{31}$) agrees with values measured in other NGLS field galaxies. We compute the M$_{\rm{H_2}}$ value and find that it is robust against the value of $R_{31}$ used. Using \textsc{Hi} data from the The \textsc{Hi} Nearby Galaxy Survey (THINGS) survey, we find a tight correlation between surface density of H$_2$ and star formation rate density for NGC 3351 when $^{12}$CO \textit{J=3$\rightarrow$2} data are used. Finally, we compare the $^{12}$CO \textit{J=3$\rightarrow$2} intensity with the PAH 8 $\mu$m surface brightness and find a good correlation in the high surface brightness regions. We extend this study to include all 25 \textit{Spitzer} Infrared Nearby Galaxies Survey (SINGS) galaxies within the NGLS sample and find a tight correlation at large spatial scales. We suggest that both PAH 8 $\mu$m and $^{12}$CO \textit{J=3$\rightarrow$2} are likely to originate in regions of active star formation.